SBI Clerk — fact-checked notes

Cloze Test — Study Notes for SBI Clerk Prelims

Overview

A cloze test is a passage with several blanks where you must select the most appropriate word from given options. In SBI Clerk Prelims, you typically encounter one cloze passage with 5–6 blanks, each carrying one mark. This section tests your vocabulary, grammar awareness, and ability to understand context—all in a time-pressured environment.

Cloze tests reward students who read regularly and have developed an intuitive sense of how English sentences flow. Unlike direct grammar questions, cloze tests require you to understand the passage's theme, tone, and logical progression before filling each blank.

The passages are usually drawn from topics like economy, banking, social issues, technology, or environment—themes relevant to banking exams. The difficulty level is moderate, and most blanks test common vocabulary rather than obscure words.

Key Concepts

• Context is king: The correct answer must fit grammatically AND make sense within the overall passage meaning. Never choose a word based on the blank sentence alone.
• Read the full passage first: Before attempting any blank, read the entire passage to grasp the central idea, tone (positive/negative/neutral), and flow of argument.
• Identify the part of speech needed: Determine whether the blank requires a noun, verb, adjective, adverb, preposition, or conjunction. This eliminates wrong options immediately.
• Look for contextual clues: Words like "however," "therefore," "although," and "moreover" signal the relationship between ideas. Use these to predict what kind of word fits the blank.
• Collocations matter: English has fixed word partnerships. We say "make a decision" not "do a decision," "heavy rain" not "strong rain."
• Maintain tense consistency: If the passage is in past tense, the blank likely needs a past tense verb unless there's a clear reason for a shift.
• Eliminate and choose: If two options seem similar, re-read the surrounding sentences. One will always fit better in terms of meaning, formality, or grammatical precision.

Formulas / Key Facts

Confusable word pairs to know:

• Affect (verb) vs Effect (noun)
• Advice (noun) vs Advise (verb)
• Complement vs Compliment
• Principal vs Principle
• Stationary vs Stationery
• Accept vs Except
• Emigrate vs Immigrate

Worked Examples

Sample Passage:

The government has (1) several measures to boost the rural economy. These initiatives (2) at providing employment opportunities to farmers during the non-agricultural season. (3) the schemes have faced implementation challenges, they have shown positive results in many states.

Options:

Blank (1): (a) announced (b) provided (c) surrendered (d) rejected (e) managed

Blank (2): (a) aim (b) aims (c) aimed (d) aiming (e) will aim

Blank (3): (a) Although (b) Because (c) Therefore (d) Moreover (e) Unless

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Step-by-step solution:

Blank (1):

• The sentence talks about government introducing measures.
• "Surrendered" and "rejected" are negative—don't fit context.
• "Provided measures" is grammatically odd; we provide services, not measures.
• "Managed measures" doesn't make sense.
• "Announced measures" is a natural collocation.
• Answer: (a) announced

Blank (2):

• Subject is "initiatives" (plural noun).
• We need a verb that agrees with plural subject.
• "Aims" is singular, "aimed" is past tense (but passage context is present).
• "These initiatives aim at" is grammatically correct.
• Answer: (a) aim

Blank (3):

• The sentence structure: [First part: challenges faced] + [Second part: positive results]
• This shows contrast between negative and positive outcomes.
• "Because," "Therefore," "Moreover" show cause/addition, not contrast.
• "Unless" is conditional, doesn't fit.
• "Although" shows contrast perfectly.
• Answer: (a) Although

Common Mistakes

• Choosing based on vocabulary alone → Fix: Always check if the word fits grammatically Students often pick a word because they know its meaning without checking if it's the right part of speech. A noun cannot fill a verb's position.
• Ignoring subject-verb agreement → Fix: Identify the subject before selecting verb forms "The list of items were" seems fine but is wrong. "List" is singular, so "was" is correct. Always trace back to the actual subject.
• Selecting the first option that seems right → Fix: Read all options before deciding Two or three options may seem correct initially. Compare them against the specific context to find the best fit.
• Not reading beyond the blank → Fix: Read the complete sentence and the next sentence Sometimes the clue for a blank appears after it, not before. The word "however" in the next sentence might indicate you need a contrasting idea in the current blank.
• Confusing similar-sounding words → Fix: Memorize common confusable pairs "Ensure" vs "insure," "beside" vs "besides," "later" vs "latter"—these trap careless readers.

Quick Reference

• Read the full passage before filling any blank.
• Identify part of speech needed: noun, verb, adjective, preposition, or conjunction.
• Check subject-verb agreement for every verb blank.
• Use conjunctions as signposts: "however" = contrast, "therefore" = result, "moreover" = addition.
• Trust collocations: "pose a threat," "raise concerns," "draw conclusions."
• When stuck between two options, the simpler, more common word is usually correct at Clerk level.

Error Spotting — Study Notes for SBI Clerk Prelims

Overview

The format is straightforward: a sentence is divided into parts (usually 3–4), and you must identify which part contains a grammatical error. Sometimes, "No Error" is also an option.

This topic tests your command of English grammar fundamentals — subject-verb agreement, tense consistency, preposition usage, article placement, and more. Unlike Reading Comprehension, where context helps, Error Spotting demands precise grammatical knowledge. The good news: the error categories are finite and predictable.

For SBI Clerk Prelims, errors are usually clear-cut rather than subtle. Focus on recognizing patterns quickly — you should spend no more than 30–40 seconds per question.

Key Concepts

• Subject-Verb Agreement: The verb must match the subject in number. Intervening phrases between subject and verb often create confusion. ("The list of items is ready" — not are.)
• Tense Consistency: A sentence should maintain the same tense unless there's a logical reason to shift. Watch for sudden jumps from past to present.
• Correct Preposition Usage: Many verbs and adjectives take specific prepositions. ("Depend on", "consist of", "different from" — not interchangeable.)
• Article Errors (A/An/The): Use "a" before consonant sounds, "an" before vowel sounds. "The" for specific or previously mentioned nouns. Omit articles with uncountable abstract nouns used generally.
• Pronoun-Antecedent Agreement: Pronouns must match their antecedents in number and gender. ("Each student must bring his or her book" — not their in formal grammar.)
• Parallelism: Items in a list or comparison must follow the same grammatical structure. ("She likes reading, writing, and swimming" — not "to swim".)
• Misplaced or Dangling Modifiers: Modifying phrases must clearly refer to the correct noun. ("Walking down the street, the trees looked beautiful" — incorrect; trees weren't walking.)
• Redundancy and Word Choice: Avoid double meanings or incorrect word forms. ("Return back", "revert back" are redundant.)

Formulas / Key Facts

Subject-Verb Agreement Rules

• Singular subjects → singular verbs (adds "s"): He runs, She writes
• Plural subjects → plural verbs: They run, We write
• "Either...or", "Neither...nor" → verb agrees with the nearer subject
• Collective nouns (team, committee) → usually singular in Indian English

Common Preposition Pairs

Article Rules

• "An" before vowel sounds: an hour, an MBA (but "a university" — "yu" sound)
• No article: general plurals ("Dogs are loyal"), abstract nouns used generally ("Honesty is important")

Pronoun Rules

• "One" takes "one's" (not their/his)
• "Each", "every", "either", "neither" are singular
• "Who" for subjects, "Whom" for objects

Common Redundancies to Avoid

• Return back → Return
• Revert back → Revert
• Repeat again → Repeat
• Free gift → Gift
• Past history → History

Worked Examples

Example 1 Sentence: (A) Each of the students / (B) have completed / (C) their assignments / (D) before the deadline.

Analysis:

• Part A: "Each of the students" — subject is "Each" (singular) ✓
• Part B: "have completed" — "have" is plural, but subject "Each" is singular ✗
• Part C: "their assignments" — technically should be "his/her" for strict grammar, but B is the clearer error
• Part D: "before the deadline" — correct ✓

Answer: B — Should be "has completed"

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Example 2 Sentence: (A) The manager along with his team / (B) are going / (C) to attend the conference / (D) next week.

Analysis:

• Part A: "The manager along with his team" — main subject is "manager" (singular); "along with" doesn't change the subject ✓
• Part B: "are going" — should be "is going" to agree with "manager" ✗
• Part C: "to attend the conference" — correct ✓
• Part D: "next week" — correct ✓

Answer: B — Should be "is going"

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Example 3 Sentence: (A) He prefers tea / (B) than coffee / (C) because it is / (D) healthier for him.

Analysis:

• Part A: "He prefers tea" — correct ✓
• Part B: "than coffee" — "prefer" takes "to", not "than" ✗
• Part C: "because it is" — correct ✓
• Part D: "healthier for him" — correct ✓

Answer: B — Should be "to coffee"

Common Mistakes

Confusing proximity with agreement → The verb agrees with the main subject, not the nearest noun. In "The quality of the mangoes is good", "quality" is the subject, not "mangoes".

Treating "along with/as well as/together with" as conjunctions → These phrases don't make a subject plural. "The captain, along with his teammates, was present" — not were.

Using "than" after comparatives that don't take it → Words like "prefer", "superior", "inferior", "senior", "junior" take "to", not "than".

Ignoring vowel sounds for articles → It's "an hour" (silent h) but "a hotel" (audible h). It's "a European" (starts with "yu" sound) but "an MBA" (starts with "em" sound).

Missing parallelism breaks → In lists, all items must match: "He likes to read, to write, and to travel" OR "reading, writing, and travelling" — not a mix.

Quick Reference

• Subject-verb agreement: Find the true subject, ignore phrases between subject and verb.
• "Along with / as well as / together with" = subject stays singular.
• "Prefer A to B", never "than B".
• "An" before vowel sounds, not just vowel letters.
• "Either...or / Neither...nor" → verb matches the nearer subject.
• Check for redundancies: return back, revert back, repeat again = wrong.

Sentence Improvement / Phrase Replacement

Overview

Sentence Improvement (also called Phrase Replacement) is part of the SBI Clerk Prelims English section. You are given a sentence with an underlined part, and you must decide whether that part is correct as written or needs to be replaced with one of the given alternatives.

This topic tests your command of grammar rules—subject-verb agreement, tense consistency, correct preposition usage, parallelism, and idiomatic expressions. Unlike Error Spotting, where you only identify the error, here you must also select the correct replacement. The skill required is not just detection but correction.

Mastering this topic builds a foundation that helps across the English section—Reading Comprehension options often hinge on similar grammatical distinctions, and Cloze Tests require the same sensitivity to correct phrasing.

Key Concepts

• Subject-Verb Agreement: A singular subject takes a singular verb; a plural subject takes a plural verb. Watch for tricky subjects like "each," "everyone," "neither," and collective nouns.
• Tense Consistency: A sentence should maintain the same tense throughout unless there is a logical reason to shift. Past actions stay in past; present habits stay in present.
• Correct Use of Prepositions: Many verbs and adjectives pair with specific prepositions (e.g., "interested in," "comply with," "afraid of").
• Parallelism: Items in a list or comparison must follow the same grammatical structure. "She likes reading, writing, and to swim" is wrong; "reading, writing, and swimming" is correct.
• Pronoun-Antecedent Agreement: Pronouns must match their antecedents in number and gender. In strict formal usage, "Each student must bring their book" is written "Each student must bring his or her book".
• Correct Use of Modifiers: Misplaced or dangling modifiers create confusion. "Running quickly, the bus was caught" wrongly suggests the bus was running.
• Idiomatic Expressions: Certain phrases are fixed in English. "Cope up with" is wrong; "cope with" is correct.
• Redundancy and Wordiness: Phrases like "return back," "revert back," or "repeat again" are redundant. The correct forms are simply "return," "revert," and "repeat."

Formulas / Key Facts

Common preposition pairings to memorize: agree with (person), agree to (proposal), consist of, depend on, differ from, prefer X to Y, superior to, inferior to, familiar with, accustomed to.

Worked Examples

Example 1

Sentence: The manager along with his team members have completed the project.

Options: (a) has completed the project (b) have been completing the project (c) having completed the project (d) No improvement

Solution: The subject is "The manager" (singular). The phrase "along with his team members" is additional information and does not make the subject plural. A singular subject requires a singular verb.

Answer: (a) has completed the project

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Example 2

Sentence: She prefers tea than coffee in the morning.

Options: (a) tea over coffee (b) tea to coffee (c) tea instead coffee (d) No improvement

Solution: The correct idiom is "prefer X to Y." We do not use "than" or "over" with "prefer."

Answer: (b) tea to coffee

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Example 3

Sentence: The report was so lengthy that I could not read it in one go and have to take breaks.

Options: (a) had to take breaks (b) has to take breaks (c) having to take breaks (d) No improvement

Solution: The sentence is in past tense ("was," "could not read"). The phrase "have to" is present tense, breaking consistency. It should be "had to."

Answer: (a) had to take breaks

Common Mistakes

• Ignoring the hidden subject: Students see "team members" near the verb and choose a plural verb, forgetting that "along with," "as well as," "together with," and "in addition to" do not change subject number. → Always identify the true subject before the interrupting phrase.
• Choosing "No improvement" too quickly: When nothing looks obviously wrong, students assume the sentence is correct. → Read the sentence twice; subtle errors like wrong prepositions or redundancy are easy to miss.
• Overcorrecting into awkward phrasing: An option may be grammatically possible but stylistically poor or unidiomatic. → Choose the option that is both correct and natural-sounding.
• Confusing similar prepositions: "Differ from" (comparison) vs. "differ with" (disagree); "agree to" (proposal) vs. "agree with" (person). → Memorize fixed preposition collocations.
• Misreading tense signals: Words like "yesterday," "last year," "since," and "for" indicate specific tenses. → Scan the sentence for time markers before evaluating the verb form.

Quick Reference

1. True subject determines verb number—ignore interrupters like "along with" and "as well as."
2. "Prefer X to Y"—never "than" or "over."
3. "Cope with," "discuss," "emphasize"—no extra prepositions.
4. Remove redundancy: "return back" → "return"; "revert back" → "revert."
5. Maintain tense consistency—match verbs to time markers.
6. When in doubt, read aloud—awkward phrasing often reveals the error.

Para Jumbles

Overview

Para Jumbles test your ability to arrange a set of jumbled sentences into a logically coherent paragraph. In SBI Clerk Prelims, you typically encounter 5 sentences labeled A through E (or sometimes 4 or 6), and you must identify the correct sequence.

Success in Para Jumbles depends not on vocabulary strength but on understanding how ideas connect. You need to identify the opening sentence, spot linking words, track pronouns back to their nouns, and follow the logical flow of an argument or narrative. Students who learn to look for specific structural clues can solve these questions in under 60 seconds each—crucial for the time-pressured Prelims exam.

Key Concepts

• Opening sentence identification: The first sentence introduces a topic without referring to previous context. It never starts with "This," "That," "Such," "These," or pronouns like "He/She/They" without an antecedent.
• Closing sentence identification: The last sentence concludes the discussion—it summarizes, gives a result, or provides a final thought. Words like "Thus," "Hence," "Therefore," "Finally," or "In conclusion" often signal this.
• Pronoun-antecedent linking: A sentence with "He," "She," "It," "They," "This," or "These" must follow the sentence that introduces the noun it refers to.
• Article progression: "A/An" introduces something new; "The" refers to something already mentioned. A sentence with "the committee" must follow one that first mentions "a committee."
• Transition and linking words: Words like "However," "Moreover," "Furthermore," "But," "Also," "In addition," "On the other hand" indicate how a sentence connects to the previous one.
• Chronological/logical flow: Look for time markers (first, then, later, finally) or cause-effect relationships (because, therefore, as a result) that dictate order.
• Mandatory pairs: Some sentences must appear consecutively because one directly continues or responds to the other. Identifying these pairs narrows down options quickly.

Key Facts

1. Never start with connectors: Sentences beginning with However, But, Moreover, Therefore, Hence, Thus, or This/These/That rarely open a paragraph.
2. Proper nouns before pronouns: A person's full name or title appears before "he/she" references them.
3. General statement before specific explanation: A concept is introduced before it is elaborated upon or examples are given.
4. Cause before effect: The reason appears before the consequence in logical flow.
5. "A/An" before "The": Indefinite article introduction precedes definite article reference for the same noun.
6. Contrasting pairs stay close: If one sentence presents an idea and another contradicts it (using "however," "but," "on the contrary"), they typically appear consecutively.
7. Examples follow statements: Sentences with "For example," "For instance," or "Such as" follow the general statement they illustrate.
8. Abbreviations after full forms: The full form of an acronym appears before subsequent use of the acronym alone.

Worked Examples

Example 1

Arrange the following sentences:

A. This has led to a significant reduction in pollution levels. B. The government introduced a policy to limit industrial emissions. C. However, critics argue that the policy affects economic growth. D. Many factories have since adopted cleaner technologies. E. The debate continues as both sides present valid concerns.

Solution:

• Step 1: Find the opener. Sentence B introduces "a policy" with indefinite reference—no prior context needed. B is the opening sentence.
• Step 2: Sentence A starts with "This"—it must follow something. What caused "reduction in pollution"? Sentence D mentions factories adopting cleaner technologies. So D → A.
• Step 3: Sentence D follows B because factories responded to the policy. Order so far: B → D → A.
• Step 4: Sentence C says "However, critics argue"—this contrasts with the positive outcome in A. So A → C.
• Step 5: Sentence E concludes with "The debate continues"—a summary statement.

Answer: B-D-A-C-E

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Example 2

Arrange the following sentences:

A. Moreover, regular exercise improves mental health as well. B. Physical fitness has numerous benefits for the human body. C. It strengthens the cardiovascular system and builds muscle mass. D. Therefore, experts recommend at least 30 minutes of daily activity.

Solution:

• Step 1: Sentence B is a general statement introducing the topic—no connectors, no pronouns referring back. B opens.
• Step 2: Sentence C starts with "It"—referring to "Physical fitness" in B. So B → C.
• Step 3: Sentence A says "Moreover"—adding another benefit. It follows C. Order: B → C → A.
• Step 4: Sentence D says "Therefore"—a concluding recommendation based on all benefits mentioned.

Answer: B-C-A-D

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Example 3

Arrange the following sentences:

A. The tiger is one of the most endangered species in the world. B. These measures include habitat preservation and anti-poaching laws. C. Conservationists have implemented several measures to protect them. D. As a result, tiger populations have shown slight recovery.

Solution:

• Step 1: Sentence A introduces "The tiger" as the subject—general topic statement. A opens.
• Step 2: Sentence C mentions "them" (referring to tigers) and introduces "measures." So A → C.
• Step 3: Sentence B says "These measures"—directly referring to measures in C. So C → B.
• Step 4: Sentence D says "As a result"—the outcome of the measures. D concludes.

Answer: A-C-B-D

Common Mistakes

• Choosing a sentence with "This/These" as the opener → Check that any demonstrative pronoun has a clear antecedent; if it doesn't appear in prior options, that sentence cannot open.
• Ignoring article clues → Students miss that "the policy" requires "a policy" to have appeared earlier. Always track indefinite-to-definite article progression.
• Forcing sentences based on content similarity alone → Two sentences about the same topic don't necessarily go together. Focus on grammatical and logical connectors, not just theme.
• Not eliminating using answer options → If options are BDACE, BDCAE, BDAEC, etc., and you're sure B opens and D follows B, eliminate options that don't start with BD. Use the choices strategically.
• Rushing without identifying the closer → Students focus only on finding the opener. Identifying the concluding sentence (look for "Thus," "Hence," "Finally," summary statements) lets you eliminate from both ends.

Quick Reference

• Opener: No backward reference—introduces the main subject fresh.
• Closer: Uses "Thus/Hence/Therefore/Finally" or summarizes the discussion.
• Pronoun rule: "He/She/It/They/This/These" must follow their noun.
• Article rule: "A/An" introduces; "The" refers back.
• Connector logic: "However" = contrast; "Moreover/Furthermore" = addition; "Therefore" = conclusion.
• Mandatory pairs: Find two sentences that must be consecutive, then match to answer options.

Sentence Rearrangement

Overview

Sentence Rearrangement tests your ability to recognize how parts of a single sentence connect grammatically and logically. Unlike Para Jumbles where you arrange complete sentences, here you receive one sentence split into fragments (usually labeled P, Q, R, S) and must place them in the correct order to form a meaningful, grammatically sound sentence.

The difficulty level is moderate—questions reward students who understand basic sentence structure rather than complex grammar rules. Mastering this topic provides quick, reliable marks because the correct answer must satisfy both meaning and grammar simultaneously, which often eliminates multiple options at once.

Success requires recognizing subject-verb relationships, spotting connectors, identifying article-noun links, and understanding how modifiers attach to the words they describe. Speed comes with practice—once you internalize common patterns, you can solve these in under 45 seconds each.

Key Concepts

• Fixed Starters: The opening part often contains the subject or a dependent clause that sets context. Look for capital letters, articles (A/An/The) followed by nouns, or subordinating conjunctions (Although, When, If, Because).
• Subject-Verb-Object Order: English follows SVO structure. The subject must come before its verb, and the verb before its object. Identify these elements across fragments.
• Article-Noun Binding: Articles (a, an, the) must immediately precede their noun or noun phrase. A fragment ending in "the" must be followed by a fragment starting with a noun.
• Preposition-Object Pairing: Prepositions (of, to, for, with, by) require objects. A fragment ending in a preposition connects to the next noun phrase.
• Connector Logic: Words like "and," "but," "which," "who," "that" link specific grammatical elements. "Which/who/that" introduce relative clauses and must follow the noun they describe.
• Meaning Continuity: Beyond grammar, the assembled sentence must make logical sense. An action must follow its subject; a result must follow its cause.
• Elimination Through Fixed Pairs: Often two fragments clearly link together. Finding one such pair can eliminate 2–3 answer options immediately.

Key Facts

1. Common Starter Elements: Subject nouns, proper nouns, articles + nouns, subordinating conjunctions (Although, Since, When, While, If).
2. Common Ender Elements: Main verb phrases, objects, prepositional phrases that complete meaning, punctuation-bound phrases.
3. Relative Pronoun Rule: "Who" follows persons, "which" follows things/animals, "that" follows either—all must immediately follow their antecedent noun.
4. Infinitive Completion: "To" at the end of a fragment signals a verb coming next (to + verb = infinitive).
5. Conjunction Placement: "And/but/or" connect parallel structures—what comes before and after should be grammatically similar.
6. The Definite Article Signal: "The" refers to something specific, often previously mentioned or about to be specified by a following phrase.
7. Participial Phrases: Fragments starting with -ing or -ed words typically modify the subject and often come at the beginning or attach directly to the noun they modify.
8. Appositive Phrases: Explanatory phrases (often between commas) must sit next to the noun they explain.

Worked Examples

Example 1

Arrange P, Q, R, S to form a meaningful sentence:

The government has decided to P: in the country Q: all major infrastructure projects R: launch S: to boost employment

Solution:

• Start with given opening: "The government has decided to"
• "Decided to" needs a verb → R (launch) follows
• "Launch" needs an object → Q (all major infrastructure projects)
• Projects need location/context → P (in the country)
• Purpose clause comes last → S (to boost employment)

Correct Order: R-Q-P-S

Final Sentence: The government has decided to launch all major infrastructure projects in the country to boost employment.

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Example 2

Arrange P, Q, R, S:

The scientist P: who discovered the new element Q: received the prestigious award R: at the international conference S: last month

Solution:

• "The scientist" is the subject, needs description or verb
• P ("who discovered...") describes the scientist → follows immediately
• After the relative clause, main verb needed → Q (received the award)
• Where? → R (at the international conference)
• When? → S (last month)

Correct Order: P-Q-R-S

Final Sentence: The scientist who discovered the new element received the prestigious award at the international conference last month.

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Example 3

Arrange P, Q, R, S:

P: with determination and hard work Q: despite facing numerous obstacles R: she managed to complete S: her research project

Solution:

• Q starts with "despite" (a preposition showing contrast) — good sentence opener
• R has subject + verb ("she managed to complete")
• S provides the object ("her research project")
• P describes how — manner phrase, fits at end

Correct Order: Q-R-S-P

Final Sentence: Despite facing numerous obstacles, she managed to complete her research project with determination and hard work.

Common Mistakes

• Ignoring Grammar for Meaning: Students sometimes arrange parts that "sound right" but violate grammar rules. → Always verify subject-verb agreement and that articles attach to nouns properly.
• Placing Relative Clauses Incorrectly: Putting "who/which/that" fragments away from the noun they describe creates confusion. → Relative pronouns must immediately follow their antecedent.
• Breaking Verb Phrases: Separating "has been" from its main verb or "decided to" from its infinitive. → Keep auxiliary + main verb combinations together across fragments.
• Misplacing Modifiers: Putting descriptive phrases (especially -ing phrases) next to the wrong noun. → Modifiers attach to the nearest logical noun.
• Not Testing the Final Sentence: Selecting an answer without reading the complete assembled sentence aloud mentally. → Always construct and verify the full sentence before marking.

Quick Reference

• Find the subject first—it usually starts the sentence or comes after an opening subordinate clause.
• "To" at fragment end signals verb next; "the/a/an" at end signals noun next.
• Relative pronouns (who/which/that) glue directly onto the noun they describe.
• Purpose clauses (to + verb) and manner phrases (with/by + noun) typically end sentences.
• Fixed pairs eliminate options—find one definite link, then check which answers contain it.
• Read your final answer as one complete sentence—grammar AND meaning must both work.

Fill in the Blanks — Study Notes for SBI Clerk Prelims

Overview

Fill in the Blanks is a vocabulary-intensive section in SBI Clerk Prelims English Language paper. This tests your grasp of word meanings, collocations (words that naturally go together), and contextual usage.

This topic rewards consistent vocabulary building rather than last-minute cramming. Questions range from straightforward vocabulary recall to nuanced choices where two options seem similar but only one fits the sentence's tone and grammar. Scoring well here requires reading the entire sentence carefully, understanding its meaning, and eliminating options systematically.

For double-blank questions, both words must fit perfectly — if even one word is wrong, the entire option is wrong. This makes elimination strategy particularly powerful for these questions.

Key Concepts

• Context is king: The sentence's overall meaning determines the correct word. Never choose based on the blank alone — read the full sentence first.
• Tone matching: A formal sentence needs formal vocabulary. If the sentence discusses a serious economic issue, casual or colloquial words are unlikely answers.
• Grammatical fit: The blank must match in part of speech. If the sentence needs a verb, an adjective option is automatically wrong regardless of meaning.
• Collocations matter: Certain words naturally pair with others. We say "make a decision" not "do a decision." Knowing common collocations helps eliminate wrong options.
• Signal words guide meaning: Words like "although," "despite," "therefore," and "moreover" signal relationships — contrast, cause-effect, addition — that determine what meaning the blank requires.
• Double-blank strategy: Both words must work. Test each blank independently, then verify the combination makes sense together.
• Elimination over selection: Often easier to eliminate three wrong options than to directly identify the correct one.

Formulas / Key Facts

Must-Remember Vocabulary Patterns:

1. Positive-Negative pairs: Distinguish between words like prudent/reckless, diligent/negligent, enhance/diminish.
2. Degree differences: Know subtle differences — angry vs furious vs irate; big vs enormous vs colossal.
3. Common confusables:
   • Affect (verb) vs Effect (noun/verb)
   • Principal (main/head) vs Principle (rule)
   • Compliment (praise) vs Complement (complete)
   • Stationary (still) vs Stationery (paper items)
   • Elicit (draw out) vs Illicit (illegal)
4. Useful exam words: Stringent, resilient, pragmatic, volatile, lucrative, sporadic, plausible, viable, ambiguous, coherent.
5. Preposition-dependent words:
   • Comply WITH, conform TO
   • Abstain FROM, refrain FROM
   • Conducive TO, detrimental TO
   • Proficient IN, deficient IN
6. Signal word categories:
   • Contrast: although, despite, however, nevertheless, whereas
   • Cause-effect: therefore, consequently, hence, thus
   • Addition: moreover, furthermore, besides, additionally

Worked Examples

Example 1: Single Blank

The government's _______ measures helped control inflation within six months.

Options: (a) lenient (b) stringent (c) ambiguous (d) sporadic (e) volatile

Solution:

• Step 1: Understand context — measures that successfully controlled inflation.
• Step 2: Inflation control requires strict, tight measures.
• Step 3: Evaluate options:
  • Lenient (relaxed) — opposite of what's needed
  • Stringent (strict) — fits perfectly
  • Ambiguous (unclear) — doesn't relate to effectiveness
  • Sporadic (irregular) — doesn't suggest success
  • Volatile (unstable) — negative connotation
• Answer: (b) stringent

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Example 2: Single Blank with Signal Word

Although the evidence was _______, the jury delivered a guilty verdict.

Options: (a) conclusive (b) overwhelming (c) insufficient (d) concrete (e) substantial

Solution:

• Step 1: "Although" signals contrast between the evidence and the verdict.
• Step 2: Guilty verdict is normally based on strong evidence. Contrast means evidence was weak.
• Step 3: Only "insufficient" suggests weak evidence that contrasts with conviction.
• Answer: (c) insufficient

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Example 3: Double Blank

The manager's _______ approach to the crisis _______ the employees' confidence in leadership.

Options: (a) calm ... restored (b) panicked ... enhanced (c) indifferent ... boosted (d) aggressive ... maintained (e) chaotic ... improved

Solution:

• Step 1: Check logical pairing — what approach leads to what effect on confidence?
• Step 2: Test each:
  • Calm approach → restored confidence ✓ (makes sense)
  • Panicked approach → enhanced confidence ✗ (illogical)
  • Indifferent approach → boosted confidence ✗ (illogical)
  • Aggressive approach → maintained confidence ✗ (unlikely)
  • Chaotic approach → improved confidence ✗ (illogical)
• Answer: (a) calm ... restored

Common Mistakes

• Choosing based on partial fit: Students pick an option because one word in a double-blank question fits, ignoring that the second word is wrong. → Always verify BOTH blanks independently before finalizing.
• Ignoring sentence tone: Selecting a word that means roughly the right thing but doesn't match formality level. "The CEO commenced the meeting" works; "The CEO kicked off the meeting" is too informal. → Match vocabulary register to sentence style.
• Overlooking signal words: Missing contrast signals like "although" or "despite" and choosing a word that continues rather than contrasts. → Circle signal words before attempting the blank.
• Confusing similar-sounding words: Mixing up words like "eminent/imminent," "judicial/judicious," or "economic/economical." → Maintain a personal list of confusable pairs and review regularly.
• Not reading all options: Settling on the first seemingly correct option without checking others. Sometimes a better fit exists. → Read all five options before marking your answer.

Quick Reference

• Read the FULL sentence before looking at options.
• Circle signal words — they reveal required meaning.
• For double blanks, BOTH words must fit; one wrong word disqualifies the option.
• Eliminate grammatically impossible options first (wrong part of speech).
• When stuck between two options, choose the more commonly used collocation.
• Build vocabulary daily — 10 new words with example sentences is more effective than memorizing 50 word-meanings.

Word Swap — Study Notes for SBI Clerk (Prelims)

Overview

Word Swap is a relatively newer question format that is part of SBI Clerk Prelims. In these questions, you are given a sentence where two words have been interchanged, making the sentence grammatically incorrect or meaningless. Your task is to identify which two words need to be swapped back to make the sentence correct.

This question type tests your understanding of sentence structure, subject-verb agreement, collocations, and logical meaning—all at once. The key skill here is recognizing when something "sounds wrong" and pinpointing exactly which two words are out of place.

Unlike error spotting where you find one mistake, word swap requires you to identify a pair of misplaced words. This means you must read the entire sentence, understand its intended meaning, and then logically determine which swap fixes both grammar and sense.

Key Concepts

• Sentence Logic First: Before checking grammar, understand what the sentence is trying to say. The correct meaning will guide you to the swapped words.
• Subject-Verb Mismatch: Often, swapping creates a subject-verb agreement error. A singular subject paired with a plural verb (or vice versa) signals a potential swap.
• Adjective-Noun Pairing: Adjectives must logically modify their nouns. If "economic growth" becomes "growth economic" or an adjective describes the wrong noun, a swap is needed.
• Verb-Object Relationship: Verbs must take appropriate objects. "Drink food" or "eat water" indicates swapped words.
• Preposition Collocations: Fixed phrases like "interested in" or "capable of" get broken when words are swapped. Recognize standard collocations.
• Connector and Conjunction Logic: Words like "although," "because," "despite" create specific logical relationships. Swapping disrupts these relationships.
• Position Clues: Typically, one word comes early in the sentence and the other comes later. Rarely are adjacent words swapped.
• "No Swap Required" Option: Some questions include this option. If the sentence reads perfectly, choose it—but verify twice.

Formulas / Key Facts

1. Read for meaning first, grammar second — A grammatically correct but meaningless sentence is still wrong.
2. Swap candidates are usually the same part of speech — Nouns swap with nouns, verbs with verbs, adjectives with adjectives.
3. Subject and object are common swap pairs — "The cat chased the dog" vs. "The dog chased the cat" changes meaning entirely.
4. Look for broken collocations — "Make a decision" swapped to "take a decision" might still work, but "heavy rain" swapped to "strong rain" sounds off.
5. Verbs in different tenses rarely swap — If you see "was" and "were" both present, one might be in the wrong position due to subject agreement.
6. Check articles with their nouns — "A" goes with singular countable, "the" is specific. If articles seem mismatched, check if their nouns were swapped.
7. Prepositions follow specific verbs/nouns — "Depend on," "consist of," "afraid of" are fixed. Disruption indicates swap.
8. In 5-word option sets, try each swap mentally — Most questions give options like (A-B), (B-C), etc. Test each quickly.

Worked Examples

Example 1

Sentence: The government has financial new announced incentives for small businesses.

Analysis: Read it aloud—"has financial new announced" makes no sense. The intended meaning is about the government announcing financial incentives.

• "financial" should describe "incentives"
• "announced" is the main verb that should follow "has"

Correct sentence: The government has announced new financial incentives for small businesses.

Answer: Swap "financial" and "announced"

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Example 2

Sentence: Despite being success, the actor remained humble and grounded throughout his successful.

Analysis: "being success" is wrong—should be "being successful" (adjective). Also, "throughout his successful" is incomplete—should be "throughout his success" (noun).

• "success" (noun) and "successful" (adjective) are swapped

Correct sentence: Despite being successful, the actor remained humble and grounded throughout his success.

Answer: Swap "success" and "successful"

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Example 3

Sentence: The teacher asked the students to carefully the instructions read before attempting the questions.

Analysis: "to carefully the instructions read" is jumbled. Correct structure needs "to read the instructions carefully" or "to carefully read the instructions."

• "the instructions" cannot come before "read"
• "carefully" should modify "read"

Wait—let's re-examine. The issue is "read" and "carefully" or "instructions" and "read"?

Actually: "to carefully the instructions read" → "to read the instructions carefully"

Answer: Swap "read" and "carefully" — and this works. (Swapping "instructions" and "read" would give "to carefully the read instructions", which is still wrong.) Check:

"to read the instructions carefully" — Yes!

Answer: Swap "read" and "carefully"

Correct sentence: The teacher asked the students to read the instructions carefully before attempting the questions.

Common Mistakes

• Swapping based on sound alone → Always verify that both grammar AND meaning become correct after the swap. Sometimes a swap fixes grammar but creates nonsense.
• Ignoring the "No swap required" option → Students often force a swap even when the sentence is correct. Read the original carefully before hunting for errors.
• Swapping adjacent words → Exam setters usually swap words that are farther apart. If you think two neighboring words need swapping, reconsider.
• Focusing only on the first half → Many students find one odd word early and assume the swap partner is nearby. Scan the entire sentence—the second word could be at the very end.
• Confusing word swap with jumbled sentences → In word swap, only TWO specific words are interchanged. The rest of the sentence is in correct order. Don't try to rearrange multiple words.

Quick Reference

1. Understand meaning → then check grammar → then identify swap.
2. Swapped words are usually the same part of speech (noun-noun, verb-verb, adjective-adjective).
3. Subject-object swaps and adjective-noun swaps are common.
4. Always test your answer by reading the corrected sentence aloud.
5. If nothing sounds wrong, "No swap required" may be correct.
6. Broken collocations (fixed phrases) are strong indicators of swapped words.

Synonyms and Antonyms

Overview

Synonyms and antonyms form the vocabulary backbone of the English Language section in SBI Clerk Prelims. These questions typically appear embedded within Reading Comprehension passages, where you must identify words with similar meanings (synonyms) or opposite meanings (antonyms) to a highlighted word from the passage.

This topic tests your working vocabulary rather than rote memorization. The examiner wants to know if you can understand word meanings in context—a skill that directly impacts your RC speed and accuracy.

Mastering this area gives you a double advantage: you score on direct vocabulary questions AND improve your overall reading comprehension since understanding word meanings helps decode passage content faster.

Key Concepts

• Context is king: The same word can have different meanings in different sentences. "Bank" in a financial passage means something different from "bank" in a river description. Always read the surrounding sentence before choosing.
• Synonyms share core meaning, not exact meaning: "Happy" and "elated" are synonyms, but "elated" is stronger. Pick the option that matches the intensity and tone of the original word.
• Antonyms are direct opposites: Look for words that negate the core meaning. The antonym of "generous" is "stingy," not "poor" (which relates to a different concept).
• Beware of partial matches: Options often include words related to the topic but not actual synonyms/antonyms. "Doctor" and "hospital" are related, but not synonyms.
• Word roots help decode unfamiliar words: Prefixes like "un-," "dis-," "anti-," "mis-" typically create antonyms. Suffixes like "-ful" and "-less" are opposites.
• Part of speech must match: The synonym/antonym of a noun will be a noun; a verb's synonym will be a verb. This eliminates wrong options quickly.
• Degree matters: "Warm" and "hot" are not synonyms—they differ in degree. Similarly, "cool" is not an exact antonym of "hot."

Key Facts

• Common prefix antonym pairs:
  • "un-" reverses meaning: happy/unhappy, able/unable
  • "dis-" indicates opposite: agree/disagree, appear/disappear
  • "im-/in-/il-/ir-" negate: possible/impossible, regular/irregular
  • "mis-" indicates wrongly: understand/misunderstand
• Useful synonym groups for banking exams:
  • Increase: augment, escalate, surge, amplify, boost
  • Decrease: diminish, dwindle, decline, plummet, wane
  • Important: crucial, vital, significant, pivotal, paramount
  • Problem: issue, predicament, dilemma, obstacle, hurdle
• Commonly confused pairs:
  • Accept (receive) vs Except (exclude)
  • Affect (verb: influence) vs Effect (noun: result)
  • Complement (complete) vs Compliment (praise)
• Absolute words have clear antonyms: Always/never, all/none, maximum/minimum, permanent/temporary
• Abstract words have trickier synonyms: for example, "integrity," "resilience," "pragmatic"
• Tone-matching rule: Formal words have formal synonyms. "Commence" matches "begin" or "initiate," not casual words like "kick off"

Worked Examples

Example 1: Synonym in Context

Passage excerpt: "The government's decision to curtail subsidies led to widespread protests."

Question: Choose the word most similar in meaning to CURTAIL.

Options: (a) Extend (b) Reduce (c) Continue (d) Support

Solution:

• Step 1: Read the sentence. The context suggests limiting or cutting subsidies.
• Step 2: "Curtail" means to reduce or cut short.
• Step 3: Check options—"Reduce" matches the meaning.
• Answer: (b) Reduce

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Example 2: Antonym in Context

Passage excerpt: "Despite the temporary setback, the company remained optimistic about its long-term prospects."

Question: Choose the word most opposite in meaning to TEMPORARY.

Options: (a) Brief (b) Permanent (c) Short-lived (d) Fleeting

Solution:

• Step 1: "Temporary" means lasting for a limited time.
• Step 2: We need the opposite—something lasting forever.
• Step 3: "Brief," "short-lived," and "fleeting" are synonyms of temporary.
• Step 4: "Permanent" means lasting indefinitely—the exact opposite.
• Answer: (b) Permanent

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Example 3: Tricky Synonym

Passage excerpt: "The minister gave an ambiguous statement regarding the policy change."

Question: Choose the word most similar in meaning to AMBIGUOUS.

Options: (a) Clear (b) Vague (c) Detailed (d) Confident

Solution:

• Step 1: "Ambiguous" means unclear, open to multiple interpretations.
• Step 2: "Clear" and "detailed" are opposites. "Confident" is unrelated.
• Step 3: "Vague" means unclear or uncertain—matches perfectly.
• Answer: (b) Vague

Common Mistakes

• Choosing topic-related words instead of meaning-related words: Students see "economy" in the passage and pick "financial" as a synonym for "growth" just because both relate to economics. Fix: Focus only on the specific word's meaning, ignore passage topic.
• Ignoring context and using memorized meanings: "Grave" can mean serious (grave concern) or burial site. Students pick "cemetery" when the passage uses "grave" as an adjective. Fix: Always re-read the exact sentence containing the word.
• Confusing similar-sounding words: Picking "eminent" (famous) as synonym for "imminent" (about to happen). Fix: Read each option carefully; similar spelling does not mean similar meaning.
• Selecting moderate words as antonyms of extreme words: Choosing "good" as antonym of "excellent" when the correct answer is "terrible." Fix: Match the intensity level—extreme words need extreme opposites.
• Overthinking simple words: Second-guessing obvious answers because they seem "too easy." If "happy" appears and "joyful" is an option, it is likely correct. Fix: Trust straightforward matches; not every question is a trap.

Quick Reference

• Read the full sentence containing the target word before looking at options.
• Synonym = same meaning; Antonym = opposite meaning.
• Match part of speech: noun with noun, verb with verb.
• Prefixes un-, dis-, in-, im- typically create antonyms.
• Eliminate options that relate to the topic but not the specific word.
• When stuck, substitute each option into the original sentence—the correct synonym will fit naturally.

Idioms and Phrases

Overview

Idioms and phrases are part of SBI Clerk Prelims. These questions typically appear within Reading Comprehension passages or as standalone items asking you to identify the correct meaning of an underlined idiomatic expression. Since idioms carry meanings that cannot be deduced from their individual words, rote familiarity is essential—you either know the idiom or you don't.

Questions are straightforward—no tricks, no deep inference—just match the idiom to its meaning.

Your goal: build a mental dictionary of common idioms, understand their contextual usage, and avoid confusing literal meanings with figurative ones.

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Key Concepts

• Idiom vs. Phrase: An idiom is a fixed expression whose meaning differs from literal word meanings (e.g., "kick the bucket" = die). A phrase is any group of words functioning as a unit; not all phrases are idioms.
• Context is King: Even if you half-remember an idiom, the sentence context often reveals whether your guess fits logically. Eliminate options that make no contextual sense.
• Figurative, Not Literal: Never interpret idioms word-by-word. "Break the ice" has nothing to do with actual ice—it means to initiate conversation in an awkward situation.
• Fixed Structure: Idioms rarely change form. "Bite the dust" stays as is; you cannot say "biting the dusts" and retain the idiomatic meaning.
• Positive / Negative / Neutral Tone: Categorizing idioms by tone helps quick elimination. "Feather in one's cap" (positive) cannot mean something negative.
• Verb-Based Idioms Dominate: Most exam idioms start with verbs—burn, break, call, carry, turn, hold, bring, etc. Grouping idioms by their lead verb aids memorization.
• Origin Doesn't Matter: You don't need to know why "let the cat out of the bag" means revealing a secret. Just know the meaning.

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Formulas / Key Facts

Below are 40 common idioms for SBI Clerk. Memorize meaning and tone.

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Worked Examples

Example 1

Sentence: After months of conflict, the two partners decided to bury the hatchet and work together again.

Question: "Bury the hatchet" means: (a) Hide a weapon (b) End a disagreement and make peace (c) Dig the ground (d) Forget the partnership

Solution: Step 1 – Literal meaning ("hide a weapon") makes no contextual sense with "work together again." Step 2 – The context shows reconciliation after conflict. Step 3 – "Bury the hatchet" = end a quarrel, make peace. Answer: (b)

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Example 2

Sentence: She was on cloud nine after receiving the promotion letter.

Question: The phrase "on cloud nine" means: (a) Confused (b) Extremely happy (c) In a difficult situation (d) Lost in thought

Solution: Step 1 – Promotion is positive news → idiom should convey happiness. Step 2 – "On cloud nine" = state of extreme happiness or elation. Answer: (b)

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Example 3

Sentence: The manager asked us not to beat around the bush and come straight to the point.

Question: "Beat around the bush" means: (a) Strike the bushes (b) Speak evasively (c) Work in a garden (d) Arrive early

Solution: Step 1 – Context: "come straight to the point" is the opposite action. Step 2 – So the idiom must mean avoiding directness. Step 3 – "Beat around the bush" = speak indirectly, avoid the main topic. Answer: (b)

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Common Mistakes

1. Literal Interpretation Trap Wrong: "Let the cat out of the bag" = release an animal. Correct: It means to accidentally reveal a secret. Always think figuratively first.
2. Confusing Similar Idioms Wrong: Mixing "spill the beans" with "full of beans." Correct: "Spill the beans" = reveal secrets; "full of beans" = energetic and lively. Note the verb difference.
3. Ignoring Sentence Context Wrong: Selecting a memorized meaning without checking if it fits the sentence. Correct: Plug the meaning back into the sentence. If it sounds odd, reconsider.
4. Guessing Based on One Word Wrong: "A hot potato" must be about food or temperature. Correct: It means a controversial issue that people avoid handling. The word "hot" suggests danger, not heat literally.
5. Overthinking Rare Idioms Wrong: Spending too long on an unfamiliar idiom. Correct: Use elimination—remove options that clearly don't fit the tone or context, then make an educated guess.

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Quick Reference

• Beat around the bush → Avoid speaking directly
• Break the ice → Start a conversation / ease awkwardness
• Once in a blue moon → Very rarely
• Cost an arm and a leg → Extremely expensive
• Hit the nail on the head → Be exactly correct
• Under the weather → Feeling unwell

Spelling Check — Study Notes for SBI Clerk Prelims

Overview

Spelling Check questions test your ability to identify correctly or incorrectly spelt words from a given set of options. Unlike grammar or comprehension, spelling questions have no grey area — the answer is either right or wrong, making them high-scoring if you have prepared well.

The challenge is that English spelling often defies logical patterns. Words borrowed from Latin, Greek, French, and other languages follow different rules, and many common words have silent letters, doubled consonants, or unusual vowel combinations. By learning the patterns behind common spelling errors, you can quickly eliminate wrong options and secure easy marks.

This topic rewards consistent reading habits over last-minute cramming. Students who read newspapers, editorials, or English books regularly develop an intuitive sense for correct spellings. For those starting fresh, focus on the high-frequency error patterns listed below.

Key Concepts

• Silent letters are spelling traps: Words like "knowledge," "psychology," "debt," and "receipt" contain letters you don't hear when speaking.
• Double consonants follow specific patterns: Words ending in a single vowel + single consonant usually double the consonant before adding -ed or -ing (occur → occurred, refer → referred). Exceptions exist.
• The "i before e except after c" rule has many exceptions: "Receive," "ceiling," and "deceive" follow the rule, but "weird," "seize," and "neither" break it.
• Suffixes change spelling in predictable ways: Adding -ful creates one 'l' (beautiful, not beautifull). Adding -ly to words ending in 'l' keeps both (finally, usually).
• American vs British spellings both appear: Common pairs: color/colour, center/centre, honor/honour, realize/realise.
• Greek and Latin roots have fixed spellings: Words with "ph" for 'f' sound (philosophy, phenomenon), "ch" for 'k' sound (character, chemistry), and "ps" for 's' sound (psychology, pseudonym).
• Homophones are deliberate traps: Words that sound alike but spell differently (stationary/stationery, principal/principle, affect/effect) are easily confused.
• Prefixes generally don't change the root spelling: Mis + spell = misspell (two s's). Un + necessary = unnecessary (two n's). Dis + satisfied = dissatisfied (two s's).

Formulas / Key Facts

Must-Remember Spelling Rules:

1. -ie/-ei rule: Use 'i' before 'e' except after 'c' when the sound is 'ee'. Exceptions: weird, seize, neither, leisure, protein.
2. Final 'e' drops before vowel suffixes: hope → hoping, make → making. But keeps before consonant suffixes: hope → hopeful.
3. Final 'y' changes to 'i' before suffixes: happy → happiness, beauty → beautiful. Exception: when suffix starts with 'i' (study → studying).
4. -ible vs -able: Use -ible after soft 'g' or 'c' (legible, forcible) and Latin roots (visible, terrible). Use -able after complete words (dependable, laughable).
5. -tion vs -sion: Use -tion after most consonants. Use -sion after 'l', 'n', 'r', or 's' (expulsion, extension, immersion, discussion).

Commonly Misspelt Words in Bank Exams:

Worked Examples

Example 1: Find the correctly spelt word

Options: (a) Ocassion (b) Occassion (c) Occasion (d) Ocasion

Solution:

• Check the 'c' and 's' pattern. The word has two c's and one s.
• "Occasion" follows the pattern: oc-ca-sion (double c, single s).
• Answer: (c) Occasion

Example 2: Find the incorrectly spelt word

Options: (a) Surveillance (b) Perseverance (c) Maintenance (d) Attendence

Solution:

• Surveillance — correct (French origin, -ance ending)
• Perseverance — correct (-ance ending after 'r')
• Maintenance — correct (maintain + -ance, but note spelling)
• Attendence — incorrect. Should be "Attendance" (attend + -ance)
• Answer: (d) Attendence

Example 3: Find the correctly spelt word

Options: (a) Recomendation (b) Reccommendation (c) Recommendation (d) Recommandation

Solution:

• Root word is "recommend" — one 'c', two 'm's.
• Adding -ation: recommend + ation = recommendation.
• Answer: (c) Recommendation

Common Mistakes

Wrong thinking: "I'll spell it how it sounds." Correct fix: English pronunciation often misleads. "February" has two 'r's, "Wednesday" has a silent 'd', "library" has two 'r's. Learn visual patterns, not phonetic guesses.

Wrong thinking: "Double consonants appear randomly." Correct fix: Doubling follows rules. One-syllable words with short vowels double the final consonant (run → running). Two-syllable words double when stress is on the second syllable (occur → occurred, but offer → offered).

Wrong thinking: "All -ance and -ence words sound the same, so I'll guess." Correct fix: Build word families. Attend → attendance, depend → dependence. The verb form often hints at the suffix. Words ending in -ant take -ance; words ending in -ent take -ence.

Wrong thinking: "I recognize this word, so it's correct." Correct fix: Exam setters use near-correct spellings that look familiar. Always check each letter systematically, especially double letters and vowel combinations.

Wrong thinking: "The longest or most complex-looking option must be wrong." Correct fix: Some correctly spelt words are genuinely long (conscientious, entrepreneurship). Judge by spelling rules, not length.

Quick Reference

• Double c, double m: accommodation (cc, mm), recommend (one c, mm), accidental (cc)
• Double r: occurrence, embarrass, irregular
• Silent letters: knowledge (k), psychology (p), receipt (p), debt (b)
• -ance vs -ence: maintenance, attendance, independence, excellence
• -able vs -ible: available, responsible, comfortable, flexible
• ie/ei: believe, receive, achieve, ceiling, weird (exception)

Percentage

Overview

Percentage is one of the most fundamental topics in SBI Clerk Prelims. It forms the foundation for several other arithmetic topics including Profit and Loss, Simple and Compound Interest, Data Interpretation, and Ratio problems. You cannot afford to be slow or inaccurate here.

In the exam, percentage questions appear both as direct calculation problems in the Simplification/Approximation section and as applied concepts within DI sets. Mastery means two things: knowing the fraction-to-percentage conversions by heart, and being able to quickly compute percentage change in either direction. Speed is everything.

The key skill is mental calculation. Memorize common percentage-fraction equivalents and practice computing 10%, 5%, 1% of any number instantly. This forms your calculation base for deriving any percentage quickly.

Key Concepts

• Percentage means "per hundred": x% = x/100. Converting between fractions, decimals, and percentages must be instantaneous.
• Percentage of a number: x% of N = (x × N)/100. Always compute 10% first, then build up or down.
• Percentage change formula: Change% = (Difference / Original) × 100. The denominator is always the original value, not the new value.
• Successive percentage changes: Two changes of a% and b% give net change = a + b + (ab/100). This avoids multi-step calculation.
• Percentage increase vs decrease reversal: A p% increase followed by reversal requires a decrease of [100p/(100+p)]%, not p%.
• Population/Depreciation formula: Final = Initial × (1 ± r/100)^n, where n is time periods and r is rate per period.
• Fraction-Percentage equivalents are non-negotiable: 1/2 = 50%, 1/3 ≈ 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 ≈ 16.67%, 1/8 = 12.5%, 1/9 ≈ 11.11%.

Formulas / Key Facts

Must-memorize conversions:

• 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%
• 1/6 = 16.67%, 1/7 = 14.29%, 1/8 = 12.5%, 1/9 = 11.11%, 1/10 = 10%
• 1/11 = 9.09%, 1/12 = 8.33%, 1/15 = 6.67%, 1/20 = 5%

Worked Examples

Example 1: Basic percentage of a number

Find 35% of 1200.

Step 1: 10% of 1200 = 120 Step 2: 30% = 3 × 120 = 360 Step 3: 5% = half of 10% = 60 Step 4: 35% = 360 + 60 = 420

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Example 2: Percentage change

A product's price increased from ₹450 to ₹540. Find the percentage increase.

Difference = 540 − 450 = 90 Percentage increase = (90/450) × 100 = (1/5) × 100 = 20%

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Example 3: Successive percentage change

A shopkeeper increases price by 20% and then gives a 10% discount. What is the net percentage change in price?

Using formula: Net change = a + b + ab/100 Here a = +20, b = −10 Net change = 20 + (−10) + (20 × −10)/100 Net change = 20 − 10 − 2 = +8% (increase)

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Example 4: Reversal percentage

If A's salary is 25% more than B's salary, by what percentage is B's salary less than A's?

Using formula: Required % = 100x/(100+x) = (100 × 25)/(100 + 25) = 2500/125 = 20%

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Example 5: Population growth

The population of a town is 50,000. It increases by 10% in the first year and 20% in the second year. Find the population after 2 years.

After Year 1: 50,000 × 1.10 = 55,000 After Year 2: 55,000 × 1.20 = 66,000

Alternative: 50,000 × 1.10 × 1.20 = 50,000 × 1.32 = 66,000

Common Mistakes

• Using final value as base for percentage change → Always use the original value as denominator. If price goes from 80 to 100, increase = 20/80 = 25%, not 20/100 = 20%.
• Assuming successive equal changes cancel out → A 20% increase followed by 20% decrease does NOT return to original. Net effect = 20 + (−20) + (20 × −20)/100 = −4%. There's always a net loss.
• Confusing "more than" with "of" → "A is 25% more than B" means A = 1.25B. "A is 25% of B" means A = 0.25B. Read carefully.
• Reversing percentage incorrectly → If A is 20% more than B, students often say B is 20% less than A. Wrong. B is 100×20/120 = 16.67% less than A.
• Not simplifying fractions first → Calculate 45/300 as 45/300 = 3/20 = 15%, not by dividing decimals. Fraction simplification saves time.

Quick Reference

• 10% of any number: Move decimal one place left
• Successive changes: a + b + ab/100 (watch signs carefully)
• x% more → reverse is [100x/(100+x)]% less
• x% less → reverse is [100x/(100−x)]% more
• 25% = 1/4, 33.33% = 1/3, 12.5% = 1/8, 16.67% = 1/6
• Always base percentage change on the ORIGINAL value

Tabular DI — Study Notes

Overview

Unlike complex DI formats, tabular DI presents data in rows and columns, making extraction straightforward — the real test is your calculation speed and accuracy under time pressure.

In SBI Clerk Prelims, you typically encounter tables showing production figures, sales data, population statistics, or employee counts across different years, companies, or categories. Questions demand direct calculations: finding totals, averages, percentages, ratios, and percentage changes. Since Prelims is about speed (you have roughly 20 minutes for 35 quant questions), mastering quick mental math with tables gives you an edge.

This topic connects directly with percentage, ratio, and average concepts. Students who practice tabular DI also strengthen their overall calculation ability, which helps across the entire Numerical Ability section.

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Key Concepts

• Data Extraction First: Before touching your pen, spend 10–15 seconds understanding what the rows and columns represent.
• Row vs Column Totals: Questions often ask for totals across a row (one entity, multiple time periods) or down a column (multiple entities, one time period). Know which direction you're summing.
• Percentage Calculation: Most questions boil down to (Part/Whole) × 100. Identify what's the "part" and what's the "whole" from context.
• Percentage Change Formula: Always uses the base (earlier/original) value in the denominator. Direction matters — increase vs decrease.
• Ratio Simplification: After extracting two values, find HCF quickly to express ratios in lowest terms.
• Average Across Categories: Sum all values, divide by count. Watch out for weighted averages when quantities differ.
• Approximation is Your Friend: When numbers are large and options are spread apart, round to nearest tens or hundreds before calculating.

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Formulas / Key Facts

Percentage of A out of B = (A / B) × 100

Percentage Increase = [(New – Old) / Old] × 100

Percentage Decrease = [(Old – New) / Old] × 100

Ratio of A to B = A : B (simplify by dividing both by HCF)

Average = Sum of all values / Number of values

Difference as Percentage of a Value = [(A – B) / Reference Value] × 100

Quick Fraction-to-Percentage Conversions

• 1/2 = 50%, 1/3 ≈ 33.33%, 1/4 = 25%, 1/5 = 20%
• 1/6 ≈ 16.67%, 1/7 ≈ 14.29%, 1/8 = 12.5%, 1/9 ≈ 11.11%

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Worked Examples

Sample Table: Number of laptops sold by 5 companies in 3 years (in hundreds)

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Example 1: What is the percentage increase in sales of Company E from 2021 to 2023?

Solution:

• Old value (2021) = 30
• New value (2023) = 45
• Increase = 45 – 30 = 15
• Percentage increase = (15/30) × 100 = 50%

Answer: 50%

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Example 2: What is the ratio of total sales of Company A to Company B across all three years?

Solution:

• Total for A = 45 + 52 + 60 = 157
• Total for B = 38 + 44 + 50 = 132
• Ratio = 157 : 132
• Check if simplifiable: HCF of 157 and 132 = 1 (both are coprime)

Answer: 157 : 132

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Example 3: Sales of Company C in 2022 are what percent less than its sales in 2023?

Solution:

• 2022 value = 48
• 2023 value = 62
• Difference = 62 – 48 = 14
• Base for "less than 2023" = 2023 value = 62
• Percentage = (14/62) × 100 = (7/31) × 100 ≈ 22.58%

Answer: Approximately 22.6%

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Example 4: What is the average sales of all companies in 2022?

Solution:

• 2022 values: 52 + 44 + 48 + 50 + 36 = 230
• Number of companies = 5
• Average = 230/5 = 46 hundreds = 4600 laptops

Answer: 46 (in hundreds)

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Common Mistakes

• Confusing "more than" vs "of": "A is what percent more than B" uses B as base. "A is what percent of B" also uses B as base, but no subtraction. Students swap these and get wrong answers. → Fix: "More/less than X" means X is the denominator. "Of X" also means X is the denominator.
• Misreading row/column headers: Picking 2022 data when question asks for 2023, or reading Company C row for Company D. → Fix: Underline or circle the exact cell(s) needed before calculating.
• Forgetting to convert units: Table says "in hundreds" but student calculates as if actual numbers. → Fix: Check table title and footnotes for unit multipliers.
• Using wrong base for percentage change: For "increase from X to Y," base is X (the starting point), not Y. → Fix: The word "from" indicates your base value.
• Over-calculating when approximation works: Spending 90 seconds on exact division when options are 22%, 28%, 35%, 41%. → Fix: If options differ by 5%+, approximate aggressively.

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Quick Reference

• Read table headers (rows, columns, units) before any calculation.
• Percentage change = (Difference / Base) × 100; base is the "from" or "original" value.
• For ratios, always simplify to lowest terms using HCF.
• Average = Total Sum ÷ Count of items.
• When options are spread apart, approximate; when close, calculate precisely.
• "What percent of" and "what percent more/less than" both use the reference value as denominator.

Simplification and Approximation

Overview

Simplification and Approximation is a topic in SBI Clerk Prelims Numerical Ability section. These questions reward speed over complexity—most involve basic arithmetic but under strict time pressure (about 20 minutes for 35 questions).

The core skill is applying BODMAS correctly while knowing when to calculate exactly versus when to round aggressively. Simplification questions demand precise answers; approximation questions expect you to estimate within 5–10% and pick the closest option. Mastering both modes is essential because the exam mixes them freely, and applying the wrong approach wastes precious seconds.

This topic requires no advanced concepts—just fluency with percentages, squares, cubes, fractions, and decimals.

Key Concepts

• BODMAS Rule: Brackets → Orders (powers, roots) → Division → Multiplication → Addition → Subtraction. Division and multiplication have equal priority, as do addition and subtraction; within each pair, work left to right.
• Approximation Threshold: When a question says "approximate value" or "≈", round numbers to nearest convenient values before calculating. Typically round to nearest 5, 10, or whole number.
• Percentage-Decimal-Fraction Equivalence: Instantly convert between forms. For example, 12.5% = 1/8 = 0.125. This speeds up mixed calculations.
• Square and Cube Recognition: Identify perfect squares (1 to 30) and cubes (1 to 15) on sight. Many expressions contain hidden squares/cubes.
• Fraction Simplification: Always reduce fractions before multiplying. Cancel common factors across numerator and denominator early.
• "Of" Means Multiply: In expressions like "40% of 250", treat "of" as multiplication: 0.4 × 250.
• Decimal Alignment: When adding/subtracting decimals, mentally align decimal points. Careless misalignment causes wrong answers.
• Answer Option Spread: In approximation, check how far apart options are. Wide gaps (e.g., 450, 520, 600, 680) allow rougher estimates; close options need tighter calculation.

Formulas / Key Facts

Essential Squares (Memorize 1–30)

• 11² = 121, 12² = 144, 13² = 169, 14² = 196, 15² = 225
• 16² = 256, 17² = 289, 18² = 324, 19² = 361, 20² = 400
• 21² = 441, 22² = 484, 23² = 529, 24² = 576, 25² = 625

Essential Cubes (Memorize 1–15)

• 6³ = 216, 7³ = 343, 8³ = 512, 9³ = 729, 10³ = 1000
• 11³ = 1331, 12³ = 1728, 13³ = 2197, 14³ = 2744, 15³ = 3375

Fraction-Percentage Equivalents

• 1/2 = 50%, 1/3 ≈ 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 ≈ 16.67%
• 1/7 ≈ 14.29%, 1/8 = 12.5%, 1/9 ≈ 11.11%, 1/10 = 10%

Square Roots (Approximate)

• √2 ≈ 1.414, √3 ≈ 1.732, √5 ≈ 2.236, √7 ≈ 2.646

Useful Products

• 25 × 4 = 100, 125 × 8 = 1000, 37.5 × 8 = 300

Worked Examples

Example 1: Pure Simplification

Question: 18 × 15 + 324 ÷ 18 – 12² = ?

Step 1: Apply BODMAS — handle division and powers first

• 324 ÷ 18 = 18
• 12² = 144

Step 2: Handle multiplication

• 18 × 15 = 270

Step 3: Addition and subtraction left to right

• 270 + 18 – 144 = 288 – 144 = 144

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Example 2: Approximation

Question: 39.97% of 4011 + 17.98% of 3499 = ?

Step 1: Round the percentages and numbers

• 39.97% ≈ 40%, 4011 ≈ 4000
• 17.98% ≈ 18%, 3499 ≈ 3500

Step 2: Calculate

• 40% of 4000 = 0.4 × 4000 = 1600
• 18% of 3500 = 0.18 × 3500 = 630

Step 3: Add

• 1600 + 630 = 2230

If options are 2180, 2230, 2285, 2340 → Answer is 2230

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Example 3: Mixed Expression with Roots and Fractions

Question: √529 + 13³ ÷ 169 – 45% of 80 = ?

Step 1: Recognize values

• √529 = 23 (since 23² = 529)
• 13³ = 2197
• 169 = 13²

Step 2: Compute division

• 2197 ÷ 169 = 13 (since 13³ ÷ 13² = 13)

Step 3: Calculate percentage

• 45% of 80 = 0.45 × 80 = 36

Step 4: Combine

• 23 + 13 – 36 = 36 – 36 = 0

Common Mistakes

• Ignoring BODMAS in left-to-right sequences → Students compute 20 – 5 + 3 as 20 – 8 = 12 instead of correct (20 – 5) + 3 = 18. Addition and subtraction are equal priority; work left to right.
• Over-approximating in close-option questions → Rounding 7.89 to 8 and 51.2 to 50 when options differ by only 10 causes wrong picks. Check option spread first; tighten estimates for close options.
• Forgetting "of" means multiplication → Reading "25% of 60% of 400" and adding instead of multiplying. Compute as 0.25 × 0.6 × 400 = 60.
• Misreading division vs. multiplication signs → Under pressure, ÷ looks like +. Slow down for half a second on operator recognition.
• Calculating squares from scratch → Computing 17² by multiplication wastes 10+ seconds. Memorize squares up to 30; recognize them instantly.

Quick Reference

• BODMAS: Brackets → Orders → Division → Multiplication → Addition → Subtraction
• For approximation: round to nearest 5 or 10, then compute
• "Of" = × (multiplication)
• Know squares 1–30 and cubes 1–15 cold
• Check option gaps before deciding how roughly to estimate
• Addition and subtraction: equal priority, work left to right

Ratio and Proportion

Overview

Ratio and Proportion is a foundational arithmetic topic that appears in SBI Clerk Prelims, either as direct questions or embedded within Data Interpretation, Partnership, and Mixture problems.

The topic tests your ability to compare quantities, scale values proportionally, and solve multi-step problems involving compound ratios. Mastering ratio and proportion gives you speed advantages across the Numerical Ability section since these concepts underpin profit-sharing, mixture calculations, and even time-work problems.

For SBI Clerk Prelims, focus on quick mental calculations with simple ratios, compound ratio formation, and proportion-based equation solving. Problems are calculation-intensive but conceptually straightforward—accuracy and speed matter more than complex reasoning.

Key Concepts

• Ratio expresses the relative size of two quantities. If A:B = 3:4, it means for every 3 units of A, there are 4 units of B. Ratios have no units and can be scaled by any common multiplier.
• Proportion states that two ratios are equal. If A:B = C:D, then A×D = B×C (cross-multiplication rule). This is your primary solving tool.
• Compound Ratio is found by multiplying corresponding terms. If ratios are a:b and c:d, their compound ratio is ac:bd. Used when quantities depend on multiple factors.
• Duplicate and Triplicate Ratios: Duplicate of a:b is a²:b². Triplicate is a³:b³. Sub-duplicate is √a:√b.
• Componendo-Dividendo: If a/b = c/d, then (a+b)/(a−b) = (c+d)/(c−d). Useful for quickly solving certain proportion equations.
• Distribution in Ratio: To divide quantity Q in ratio a:b:c, the parts are Qa/(a+b+c), Qb/(a+b+c), Qc/(a+b+c).
• Combining Ratios: When A:B = 2:3 and B:C = 4:5, make B common (LCM of 3 and 4 = 12), so A:B:C = 8:12:15.
• Inverse Ratio: If A:B = 3:4, then inverse ratio is 4:3. Used when quantities are inversely related (like speed and time for same distance).

Formulas / Key Facts

Basic Ratio: If A:B = a:b, then A = ak and B = bk for some constant k.

Proportion Rule: If a:b :: c:d, then ad = bc (product of extremes = product of means).

Compound Ratio: (a:b) compounded with (c:d) = ac:bd.

Duplicate Ratio of a:b = a²:b².

Sub-duplicate Ratio of a:b = √a:√b.

Triplicate Ratio of a:b = a³:b³.

Division Formula: Share of A when amount M is divided in ratio a:b:c is M × a/(a+b+c).

Combining Two Ratios: A:B = p:q and B:C = r:s → A:B:C = pr : qr : qs (after making B equal).

Mean Proportional of a and b = √(ab). If a:x :: x:b, then x = √(ab).

Third Proportional to a and b: If a:b :: b:x, then x = b²/a.

Worked Examples

Example 1: Basic Distribution

₹2400 is divided among A, B, and C in the ratio 3:5:4. Find each person's share.

Solution:

• Sum of ratio parts = 3 + 5 + 4 = 12
• A's share = 2400 × 3/12 = 2400 × 1/4 = ₹600
• B's share = 2400 × 5/12 = ₹1000
• C's share = 2400 × 4/12 = ₹800

Example 2: Combining Ratios

If A:B = 2:3 and B:C = 5:7, find A:B:C.

Solution:

• B appears as 3 in first ratio and 5 in second
• LCM of 3 and 5 = 15
• Multiply first ratio by 5: A:B = 10:15
• Multiply second ratio by 3: B:C = 15:21
• Combined: A:B:C = 10:15:21

Example 3: Compound Ratio Application

The incomes of P and Q are in ratio 4:3. Their expenditures are in ratio 3:2. If each saves ₹1000, find their incomes.

Solution:

• Let incomes be 4x and 3x
• Let expenditures be 3y and 2y
• Savings: Income − Expenditure = 1000
• For P: 4x − 3y = 1000
• For Q: 3x − 2y = 1000
• From both equations: 4x − 3y = 3x − 2y
• Solving: x = y
• Substituting in first equation: 4x − 3x = 1000, so x = 1000
• P's income = 4 × 1000 = ₹4000
• Q's income = 3 × 1000 = ₹3000

Example 4: Finding Original Ratio

Two numbers are in ratio 3:4. If 5 is added to each, the ratio becomes 4:5. Find the numbers.

Solution:

• Let numbers be 3k and 4k
• After adding 5: (3k + 5)/(4k + 5) = 4/5
• Cross-multiply: 5(3k + 5) = 4(4k + 5)
• 15k + 25 = 16k + 20
• k = 5
• Numbers are 15 and 20

Common Mistakes

Adding/subtracting ratios directly → Wrong. 2:3 and 4:5 don't add to 6:8. Ratios must be combined using LCM method or compounding rules.

Forgetting the constant multiplier → When ratio is 3:4, actual values are 3k and 4k, not 3 and 4. Always introduce 'k' for calculations.

Confusing compound ratio with addition → Compound of 2:3 and 4:5 is 8:15, not 6:8. Multiply corresponding terms.

Misplacing terms in proportion → In a:b :: c:d, ad = bc. Students often multiply wrong pairs. Remember: extremes (first and last) multiply together.

Not simplifying final ratios → Answer 12:18 should be written as 2:3. Always reduce to lowest terms unless question specifies otherwise.

Quick Reference

• Ratio a:b means actual values are ak and bk—always use the multiplier k.
• Proportion: If a:b = c:d, then ad = bc (cross-multiply).
• Compound ratio: Multiply term-by-term (ac:bd).
• To combine A:B and B:C, make B common using LCM, then merge.
• Distribution: Part = Total × (own ratio term / sum of all terms).
• Mean proportional of a and b = √(ab).

Bar Graph DI — Study Notes for SBI Clerk Prelims

Overview

Bar Graph Data Interpretation is a topic in SBI Clerk Prelims. The calculations are usually straightforward — addition, subtraction, percentage, ratio, and average — making this a high-accuracy zone if you read the graph carefully.

Bar graphs present data visually using rectangular bars where the length or height represents the value. In single bar graphs, one variable is tracked across categories (e.g., sales of a company over 5 years). In double bar graphs, two related variables are compared side by side (e.g., production vs. sales, or male vs. female employees). Mastering quick visual estimation and avoiding silly reading errors will help you solve these sets.

Key Concepts

• Single bar graph: One set of bars representing one data series. Height of each bar = exact value for that category.
• Double bar graph: Two bars per category, usually distinguished by colour or shading. Always check the legend to identify which bar represents what.
• Scale reading: The Y-axis has a scale (e.g., 0, 100, 200...). Read values carefully — a bar ending between two gridlines requires estimation (e.g., halfway between 200 and 300 = 250).
• Percentage calculation: Questions may ask percentage increase/decrease or percentage contribution. Use: [(New − Old)/Old] × 100 for change, and [Part/Total] × 100 for contribution.
• Ratio questions: Compare two bars directly. Simplify to lowest terms. If values are large, cancel common factors early.
• Average: Add all bar values and divide by the number of bars. For double bars, be clear whether you're averaging one series or combining both.
• Total and difference: Simple addition of all bars in a series, or difference between corresponding bars of two series.

Formulas / Key Facts

Key facts to remember:

• Always note the units (thousands, lakhs, crores, etc.) mentioned in the title or axis label.
• In double bar graphs, questions often ask about "combined total" — add both bars for each category.
• Approximation is acceptable when options are far apart — saves calculation time.

Worked Examples

Example Graph (visualize): A double bar graph shows Production and Sales (in thousand units) of a company over 5 years.

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Q1: What is the percentage increase in Production from 2018 to 2022?

Step 1: Production in 2018 = 45, Production in 2022 = 70

Step 2: Increase = 70 − 45 = 25

Step 3: Percentage increase = (25/45) × 100 = 55.56%

Answer: Approximately 55.6%

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Q2: In which year is the difference between Production and Sales maximum?

Calculate difference for each year:

• 2018: 45 − 40 = 5
• 2019: 50 − 48 = 2
• 2020: 55 − 50 = 5
• 2021: 60 − 55 = 5
• 2022: 70 − 65 = 5

Answer: 2018, 2020, 2021, and 2022 all have difference = 5 (maximum). If only one option needed, check options carefully.

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Q3: What is the ratio of total Sales to total Production over all 5 years?

Step 1: Total Production = 45 + 50 + 55 + 60 + 70 = 280

Step 2: Total Sales = 40 + 48 + 50 + 55 + 65 = 258

Step 3: Ratio = 258 : 280

Step 4: Simplify by dividing both by 2 = 129 : 140

Answer: 129 : 140

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Q4: Sales in 2020 is what percent of Production in 2021?

Step 1: Sales in 2020 = 50, Production in 2021 = 60

Step 2: Required percentage = (50/60) × 100 = 83.33%

Answer: 83.33%

Common Mistakes

1. Misreading the legend → In double bar graphs, students swap which bar is Production and which is Sales. Always read the legend first and mark it mentally.
2. Ignoring units → The title says "in thousands" but you calculate as if it's actual units. This leads to wrong answers when questions ask for "total units sold." Multiply by the unit factor when needed.
3. Wrong base for percentage → When asked "A is what % more than B," the base is B, not A. Students often divide by the wrong value. Remember: "more than X" means X is the base.
4. Estimating bar values incorrectly → A bar slightly above 250 gridline might be 255 or 260, not 250. Look at the bar's position relative to gridlines carefully.
5. Adding instead of averaging → Question asks "average production" but you give the total. Read the question word by word.
6. Calculating percentage change backwards → For decrease, some students use final as base instead of initial. Always use the original (earlier) value as the base for percentage change.

Quick Reference

• Double bar = check legend first — know which shade means what before solving.
• % change formula: (Difference / Original) × 100 — original is always the base.
• Approximation saves time — if options are 45%, 52%, 67%, 78%, don't calculate to decimals.
• Units matter — "in lakhs" means multiply values by 100000 when question asks actual numbers.
• Ratio shortcut — cancel zeros first; 280 : 258 becomes 28 : 25.8, then simplify.
• Difference questions are freebies — just subtract and compare; no percentage calculation needed.

Number Series

Overview

These questions test your ability to identify patterns in sequences of numbers and either find the missing term or spot the wrong term that breaks the pattern.

At the Clerk level, series patterns are usually straightforward—based on addition, subtraction, multiplication, division, or squares and cubes. The key to scoring well is quick pattern recognition. With practice, you can solve these quickly, making them valuable time-savers in the exam.

Mastering number series builds your number sense, which indirectly helps with simplification and data interpretation as well.

Key Concepts

• Arithmetic Series (Constant Difference): Each term differs from the previous by a fixed number. Example: 3, 7, 11, 15, 19 (difference = +4).
• Geometric Series (Constant Ratio): Each term is multiplied by a fixed number. Example: 2, 6, 18, 54, 162 (ratio = ×3).
• Square-Based Series: Terms follow a pattern involving perfect squares (1, 4, 9, 16, 25...) either as terms themselves or as differences.
• Cube-Based Series: Terms follow patterns involving perfect cubes (1, 8, 27, 64, 125...).
• Two-Step Patterns: The difference between terms itself forms a pattern. Example: Differences of 2, 4, 6, 8... (increasing by 2).
• Mixed Operations: Alternating operations like +2, ×2, +2, ×2 or multiply then add a constant.
• Wrong Number Series: One term in the series does not follow the pattern. You must identify the rule and spot the outlier.
• Prime/Fibonacci-Based Series: Terms involve prime numbers (2, 3, 5, 7, 11...) or Fibonacci-like additions (each term = sum of previous two).

Formulas / Key Facts

Must-Remember Perfect Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

Must-Remember Perfect Cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000

Worked Examples

Example 1: Find the Missing Term

Series: 7, 11, 19, 31, ?, 67

Step 1: Calculate differences.

• 11 − 7 = 4
• 19 − 11 = 8
• 31 − 19 = 12
• ? − 31 = ?
• 67 − ? = ?

Step 2: Notice differences are 4, 8, 12... (increasing by 4).

Step 3: Next difference = 16, so ? = 31 + 16 = 47.

Verification: 67 − 47 = 20 (fits the pattern: 4, 8, 12, 16, 20).

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Example 2: Find the Missing Term (Multiplication Pattern)

Series: 5, 10, 30, 120, ?

Step 1: Check ratios.

• 10 ÷ 5 = 2
• 30 ÷ 10 = 3
• 120 ÷ 30 = 4

Step 2: Pattern is ×2, ×3, ×4...

Step 3: Next multiplication = ×5, so ? = 120 × 5 = 600.

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Example 3: Find the Wrong Number

Series: 2, 3, 6, 15, 52, 157.5

Step 1: Check for a pattern. Try: each term × n + something.

• 2 × 1 + 1 = 3 ✓
• 3 × 2 + 1 = 7 (but series has 6) ✗

Step 2: Try another pattern: ×1 + 1, ×2 + 0, ×3 − 3... Let's try: term × n, then add 1, 0, −3, −8

• 2 × 1 + 1 = 3 ✓
• 3 × 2 + 0 = 6 ✓
• 6 × 3 − 3 = 15 ✓
• 15 × 4 − 8 = 52 ✓

Step 3: Actually, let's recalculate with pattern ×n + something:

• 2 × 2 − 1 = 3 ✓
• 3 × 2 + 0 = 6 ✓

Better approach—check differences of differences:

• Differences: 1, 3, 9, 37, 105.5
• Ratios: 3, 3, ~4.1, ~2.9 (inconsistent)

Another forced fit (no single rule): ×1 + 1, ×2 + 0, ×2 + 3, ×3 + 7...

Let's try: 2, 3, 6, 15, 45, 157.5 (×1.5, ×2, ×2.5, ×3, ×3.5)

After testing: The pattern is a multiplier rising by 0.5 (×1.5, ×2, ×2.5, ×3, ×3.5):

• 2 × 1 + 1 = 3
• 3 × 2 = 6
• 6 × 2.5 = 15
• 15 × 3 = 45 (not 52)

Wrong number = 52 (should be 45).

Common Mistakes

• Jumping to conclusions after checking only 2 terms → Always verify your pattern holds for at least 3–4 transitions before answering.
• Confusing multiplication and addition patterns → If numbers grow slowly, think addition; if they grow rapidly, think multiplication or powers.
• Forgetting mixed operations → Don't assume a single operation. Try combinations like ×2 + 1, or alternating +/×.
• Ignoring squares and cubes → When differences are 3, 5, 7, 9 (odd numbers) or 1, 4, 9, 16, immediately think of square patterns.
• In wrong-number series, assuming the first term is wrong → Always check the full series before deciding.

Quick Reference

• First step: Always calculate differences between consecutive terms.
• If differences are constant: Arithmetic series (add the same number).
• If ratios are constant: Geometric series (multiply by the same number).
• If differences increase uniformly: Second-level arithmetic (differences of differences).
• Large jumps between terms: Think multiplication, squares, or cubes.
• For wrong number: Find the pattern using most terms, then identify the outlier.

Pie Chart DI — Study Notes for SBI Clerk Prelims

Overview

A pie chart represents data as sectors of a circle, where each sector's angle (or percentage) shows the proportion of a category relative to the whole. The entire circle represents 100% or 360°.

What makes pie charts exam-friendly is their visual simplicity but calculation intensity. You must quickly convert between percentages, degrees, and actual values. Mastering percentage calculations and ratio interpretations here directly boosts your score in the Numerical Ability section.

To excel, you need three skills: converting degrees to percentages (and vice versa), calculating actual values from given totals, and comparing sectors using ratios. Speed matters—you should aim to solve each question in 45–60 seconds.

Key Concepts

• Full circle = 360° = 100%: Every pie chart operates on this fundamental equality. A sector of 72° equals 20% of the total.
• Sector value formula: Actual Value = (Sector Percentage / 100) × Total Value, or equivalently, (Sector Angle / 360) × Total Value.
• Degree-to-percentage conversion: Percentage = (Degrees / 360) × 100. Quick shortcut: 1° = 100/360 = 5/18 %.
• Percentage-to-degree conversion: Degrees = (Percentage / 100) × 360. Quick shortcut: 1% = 3.6°.
• Comparing sectors: The ratio of two sectors equals the ratio of their percentages (or angles). No need to calculate actual values for ratio questions.
• Central angle is proportional to value: If one sector is twice the angle of another, its value is exactly double.
• Two pie charts: When given income and expenditure pie charts with separate totals, calculate each component independently before comparing.

Formulas / Key Facts

Must-remember shortcuts:

• 10% = 36°
• 20% = 72°
• 25% = 90°
• 50% = 180°
• 12.5% = 45°
• 33.33% = 120°

Ratio shortcut: Ratio of values = Ratio of percentages = Ratio of angles

Worked Examples

Example 1: Basic Value Calculation

A pie chart shows the distribution of 4500 employees across departments. The HR sector is 16%. Find the number of HR employees.

Solution: HR employees = 16% of 4500 = (16/100) × 4500 = 16 × 45 = 720 employees

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Example 2: Angle-Based Calculation

Total monthly expenditure is ₹60,000. The sector for Rent shows 90°. Find the rent amount.

Solution: Rent = (90/360) × 60,000 = (1/4) × 60,000 = ₹15,000

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Example 3: Ratio and Difference

In a company of 8000 workers, Marketing sector = 22%, Sales sector = 13%. Find (a) ratio of Marketing to Sales, and (b) difference in number of workers.

Solution: (a) Ratio = 22 : 13 (directly from percentages)

(b) Difference in percentage = 22 – 13 = 9% Difference in workers = 9% of 8000 = (9/100) × 8000 = 720 workers

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Example 4: Two Pie Charts

Income pie chart (Total = ₹50,000): Salary = 60%, Rent = 15% Expenditure pie chart (Total = ₹40,000): Food = 35%, Transport = 20% Find how much more is Salary income than Food expenditure.

Solution: Salary income = 60% of 50,000 = ₹30,000 Food expenditure = 35% of 40,000 = ₹14,000 Difference = 30,000 – 14,000 = ₹16,000

Common Mistakes

• Adding percentages from different pie charts → Each pie chart has its own 100%. You cannot add 20% from one chart to 30% from another and call it 50% of anything.
• Forgetting to convert angles to percentages before calculation → If given 54°, first convert to 15% before applying to the total, OR use (54/360) × Total directly.
• Calculating actual values for ratio questions → Waste of time. Ratio of sectors = ratio of their percentages. Skip the multiplication.
• Misreading "more than" vs "of" → "A is what percent more than B" requires [(A–B)/B] × 100. "A is what percent of B" requires (A/B) × 100. These are different.
• Using wrong total when two charts given → Always check which total applies to which chart before calculating.

Quick Reference

• 360° = 100%; 3.6° = 1%; 36° = 10%
• Sector value = (Percentage ÷ 100) × Total
• For ratios, use percentages directly—no need to find actual values
• Difference = (Percentage difference) × Total ÷ 100
• Two pie charts = two separate totals; never mix them
• When angle given: Value = (Angle ÷ 360) × Total

Quadratic Equations — SBI Clerk Prelims Study Notes

Overview

The format is highly standardized: you're given two quadratic equations (one in x, one in y), asked to solve both, and then compare the roots to determine the relationship between x and y.

This topic is a scoring opportunity because the question pattern is predictable and the solving technique is mechanical. Once you master the factorization method and the comparison rules, you can solve each question quickly. The key challenge isn't mathematical difficulty—it's speed and accuracy under time pressure.

Treat this as a "must-score" topic in your Prelims preparation.

Key Concepts

• Standard form: A quadratic equation is ax² + bx + c = 0, where a, b, c are constants and a ≠ 0.
• Two roots: Every quadratic equation yields exactly two roots (which may be equal, distinct, or complex). In bank exams, roots are almost always real integers or simple fractions.
• Sum and product of roots: For x² + bx + c = 0, the sum of roots = −b and the product of roots = c. This helps verify your factorization.
• Factorization method: Split the middle term into two parts whose product equals a×c and whose sum equals b. This is the fastest solving approach for exam questions.
• Comparison logic: After finding roots of both equations, compare all possible pairs. The relationship depends on whether one variable's roots are consistently greater, smaller, or overlap with the other's.
• Five possible answers: The standard options are x > y, x < y, x ≥ y, x ≤ y, or "cannot be determined" (when ranges overlap without a clear relationship).

Formulas / Key Facts

For equation ax² + bx + c = 0:

Sum of roots = −b/a

Product of roots = c/a

Discriminant = b² − 4ac (positive means real distinct roots, zero means equal roots)

Factorization shortcut: Find two numbers whose product = a×c and sum = b, then split the middle term.

Comparison rules (after finding roots x₁, x₂ and y₁, y₂):

• If both x values > both y values → x > y
• If both x values < both y values → x < y
• If both x values ≥ both y values (with at least one equality) → x ≥ y
• If both x values ≤ both y values (with at least one equality) → x ≤ y
• If ranges overlap → Cannot be determined

Sign pattern for factorization:

• If c is positive: both factors have the same sign (determined by sign of b)
• If c is negative: factors have opposite signs

Worked Examples

Example 1: Equation I: x² − 7x + 12 = 0 Equation II: y² − 9y + 20 = 0

Solution: For x² − 7x + 12 = 0: Find two numbers with product = 12 and sum = 7 → 3 and 4 So x² − 3x − 4x + 12 = 0 → x(x−3) − 4(x−3) = 0 → (x−3)(x−4) = 0 x = 3 or x = 4

For y² − 9y + 20 = 0: Find two numbers with product = 20 and sum = 9 → 4 and 5 y = 4 or y = 5

Comparison: x values are {3, 4}, y values are {4, 5} x = 3 < both y values; x = 4 equals one y value Since x values ≤ y values → x ≤ y

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Example 2: Equation I: x² + 5x + 6 = 0 Equation II: y² + 7y + 10 = 0

Solution: For x² + 5x + 6 = 0: Product = 6, sum = 5 → 2 and 3 (x+2)(x+3) = 0 → x = −2 or x = −3

For y² + 7y + 10 = 0: Product = 10, sum = 7 → 2 and 5 (y+2)(y+5) = 0 → y = −2 or y = −5

Comparison: x values are {−2, −3}, y values are {−2, −5} x = −2 equals y = −2; x = −3 > y = −5 but x = −3 < y = −2 Values overlap without consistent relationship → Cannot be determined

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Example 3: Equation I: 2x² − 11x + 15 = 0 Equation II: 2y² − 13y + 21 = 0

Solution: For 2x² − 11x + 15 = 0: Product = 2×15 = 30, sum = 11 → 5 and 6 2x² − 5x − 6x + 15 = 0 → x(2x−5) − 3(2x−5) = 0 → (2x−5)(x−3) = 0 x = 5/2 = 2.5 or x = 3

For 2y² − 13y + 21 = 0: Product = 2×21 = 42, sum = 13 → 6 and 7 2y² − 6y − 7y + 21 = 0 → (2y−7)(y−3) = 0 y = 7/2 = 3.5 or y = 3

Comparison: x values are {2.5, 3}, y values are {3, 3.5} x = 2.5 < both y values; x = 3 equals y = 3 Since all x ≤ all y → x ≤ y

Common Mistakes

• Sign errors with negative coefficients: When b and c are both positive in x² + bx + c = 0, both roots are negative (sum = −b is negative, product = c is positive). Students often forget the negative sign when writing final roots. → Always check: plug roots back to verify sum and product.
• Comparing only one pair of roots: Students find x = 3, y = 4 and conclude x < y, ignoring that x might have another value that's greater than y. → Always compare all four possible pairs (x₁ vs y₁, x₁ vs y₂, x₂ vs y₁, x₂ vs y₂).
• Confusing ≥ with > on boundary cases: When one root of x equals one root of y, but other comparisons are strict, the answer is ≥ or ≤, not > or <. → If there's any equality, use ≥ or ≤; pure inequalities only when no overlap exists.
• Wrong factor split for non-monic equations: For ax² + bx + c where a ≠ 1, students forget to multiply a×c for the product. → In 2x² − 11x + 15, find factors of 30 (not 15) that sum to 11.
• Rushing the "cannot be determined" option: Some students mark this when ranges partially overlap, but if one variable's maximum is still ≤ the other's minimum, a clear relationship exists. → Draw a number line mentally to visualize the ranges.

Quick Reference

• Split middle term: find two numbers with product = a×c and sum = b
• Negative b and positive c → both roots positive
• Positive b and positive c → both roots negative
• Negative c → roots have opposite signs
• Compare all four pairs; consistent inequality → definite answer; overlap → cannot determine
• Equal roots in comparison → use ≥ or ≤, not strict inequality

Profit and Loss

Overview

Profit and Loss is a cornerstone topic in SBI Clerk Prelims Numerical Ability, appearing both as standalone questions and embedded within Data Interpretation sets. The topic tests your ability to quickly calculate buying prices, selling prices, discounts, and profit percentages—skills that mirror real-world commerce scenarios.

The questions are typically straightforward but designed to trap students who confuse the base for percentage calculations. Mastering this topic requires absolute clarity on which value serves as the base (Cost Price for profit/loss, Marked Price for discount) and the ability to perform quick mental calculations with common percentage-fraction equivalents.

Key Concepts

• Cost Price (CP): The price at which an article is purchased or manufactured. This is always the base for calculating profit or loss percentage.
• Selling Price (SP): The price at which an article is sold to a customer. SP > CP means profit; SP < CP means loss.
• Marked Price (MP): The price displayed on the product tag before any discount. Also called List Price or Catalogue Price.
• Discount: Reduction offered on the Marked Price. Discount is always calculated on MP, never on CP.
• Profit/Loss Percentage: Always calculated on Cost Price unless explicitly stated otherwise.
• Successive Discounts: When multiple discounts are applied one after another, each discount applies to the reduced price from the previous discount, not the original MP.
• False Weight Concept: When a trader uses faulty weights, the profit percentage equals [Error/(True Weight − Error)] × 100.

Formulas / Key Facts

Basic Formulas:

• Profit = SP − CP
• Loss = CP − SP
• Profit% = (Profit/CP) × 100
• Loss% = (Loss/CP) × 100
• SP = CP × (100 + Profit%)/100
• SP = CP × (100 − Loss%)/100
• CP = SP × 100/(100 + Profit%)
• CP = SP × 100/(100 − Loss%)

Discount Formulas:

• Discount = MP − SP
• Discount% = (Discount/MP) × 100
• SP = MP × (100 − Discount%)/100

Quick Multipliers:

• 10% profit → SP = 1.1 × CP
• 20% profit → SP = 1.2 × CP
• 25% profit → SP = 1.25 × CP
• 10% loss → SP = 0.9 × CP
• 20% discount → SP = 0.8 × MP

Successive Discounts:

• Two successive discounts of a% and b% give effective discount = a + b − (ab/100)%

Break-even and Special Cases:

• If CP and SP are equal, there is no profit or loss
• When goods worth Rs. X are sold at the CP of goods worth Rs. Y: Profit% = [(Y−X)/X] × 100

Worked Examples

Example 1: Basic Profit Calculation A shopkeeper buys an article for Rs. 400 and sells it at 15% profit. Find the selling price.

Solution: SP = CP × (100 + Profit%)/100 SP = 400 × (115/100) SP = 400 × 1.15 = Rs. 460

Example 2: Finding CP from SP and Profit% An article is sold for Rs. 720 at a profit of 20%. What is the cost price?

Solution: CP = SP × 100/(100 + Profit%) CP = 720 × 100/120 CP = 720 × 5/6 = Rs. 600

Example 3: MP, Discount, and Profit Combined A trader marks his goods 40% above cost price and allows a discount of 20%. Find his profit percentage.

Solution: Let CP = 100 MP = 100 + 40% of 100 = 140 Discount = 20% of 140 = 28 SP = 140 − 28 = 112 Profit = 112 − 100 = 12 Profit% = (12/100) × 100 = 12%

Shortcut Formula: When marked up by m% and discount of d%, Profit% = m − d − (md/100) = 40 − 20 − (40×20/100) = 40 − 20 − 8 = 12%

Example 4: Successive Discounts Find the single equivalent discount for successive discounts of 20% and 10%.

Solution: Effective discount = 20 + 10 − (20×10/100) = 30 − 2 = 28%

Common Mistakes

• Wrong base for percentage calculation → Profit/Loss% is always on CP; Discount% is always on MP. A 20% markup followed by 20% discount does NOT give break-even—it gives a 4% loss.
• Adding successive discounts directly → Two discounts of 10% and 20% do not equal 30%. Apply them successively: effective discount is 28%.
• Confusing "profit on SP" problems → When a question says "profit is 25% of SP" (not CP), use the relation: Profit% on CP = (25/75) × 100 = 33.33%.
• Ignoring the word "each" → If 5 articles are bought for Rs. 100 and 4 are sold for Rs. 100, calculate per-article CP and SP before finding profit%.
• Misreading "sold at loss of" vs "sold at" → "Sold at 20% loss" means SP = 80% of CP. "Sold at loss of Rs. 20" means SP = CP − 20.

Quick Reference

• Profit% = (SP − CP)/CP × 100 — base is always CP
• Discount% = (MP − SP)/MP × 100 — base is always MP
• 25% profit means SP = 1.25 × CP (multiplier = 1.25)
• Successive discounts a%, b%: Net = a + b − ab/100
• Markup m%, Discount d%: Profit% = m − d − md/100
• False weight gain: Profit% = [Error/(True Value − Error)] × 100

Data Interpretation — Study Notes for SBI Clerk Prelims

Overview

Data Interpretation (DI) is an area in the SBI Clerk Prelims Numerical Ability section. The questions test your ability to extract numbers from tables, graphs, or word problems and perform quick calculations.

Mastering DI requires two skills: first, the ability to read visual data accurately; second, speed in arithmetic—percentage changes, ratios, averages, and approximations. Unlike standalone quant questions, DI rewards systematic reading before jumping to calculations.

For SBI Clerk Prelims, expect moderate difficulty. Data sets are straightforward, calculations are manageable, and time pressure is the real challenge. Your goal: solve each DI question in under 60 seconds while maintaining accuracy.

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Key Concepts

• Read the entire data set first. Spend 30–45 seconds understanding headings, units, totals, and relationships before attempting any question.
• Identify what each row/column represents. In tables, rows often represent categories (products, years, persons) while columns represent attributes (quantity, price, percentage).
• Check for totals or pre-calculated values. Many DI sets provide row/column totals—use them to verify your calculations or take shortcuts.
• Approximation is your best friend. In Prelims, answer options are usually well-spaced. Round numbers to the nearest 5 or 10 to save time.
• Convert percentages to fractions mentally. Know that 25% = 1/4, 33.33% = 1/3, 12.5% = 1/8, 16.67% = 1/6 for faster mental math.
• In pie charts, the total is always 100% or 360°. Each slice's value = (Percentage/100) × Total or (Degrees/360) × Total.
• Line graphs show trends. Look for highest, lowest, maximum increase/decrease between consecutive periods.
• Caselets require equation formation. Translate words into mathematical relationships before calculating.

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Formulas / Key Facts

Percentage Calculation Value = (Percentage/100) × Total Percentage = (Part/Whole) × 100

Percentage Change Change % = [(New – Old)/Old] × 100

Ratio Interpretation If A:B = 3:4 and total = 70, then A = (3/7) × 70 = 30

Average from Data Average = Sum of all values / Number of values

Pie Chart Conversions 1% = 3.6 degrees Degrees to Value = (Degrees/360) × Total

Bar Graph Reading Always check Y-axis scale and starting point (beware of graphs not starting at zero)

Approximation Rules

• Round 247 to 250, 493 to 500
• For division, round both numerator and denominator in the same direction for better accuracy

Quick Percentage Equivalents 10% = 1/10, 20% = 1/5, 25% = 1/4, 50% = 1/2, 75% = 3/4, 33.33% = 1/3, 66.67% = 2/3

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Worked Examples

Example 1: Table DI

Data: Production of cars (in thousands) by Company X

Question: What is the percentage increase in production from 2018 to 2022?

Solution: Increase = 400 – 240 = 160 thousand Percentage increase = (160/240) × 100 = (2/3) × 100 = 66.67%

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Example 2: Pie Chart DI

Data: Distribution of 6000 employees across departments HR = 15%, Finance = 20%, IT = 30%, Operations = 25%, Admin = 10%

Question: How many employees work in IT and Finance together?

Solution: IT + Finance = 30% + 20% = 50% Employees = 50% of 6000 = 3000

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Example 3: Caselet DI

Data: A company sold three products A, B, and C. Product A contributed 40% of total sales. Product B's sales were Rs 24,000, which was 30% of total sales.

Question: What were the sales of Product C?

Solution: If 30% = Rs 24,000 Then 100% = 24000 × (100/30) = Rs 80,000 Product C = 100% – 40% – 30% = 30% Sales of C = 30% of 80,000 = Rs 24,000

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Example 4: Bar Graph – Finding Maximum Increase

Data: Profits (in lakhs) — 2018: 40, 2019: 55, 2020: 50, 2021: 75, 2022: 70

Question: Between which two consecutive years was the increase in profit maximum?

Solution: 2018-19: 55 – 40 = 15 2019-20: 50 – 55 = –5 (decrease) 2020-21: 75 – 50 = 25 ← Maximum 2021-22: 70 – 75 = –5 (decrease)

Answer: 2020 to 2021

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Common Mistakes

Wrong: Reading the wrong row/column under time pressure. → Correct fix: Use your finger or pen to trace the exact intersection. Double-check the label before noting the number.

Wrong: Forgetting units or scale (e.g., "in thousands" or "in lakhs"). → Correct fix: Circle or underline the unit mentioned in the title. Apply it consistently to all answers.

Wrong: Calculating exact values when approximation would suffice. → Correct fix: Glance at answer options first. If they're spread apart (e.g., 34%, 52%, 67%), round aggressively.

Wrong: In percentage change, using the new value as the base instead of the old value. → Correct fix: Always use the OLD/ORIGINAL value as the denominator: (New – Old)/Old.

Wrong: In pie charts, adding degrees directly without converting to values. → Correct fix: First convert each sector to actual values using (Degrees/360) × Total, then perform operations.

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Quick Reference

• DI = Data Reading + Arithmetic Speed — practice both separately.
• Percentage change base = OLD value, not new.
• Pie chart: 1% = 3.6°; always convert to actual values before comparing.
• Approximation saves time — use it.
• Read headings, units, and footnotes BEFORE calculating anything.
• For caselets, write down relationships as equations first; calculate second.

Line Graph DI — Study Notes for SBI Clerk Prelims

Overview

Line Graph Data Interpretation is a part of the SBI Clerk Prelims Numerical Ability section.

What makes line graphs distinct from bar or pie charts is their emphasis on trends and changes. While bar graphs show static comparisons, line graphs test your ability to spot increases, decreases, turning points, and rate of change. Questions often ask about the year with maximum growth, the average across periods, or percentage change between two data points.

Mastering line graph DI requires two skills: (1) accurate data reading from the graph, and (2) quick arithmetic involving percentages, averages, and ratios. Since Prelims has strict time pressure — roughly 34 seconds per question (35 Numerical Ability questions in 20 minutes) — you must develop the habit of approximating rather than calculating exact values unless the options are close.

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Key Concepts

• Data Points and Axes: The x-axis usually represents time (years, months, quarters), while the y-axis shows the measured quantity (sales, production, population). Each point on the line corresponds to a specific value at a specific time.
• Trend Identification: An upward-sloping segment means increase; downward means decrease. A flat segment indicates no change. Steeper slopes mean faster change.
• Multiple Lines: When two or more lines appear on the same graph, they compare different entities (Company A vs Company B) or different categories (Imports vs Exports). Always check the legend.
• Reading Values: Values often fall between gridlines. Estimate carefully — if a point appears midway between 40 and 50, read it as approximately 45.
• Percentage Change Formula: Change = [(New Value − Old Value) / Old Value] × 100. Positive result means increase; negative means decrease.
• Average Calculation: Sum of all values divided by the number of data points. For line graphs, this typically means adding values across all years and dividing by the number of years.
• Ratio Comparison: When asked about the ratio of one entity to another in a specific year, simply divide the two values read from that year.

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Formulas / Key Facts

Percentage Change = [(Final Value − Initial Value) / Initial Value] × 100

Percentage Increase = (Increase / Original) × 100

Percentage Decrease = (Decrease / Original) × 100

Average = Sum of all values / Number of values

Ratio = Value of A : Value of B (simplify to lowest terms)

Difference = Higher Value − Lower Value

Rate of Change (for comparison) = Absolute change per unit time; steeper line = higher rate

Quick Percentage Benchmarks

• 10% = divide by 10
• 25% = divide by 4
• 33.33% = divide by 3
• 50% = divide by 2
• 20% = divide by 5

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Worked Examples

Example Graph Data (Production in thousand units):

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Q1: What is the percentage increase in Company X's production from 2018 to 2022?

Step 1: Initial value (2018) = 40, Final value (2022) = 75 Step 2: Increase = 75 − 40 = 35 Step 3: Percentage increase = (35 / 40) × 100 = 87.5%

Answer: 87.5%

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Q2: In which year was the difference between Company X and Company Y's production maximum?

Calculate differences:

• 2018: 40 − 30 = 10
• 2019: 50 − 45 = 5
• 2020: 50 − 45 = 5 (Y is higher, but we take absolute difference)
• 2021: 60 − 55 = 5
• 2022: 75 − 60 = 15

Answer: 2022 (difference = 15 thousand units)

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Q3: What is the average production of Company Y over all five years?

Step 1: Sum = 30 + 45 + 50 + 55 + 60 = 240 Step 2: Average = 240 / 5 = 48 thousand units

Answer: 48 thousand units

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Common Mistakes

Mistake 1: Using wrong base for percentage change Wrong thinking: Calculating percentage change from 2018 to 2019 as (50−40)/50 × 100 Correct fix: Always use the initial (earlier) value as the base — (50−40)/40 × 100 = 25%

Mistake 2: Misreading values between gridlines Wrong thinking: Assuming a point exactly on a gridline when it's actually between two lines Correct fix: Look carefully at the position; if between 40 and 50, estimate precisely (42, 45, 48, etc.)

Mistake 3: Confusing absolute change with percentage change Wrong thinking: Saying "Company X grew more because it increased by 35" when Company Y grew from 30 to 60 (increase of 30) Correct fix: Compare percentage growth rates — X grew 87.5%, Y grew 100%

Mistake 4: Ignoring the legend in multi-line graphs Wrong thinking: Reading the wrong line for the wrong company Correct fix: Always verify which line (solid, dashed, colored) represents which entity before answering

Mistake 5: Calculating average using only some years Wrong thinking: Including only extreme values or missing a year Correct fix: Count the data points carefully; for 2018–2022, there are 5 years, not 4

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Quick Reference

• Percentage change base is always the original/initial value.
• Steeper line segment = faster rate of increase or decrease.
• For "maximum difference" questions, calculate all differences first; don't trust visual estimation alone.
• Average = Total sum ÷ Number of data points — count years carefully.
• In multi-line graphs, read the legend before touching any question.
• When options are spread apart, approximate aggressively; when close, calculate precisely.

Arithmetic – Study Notes for SBI Clerk Prelims

Overview

Arithmetic forms the backbone of the Numerical Ability section in SBI Clerk Prelims. These questions test your ability to apply basic mathematical concepts quickly—speed matters more than complexity at the Clerk level.

The good news: SBI Clerk Prelims arithmetic stays at a moderate difficulty level. Questions are direct applications of formulas with 1–2 step calculations. If you master the core formulas and practice mental math shortcuts, you can solve most arithmetic questions quickly. This section rewards preparation.

Focus areas in order of importance: Percentage, Ratio & Proportion, Profit & Loss, Simple & Compound Interest, Time & Work, and Time-Speed-Distance.

Key Concepts

• Percentage is the foundation: Almost every arithmetic topic—profit/loss, interest, ratio changes—ultimately converts to percentage calculations. Master percentage first.
• Ratio thinking beats equation solving: Instead of setting up algebraic equations, think in terms of "parts" and "multipliers." A 3:5 ratio means 8 total parts—this mental model speeds up calculations.
• Work and Time are inversely proportional: If A is twice as efficient as B, A takes half the time. This inverse relationship applies to pipes/cisterns too.
• SI grows linearly, CI grows exponentially: Simple Interest adds the same amount each year. Compound Interest adds increasing amounts because interest earns interest.
• CP-SP-MP form a triangle: Cost Price → add profit margin → Selling Price. Marked Price → subtract discount → Selling Price. Most problems ask you to navigate this triangle.
• Relative speed determines meeting/crossing problems: Same direction = subtract speeds. Opposite direction = add speeds. This single rule covers trains, boats, and all motion problems.
• Mixture problems are weighted averages: Alligation is just a shortcut for finding the ratio in which two quantities at different values must be mixed to get a target value.
• Age problems create linear equations: The key insight—age differences stay constant. If A is 5 years older than B today, A will always be 5 years older.

Formulas / Key Facts

Percentage

• x% of y = y% of x = (xy)/100
• Percentage change = (Change / Original) × 100
• If a value increases by R%, new value = Original × (1 + R/100)
• Successive % changes: Net effect ≠ sum of percentages. Use: a + b + (ab/100)

Ratio and Proportion

• If a:b = c:d, then ad = bc (cross multiplication)
• Componendo: (a+b)/b = (c+d)/d
• If ratio is a:b and total is T, parts are aT/(a+b) and bT/(a+b)

Profit and Loss

• Profit% = (Profit/CP) × 100
• SP = CP × (100 + Profit%)/100
• Discount% = (Discount/MP) × 100
• SP = MP × (100 − Discount%)/100

Simple Interest

• SI = (P × R × T)/100
• Amount = P + SI

Compound Interest

• Amount = P × (1 + R/100)^T
• CI = Amount − P
• For 2 years: CI − SI = P × (R/100)²

Time and Work

• If A does work in 'a' days, A's 1 day work = 1/a
• Combined work: 1/a + 1/b = 1/T (T = time together)
• Efficiency ratio = Inverse of time ratio

Time, Speed and Distance

• Distance = Speed × Time
• Average speed (same distance) = 2ab/(a+b) where a, b are speeds
• Relative speed: Same direction = |a−b|, Opposite = a+b

Mixture and Alligation

• Alligation rule: Ratio = (Higher value − Mean) : (Mean − Lower value)

Partnership

• Profit share ∝ Capital × Time

Problems on Ages

• Present age problems: Let present ages be x and y, form equations from given conditions

Worked Examples

Example 1: Profit and Loss A shopkeeper marks goods 25% above CP and gives 10% discount. Find profit%.

Solution: Let CP = 100 MP = 100 + 25% of 100 = 125 Discount = 10% of 125 = 12.5 SP = 125 − 12.5 = 112.5 Profit = 112.5 − 100 = 12.5 Profit% = (12.5/100) × 100 = 12.5%

Example 2: Time and Work A can complete work in 12 days, B in 18 days. They work together for 4 days, then A leaves. How many more days will B take to finish?

Solution: A's 1 day work = 1/12, B's 1 day work = 1/18 Together in 1 day = 1/12 + 1/18 = 5/36 Work done in 4 days = 4 × 5/36 = 20/36 = 5/9 Remaining work = 1 − 5/9 = 4/9 Days for B to finish = (4/9) ÷ (1/18) = (4/9) × 18 = 8 days

Example 3: SI vs CI Find the difference between CI and SI on Rs 8000 at 5% for 2 years.

Solution: CI − SI for 2 years = P × (R/100)² = 8000 × (5/100)² = 8000 × 1/400 = Rs 20

Common Mistakes

• Adding successive percentages directly → Wrong: 10% increase then 20% increase ≠ 30% increase. Correct: Use formula a + b + ab/100 = 10 + 20 + 200/100 = 32%.
• Calculating profit% on SP instead of CP → Wrong thinking: "I sold for 120 and made 20 profit, so profit% = 20/120." Correct: Always calculate profit% on CP, so it's 20/100 = 20%.
• Confusing time taken with work done → Wrong: If A is twice as fast, A takes twice the time. Correct: A takes half the time (inverse relationship).
• Using wrong base for discount → Wrong: Discount% calculated on CP. Correct: Discount is always calculated on Marked Price.
• Forgetting units in speed problems → Mixing km/hr and m/s without conversion. Correct: km/hr × 5/18 = m/s.

Quick Reference

• Successive % changes: Net = a + b + (ab/100)
• Profit% = (SP − CP)/CP × 100; Discount% = (MP − SP)/MP × 100
• CI − SI for 2 years = P(R/100)²
• Combined work rate = Sum of individual rates
• Average speed for equal distances = 2ab/(a+b)
• Alligation ratio = (Expensive − Mean) : (Mean − Cheap)

Simple and Compound Interest

Overview

These questions test your ability to calculate interest earned on principal amounts over specified time periods, with the key distinction being whether interest is calculated only on the original principal (SI) or on the accumulated amount (CI).

For SBI Clerk level, expect direct formula application problems, comparison questions between SI and CI, and occasional questions involving half-yearly or quarterly compounding. Mastering the formulas and shortcuts is essential for quick solving.

This topic connects directly with Percentage (interest rates are percentages), Ratio and Proportion (comparing amounts), and occasionally appears in Data Interpretation sets. A solid grip here also helps in banking awareness contexts where loan and deposit calculations matter.

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Key Concepts

• Simple Interest (SI) accrues only on the original principal. The interest remains constant each year regardless of previously accumulated interest.
• Compound Interest (CI) accrues on principal plus accumulated interest. Each successive year's interest is calculated on a growing base, making CI always greater than SI for the same principal, rate, and time (when time > 1 year).
• The CI-SI difference for 2 years equals the interest on first year's interest, which gives us a powerful shortcut: CI - SI (for 2 years) = P × (R/100)².
• Compounding frequency affects the effective interest. Half-yearly compounding means rate is halved and time is doubled in periods. Quarterly means rate ÷ 4 and time × 4.
• Amount (A) is the total sum received back: A = P + Interest. In CI problems, this grows exponentially; in SI, it grows linearly.
• At equal rates, the ratio of CI to SI for 2 years is (200 + R) : 200, a quick comparison tool.
• When time = 1 year with annual compounding, SI = CI. The difference emerges only from year 2 onwards.

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Formulas / Key Facts

Simple Interest:

• SI = (P × R × T) / 100
• Amount = P + SI = P(1 + RT/100)

Compound Interest:

• Amount = P × (1 + R/100)^T
• CI = Amount - P = P[(1 + R/100)^T - 1]

2-Year Shortcuts (Most useful for Clerk):

• CI for 2 years = P × (1 + R/100)² - P
• SI for 2 years = 2PR/100
• CI - SI for 2 years = P × (R/100)² = PR²/10000

3-Year Shortcut:

• CI - SI for 3 years = PR²(300 + R) / 1000000

Half-Yearly Compounding:

• Amount = P × (1 + R/200)^(2T)

Quarterly Compounding:

• Amount = P × (1 + R/400)^(4T)

Useful Multipliers (memorize these):

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Worked Examples

Example 1: Basic SI Calculation

Find the simple interest on Rs 8,000 at 12% per annum for 3 years.

Step 1: Apply SI formula SI = (P × R × T) / 100 SI = (8000 × 12 × 3) / 100

Step 2: Calculate SI = 288000 / 100 = Rs 2,880

Answer: Rs 2,880

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Example 2: CI-SI Difference (2 Years)

The difference between CI and SI on a sum at 10% per annum for 2 years is Rs 50. Find the principal.

Step 1: Use the shortcut formula CI - SI (2 years) = P × (R/100)² 50 = P × (10/100)² 50 = P × (1/100) 50 = P/100

Step 2: Solve for P P = 50 × 100 = Rs 5,000

Answer: Rs 5,000

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Example 3: Half-Yearly Compounding

Find the compound interest on Rs 16,000 at 20% per annum for 1 year, compounded half-yearly.

Step 1: Adjust rate and time for half-yearly Rate per half-year = 20/2 = 10% Number of periods = 1 × 2 = 2

Step 2: Calculate Amount A = P × (1 + R/100)^n A = 16000 × (1.10)² A = 16000 × 1.21 = Rs 19,360

Step 3: Find CI CI = A - P = 19360 - 16000 = Rs 3,360

Answer: Rs 3,360

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Common Mistakes

• Using CI formula for SI problems → Always identify whether interest compounds or not. "Per annum" alone means SI unless "compounded" is specified.
• Forgetting to adjust both rate AND time for half-yearly/quarterly → If compounded half-yearly for 2 years at 10%, use 5% rate for 4 periods, not 10% for 4 periods.
• Confusing Amount with Interest → Amount = Principal + Interest. If asked for CI, don't report the Amount. Subtract P from A.
• Applying 2-year CI-SI shortcut to 3-year problems → The formula PR²/10000 works only for 2 years. For 3 years, use the separate formula or calculate directly.
• Calculation errors with decimals → When multiplying (1.10)² or (1.05)³, memorize common values or work step-by-step to avoid errors under pressure.

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Quick Reference

• SI = PTR/100 | CI = P[(1 + R/100)^T - 1]
• CI - SI (2 years) = PR²/10000
• Half-yearly: Rate ÷ 2, Time × 2
• 10% for 2 years → Multiplier = 1.21
• Amount = Principal + Interest (don't confuse the two)
• SI = CI when T = 1 year (annual compounding)

Caselet DI

Overview

Caselet DI (Data Interpretation) presents numerical data embedded within a paragraph of text rather than in tables, charts, or graphs. You must extract the data, organize it mentally (or on rough paper), and then answer questions based on that information. This format tests both reading comprehension and calculation skills simultaneously.

The difficulty is moderate—data relationships are straightforward, but the absence of visual aids means careless reading leads to errors. Mastering Caselet DI requires a systematic approach: read once for structure, read again for numbers, build your own mini-table, then solve.

The key skill is patience—rushing through the paragraph causes missed conditions and wrong answers.

Key Concepts

• Data Extraction: The paragraph contains all numerical relationships. Identify entities (people, items, years) and their attributes (amounts, percentages, ratios).
• Implicit vs. Explicit Data: Some values are stated directly ("A has 240 apples"), others require calculation ("B has 20% more than A").
• Base Value Identification: Many caselets build all data around one anchor value. Find this base first—everything else follows.
• Percentage and Ratio Chains: Data often links through "X is 25% less than Y, Y is in ratio 3:4 with Z." Track these chains carefully.
• Total and Part Relationships: If given parts, you may need the total. If given total and some parts, find the remaining part.
• Conditional Statements: Watch for words like "remaining," "rest," "after giving," "out of which"—these signal derived quantities.
• Unit Consistency: Ensure all values are in the same unit before comparing or calculating.

Formulas / Key Facts

Percentage Increase: New Value = Original × (1 + P/100)

Percentage Decrease: New Value = Original × (1 – P/100)

Finding Original from Increased Value: Original = Increased Value / (1 + P/100)

Finding Original from Decreased Value: Original = Decreased Value / (1 – P/100)

Ratio to Actual: If A:B = 3:4 and total = 700, then A = (3/7) × 700

Successive Percentage: For two changes of a% and b%, net effect = a + b + (ab/100)

Fraction-Percentage Equivalents:

• 1/4 = 25%, 1/5 = 20%, 1/6 = 16.67%, 1/8 = 12.5%
• 2/5 = 40%, 3/4 = 75%, 5/6 = 83.33%

"More than" vs. "Of": "A is 25% more than B" means A = 1.25B. "A is 25% of B" means A = 0.25B.

Worked Examples

Example 1: Basic Caselet

Paragraph: A company has three departments—HR, Finance, and IT. HR has 120 employees. Finance has 25% more employees than HR. IT has 20% fewer employees than Finance. Find the total employees.

Solution:

• HR = 120
• Finance = 120 × 1.25 = 150
• IT = 150 × 0.80 = 120
• Total = 120 + 150 + 120 = 390 employees

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Example 2: Ratio-Based Caselet

Paragraph: Three friends A, B, and C have savings in the ratio 2:3:5. C has Rs. 4000 more than A. B spends 40% of his savings. Find how much B has left.

Solution:

• Let savings be 2x, 3x, and 5x
• C – A = 5x – 2x = 3x = 4000
• So x = 4000/3 ≈ 1333.33
• B's savings = 3x = 4000
• B spends 40%, keeps 60%
• B has left = 4000 × 0.60 = Rs. 2400

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Example 3: Multi-Step Caselet

Paragraph: A shop sold 600 items in three categories—Electronics, Clothing, and Books. Electronics formed 35% of total sales. Clothing sales were 2/3 of Electronics sales. The rest were Books. If profit on Electronics is 20%, Clothing is 15%, and Books is 25%, and each Electronics item costs Rs. 500, each Clothing item costs Rs. 300, and each Book costs Rs. 100, find total profit.

Solution: Step 1: Find quantities

• Electronics = 35% of 600 = 210
• Clothing = (2/3) × 210 = 140
• Books = 600 – 210 – 140 = 250

Step 2: Find total cost price

• Electronics CP = 210 × 500 = Rs. 105000
• Clothing CP = 140 × 300 = Rs. 42000
• Books CP = 250 × 100 = Rs. 25000

Step 3: Find profit

• Electronics profit = 20% of 105000 = Rs. 21000
• Clothing profit = 15% of 42000 = Rs. 6300
• Books profit = 25% of 25000 = Rs. 6250
• Total profit = Rs. 33550

Common Mistakes

Mistake: Applying percentage on wrong base. → Fix: "A is 20% more than B" means calculate 20% of B, not of A. Always identify which value is the base.

Mistake: Confusing "more than" with "of." → Fix: "20% more than 100" = 120. "20% of 100" = 20. Read the phrasing precisely.

Mistake: Forgetting to account for "remaining" or "rest." → Fix: When told "the rest are X," calculate: Rest = Total – Sum of stated parts.

Mistake: Not creating a rough table. → Fix: Always jot down entities in rows, attributes in columns. This prevents re-reading the paragraph repeatedly.

Mistake: Calculation errors under time pressure. → Fix: Use approximation for verification. If Finance = 25% more than 120, it should be between 120 and 180. Quick sanity checks catch errors.

Mistake: Misreading ratio direction. → Fix: "Ratio of A to B is 3:4" means A = 3 parts, B = 4 parts. Don't swap them.

Quick Reference

• Read the caselet twice: first for structure, second for numbers.
• Build a mini-table on rough paper before attempting any question.
• Identify the anchor/base value—most other data derives from it.
• "X% more than Y" → value = Y × (1 + X/100); "X% of Y" → value = Y × (X/100).
• Check units and ensure all calculations use consistent values.
• Verify answers with quick mental approximation—catch silly errors before moving on.

Time and Work

Overview

The core concept is simple: work is measured by how much a person or machine completes per unit time (efficiency), and total work equals efficiency multiplied by time.

This topic connects directly with Pipes and Cisterns (filling/emptying tanks) and often combines with Ratio and Proportion. Mastering the efficiency method—where you assume total work as the LCM of given days—drastically speeds up calculations.

Students who build strong mental math around LCM and fraction addition will find these questions among the easiest marks in the Numerical Ability section.

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Key Concepts

• Efficiency = Work done per day. If A completes a job in 10 days, A's efficiency = 1/10 of the work per day.
• Total Work = Efficiency × Time. When using the LCM method, total work becomes a concrete number (like 60 units), making calculations cleaner.
• Combined Work: When A and B work together, their efficiencies add up. If A does 1/10 and B does 1/15 per day, together they do 1/10 + 1/15 = 1/6 per day.
• LCM Method: Assume total work = LCM of all given days. This converts fractions to whole-number efficiencies, eliminating fraction arithmetic.
• Negative Efficiency: When someone destroys work or a pipe empties a tank, treat their efficiency as negative.
• Work Equivalence: Man-days (or person-days) measure total work. 10 men working 5 days = 50 man-days of work.
• Alternating Work: When A and B work on alternate days, calculate work done in a 2-day cycle and find how many complete cycles fit.

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Formulas / Key Facts

Basic Formula

• Time = Total Work / Efficiency
• Efficiency = Total Work / Time
• Work = Efficiency × Time

Combined Work

• If A takes 'a' days and B takes 'b' days alone:
  • Together: Time = (a × b) / (a + b) days

LCM Method Setup

• Total Work = LCM(days of A, days of B, ...)
• Efficiency of A = Total Work / Days of A

Man-Days Formula

• M₁ × D₁ × H₁ = M₂ × D₂ × H₂ (for same work)
• M₁ × D₁ × H₁ / W₁ = M₂ × D₂ × H₂ / W₂ (for different work amounts)

Wages Distribution

• Wages are distributed in the ratio of work done (i.e., ratio of efficiencies × days worked)

Pipes and Cisterns

• Filling pipe = positive efficiency
• Emptying pipe/leak = negative efficiency
• Net efficiency = Sum of all efficiencies (with signs)

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Worked Examples

Example 1: Basic Combined Work

A can do a work in 12 days, B can do it in 18 days. In how many days will they finish working together?

LCM Method:

• Total Work = LCM(12, 18) = 36 units
• A's efficiency = 36/12 = 3 units/day
• B's efficiency = 36/18 = 2 units/day
• Combined efficiency = 3 + 2 = 5 units/day
• Time = 36/5 = 7.2 days = 7⅕ days (or 36/5 days)

Formula Method:

• Time = (12 × 18)/(12 + 18) = 216/30 = 7.2 days ✓

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Example 2: Work Left After Partial Contribution

A can complete a work in 20 days. He works for 8 days and leaves. B finishes the remaining work in 9 days. How long would B take alone?

• Work done by A in 8 days = 8/20 = 2/5
• Remaining work = 1 - 2/5 = 3/5
• B completes 3/5 work in 9 days
• B's rate = (3/5)/9 = 3/45 = 1/15 per day
• B alone takes 15 days

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Example 3: Alternating Work

A can do a work in 10 days, B in 15 days. They work on alternate days starting with A. In how many days will the work be completed?

• Total Work = LCM(10, 15) = 30 units
• A's efficiency = 3 units/day
• B's efficiency = 2 units/day
• Work in 2-day cycle (A then B) = 3 + 2 = 5 units
• Complete cycles needed = 30/5 = 6 cycles = 12 days

Since 6 complete cycles finish exactly 30 units, work completes in 12 days.

Note: If work didn't divide evenly, check who works on the final day and calculate partial day.

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Common Mistakes

Wrong: Adding times instead of efficiencies → Correct: If A takes 10 days and B takes 15 days, together they DON'T take 25 days or 12.5 days. Add rates: 1/10 + 1/15 = 5/30 = 1/6, so 6 days together.

Wrong: Forgetting to subtract when someone leaves or destroys work → Correct: If A works for some days and leaves, first calculate work done, then find remaining work. For pipes/leaks, subtract the leak's rate.

Wrong: Using wrong LCM leading to calculation errors → Correct: Double-check LCM before proceeding. LCM(12, 18) = 36, not 72 or 24.

Wrong: In alternating work, assuming work divides exactly into cycles → Correct: Always verify. If total work is 28 units, 5 cycles of 5 units each leave 3 units, so the 6th cycle may end mid-way.

Wrong: Distributing wages by time worked instead of work done → Correct: Wages ∝ (Efficiency × Days worked). If A is twice as efficient and works same days, A gets double the share.

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Quick Reference

• LCM method: Total work = LCM of days; Efficiency = Total work ÷ Days
• Together formula: Time = (a × b)/(a + b) days
• Man-days constant: M₁D₁ = M₂D₂ for same work
• Efficiency adds when working together, subtracts for leaks/destroyers
• Wages ratio = Work done ratio = Efficiency × Time ratio
• Alternating work: Find 2-day cycle work, then count complete cycles + remainder

Permutation and Combination

Overview

Permutation and Combination forms the foundation of counting problems in competitive exams.

The core distinction is simple: Permutation counts arrangements where order matters (who stands first vs second), while Combination counts selections where order doesn't matter (choosing 3 people from 5).

Students who grasp the fundamental formulas and practice recognizing whether a problem needs "arrangement" or "selection" can quickly secure these marks. The calculations involved are straightforward once you identify the correct approach.

Key Concepts

• Fundamental Counting Principle: If task A can be done in 'm' ways and task B in 'n' ways, both tasks together can be done in m × n ways (for AND) or m + n ways (for OR).
• Factorial (n!): Product of all positive integers from 1 to n. Example: 5! = 5 × 4 × 3 × 2 × 1 = 120. Special case: 0! = 1.
• Permutation (nPr): Number of ways to arrange 'r' items from 'n' distinct items. Order matters—ABC is different from BAC.
• Combination (nCr): Number of ways to select 'r' items from 'n' distinct items. Order doesn't matter—selecting A, B, C is same as selecting B, C, A.
• Key relationship: nPr = nCr × r! (Every combination can be arranged in r! ways to get permutations).
• Complementary property: nCr = nC(n-r). Choosing 3 items from 10 equals choosing 7 items to leave out.
• Repeated items in permutation: When arranging n items where some are identical, divide by factorials of repeated counts.

Formulas / Key Facts

Permutation formula: nPr = n! / (n-r)!

Combination formula: nCr = n! / [r! × (n-r)!]

Permutation with repetition allowed: n^r (each of r positions can be filled in n ways)

Arrangement of n items with repetitions: n! / (p! × q! × r!...) where p, q, r are counts of identical items

Quick values to memorize:

• 5! = 120
• 6! = 720
• 7! = 5040
• 5C2 = 10
• 6C2 = 15
• 6C3 = 20
• 10C2 = 45
• 10C3 = 120

Selection with "at least one" condition: Total selections − selections with none = selections with at least one

Worked Examples

Example 1: Basic Permutation How many 3-digit numbers can be formed using digits 1, 2, 3, 4, 5 without repetition?

Step 1: We need to fill 3 positions using 5 digits, and order matters (123 ≠ 321). Step 2: This is permutation: 5P3 = 5!/(5-3)! = 5!/2! = 120/2 = 60

Answer: 60

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Example 2: Basic Combination In how many ways can a committee of 3 members be formed from 8 people?

Step 1: We're selecting 3 from 8. Order doesn't matter (selecting A, B, C same as B, A, C). Step 2: This is combination: 8C3 = 8!/(3! × 5!) Step 3: = (8 × 7 × 6)/(3 × 2 × 1) = 336/6 = 56

Answer: 56

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Example 3: Arrangement with Repeated Letters How many different words can be formed using all letters of "BANANA"?

Step 1: Total letters = 6 (B=1, A=3, N=2) Step 2: If all were distinct: 6! arrangements Step 3: Divide by repetitions: 6!/(3! × 2! × 1!) = 720/(6 × 2 × 1) = 720/12 = 60

Answer: 60

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Example 4: Selection with Conditions From 5 men and 4 women, a committee of 4 is to be formed with at least 2 women. How many ways?

Step 1: "At least 2 women" means 2W+2M or 3W+1M or 4W+0M Step 2: Case 1 (2W, 2M): 4C2 × 5C2 = 6 × 10 = 60 Step 3: Case 2 (3W, 1M): 4C3 × 5C1 = 4 × 5 = 20 Step 4: Case 3 (4W, 0M): 4C4 × 5C0 = 1 × 1 = 1 Step 5: Total = 60 + 20 + 1 = 81

Answer: 81

Common Mistakes

Wrong: Using permutation when combination is needed. Fix: Ask yourself—does rearranging the same items create a different outcome? If selecting people for a committee, order doesn't matter (use nCr). If arranging people in a line, order matters (use nPr).

Wrong: Forgetting to account for repeated elements when calculating arrangements. Fix: When letters/digits repeat, always divide total factorial by the factorial of each repeated element's count.

Wrong: Calculating nCr by expanding full factorials. Fix: Use shortcut: for 10C3, write (10 × 9 × 8)/(3 × 2 × 1). Take only 'r' terms in numerator starting from n.

Wrong: Adding cases when you should multiply (or vice versa). Fix: "AND" situations = multiply. "OR" situations = add. Forming a committee needs member 1 AND member 2 (multiply). Having 2 women OR 3 women means either works (add).

Wrong: Double-counting in problems with restrictions. Fix: When items must be together, treat them as a single unit first, then arrange within the unit.

Quick Reference

• Order matters → Permutation (nPr); Order doesn't matter → Combination (nCr)
• nPr = n!/(n-r)! and nCr = n!/[r!(n-r)!]
• Repeated letters: Divide n! by factorial of each repetition count
• nCr = nC(n-r) — use smaller value for faster calculation
• At least one = Total − None
• AND = Multiply, OR = Add

Time, Speed and Distance

Overview

Time, Speed and Distance (TSD) is an arithmetic topic in SBI Clerk Prelims, appearing both as standalone questions and within Data Interpretation sets. The core relationship is deceptively simple—Distance = Speed × Time—but examiners test your ability to apply this formula across varied scenarios: relative motion, unit conversions, and special cases like trains and boats.

Mastery here offers quick marks since these problems follow predictable patterns. The key is building speed through formula recall and recognizing problem types instantly.

Focus on unit conversion (km/hr to m/s and vice versa), relative speed concepts, and the standard boat-stream formulas.

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Key Concepts

• Fundamental relationship: Distance = Speed × Time. Rearrange as needed: Speed = Distance/Time, Time = Distance/Speed.
• Unit conversion is non-negotiable: Most train problems give speed in km/hr but lengths in meters.
• Relative speed determines time in motion problems: When two objects move, what matters is how fast the gap between them changes, not their individual speeds.
• Same direction = subtract speeds; Opposite direction = add speeds: This applies to trains crossing each other and any two-body motion problem.
• Train crosses an object by covering (Train length + Object length): The "distance" in train problems is always the total length the train must travel for complete crossing.
• Still water speed vs. current speed: A boat has an inherent speed in still water. The stream either aids (downstream) or opposes (upstream) this speed.
• Average speed ≠ arithmetic mean of speeds: When covering equal distances at different speeds, use the harmonic mean formula, not simple averaging.

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Formulas / Key Facts

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Worked Examples

Example 1: Basic Train Crossing a Platform

Problem: A train 150 m long crosses a 250 m platform in 20 seconds. Find its speed in km/hr.

Solution:

• Total distance covered = Train length + Platform length = 150 + 250 = 400 m
• Time = 20 seconds
• Speed = 400/20 = 20 m/s
• Convert to km/hr = 20 × 18/5 = 72 km/hr

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Example 2: Two Trains Crossing Each Other

Problem: Two trains of lengths 120 m and 180 m are running in opposite directions at 54 km/hr and 36 km/hr. How long will they take to cross each other completely?

Solution:

• Total distance = 120 + 180 = 300 m
• Relative speed (opposite direction) = 54 + 36 = 90 km/hr
• Convert to m/s = 90 × 5/18 = 25 m/s
• Time = 300/25 = 12 seconds

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Example 3: Boats and Streams

Problem: A boat covers 24 km upstream in 4 hours and 36 km downstream in 3 hours. Find the speed of the boat in still water and the speed of the stream.

Solution:

• Upstream speed = 24/4 = 6 km/hr
• Downstream speed = 36/3 = 12 km/hr
• Speed in still water = (12 + 6)/2 = 9 km/hr
• Speed of stream = (12 − 6)/2 = 3 km/hr

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Example 4: Average Speed

Problem: A person travels from A to B at 40 km/hr and returns at 60 km/hr. Find the average speed for the entire journey.

Solution:

• Since distances are equal, use harmonic mean
• Average speed = 2 × 40 × 60 / (40 + 60) = 4800/100 = 48 km/hr
• Note: Simple average would give 50 km/hr—this is wrong!

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Common Mistakes

• Forgetting to add train length in platform problems → The train hasn't "crossed" until its tail clears the platform. Always add both lengths.
• Using km/hr directly with meter-based lengths → You'll get nonsense answers. Convert speed to m/s first when lengths are in meters.
• Adding speeds when trains move in the same direction → Same direction means the faster train slowly overtakes. Subtract speeds to get relative speed.
• Confusing upstream and downstream formulas → Remember: downstream = going with the flow = faster = add. Upstream = against = slower = subtract.
• Calculating average speed as (S₁ + S₂)/2 → This only works when time spent at each speed is equal, not when distance is equal. For equal distances, always use 2S₁S₂/(S₁ + S₂).
• Ignoring the direction of current in round-trip problems → A boat going upstream and returning covers the same distance but at different speeds—you need both calculations.

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Quick Reference

• D = S × T — the foundation of every problem
• km/hr → m/s: × 5/18 | m/s → km/hr: × 18/5
• Opposite direction: ADD speeds | Same direction: SUBTRACT speeds
• Train crossing anything = (Train length + Object length) / Speed
• Still water speed = (Down + Up) / 2 | Stream speed = (Down − Up) / 2
• Average speed for equal distances = 2ab/(a+b), never (a+b)/2

Probability — SBI Clerk Prelims Study Notes

Overview

Probability measures how likely an event is to occur, expressed as a number between 0 (impossible) and 1 (certain). Questions are calculation-light but concept-dependent; a clear understanding of basic definitions gets you quick marks.

This topic connects naturally with Permutation and Combination. Master the core formula, learn to identify favourable vs total outcomes, and you'll solve these quickly.

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Key Concepts

• Experiment and Outcome: An experiment is any action with uncertain results (tossing a coin). Each possible result is an outcome (Head or Tail).
• Sample Space (S): The set of all possible outcomes. For one die, S = {1, 2, 3, 4, 5, 6}, so n(S) = 6.
• Event (E): A subset of the sample space that we care about. "Getting an even number" means E = {2, 4, 6}.
• Favourable Outcomes: Outcomes that satisfy the event condition. Count them carefully.
• Probability Range: Always between 0 and 1 inclusive. If your answer exceeds 1 or is negative, recheck immediately.
• Complementary Events: P(Event not happening) = 1 − P(Event happening). Useful when "at least one" type wording appears.
• Equally Likely Outcomes: Probability formulas assume each outcome has the same chance. A fair coin, fair die, or well-mixed bag satisfies this.
• Mutually Exclusive Events: Events that cannot occur together. P(A or B) = P(A) + P(B) when A and B are mutually exclusive.

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Formulas / Key Facts

Core Formula

P(E) = Number of favourable outcomes / Total number of outcomes
     = n(E) / n(S)

Standard Sample Spaces

Coin Facts

• P(Head) = P(Tail) = 1/2
• For n coins: P(exactly k heads) requires combination counting

Dice Facts

• P(any specific number) = 1/6
• P(even number) = P(odd number) = 3/6 = 1/2
• P(prime number on die) = 3/6 = 1/2 (primes: 2, 3, 5)
• P(number > 4) = 2/6 = 1/3 (numbers: 5, 6)

Ball/Bag Facts

• Add all balls to get total outcomes
• Favourable = count of balls matching the condition
• For "at least one" problems: P(at least one) = 1 − P(none)

Complement Rule

P(not E) = 1 − P(E)

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Worked Examples

Example 1: Single Die

Problem: A fair die is rolled once. What is the probability of getting a number divisible by 3?

Solution:

• Total outcomes = 6 (numbers 1 to 6)
• Favourable outcomes = numbers divisible by 3 = {3, 6} = 2 outcomes
• P(divisible by 3) = 2/6 = 1/3

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Example 2: Bag of Balls

Problem: A bag contains 4 red balls, 5 blue balls, and 3 green balls. One ball is drawn at random. What is the probability that it is not blue?

Solution:

• Total balls = 4 + 5 + 3 = 12
• Blue balls = 5
• Not blue = Red + Green = 4 + 3 = 7
• P(not blue) = 7/12

Alternative using complement: P(not blue) = 1 − P(blue) = 1 − 5/12 = 7/12

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Example 3: Two Coins

Problem: Two fair coins are tossed simultaneously. What is the probability of getting exactly one head?

Solution:

• Sample space for 2 coins = {HH, HT, TH, TT} = 4 outcomes
• Exactly one head = {HT, TH} = 2 outcomes
• P(exactly one head) = 2/4 = 1/2

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Example 4: Cards (Basic)

Problem: One card is drawn from a well-shuffled deck of 52 cards. What is the probability that it is a face card?

Solution:

• Total cards = 52
• Face cards = Jack, Queen, King in each of 4 suits = 3 × 4 = 12
• P(face card) = 12/52 = 3/13

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Common Mistakes

Mistake 1: Miscounting total outcomes

• Wrong thinking: Forgetting to add all categories in a bag problem
• Correct fix: Always write Total = (count each type) and add before calculating

Mistake 2: Confusing "or" with "and"

• Wrong thinking: Adding probabilities when events happen together
• Correct fix: "Or" means add (for mutually exclusive); "and" means multiply (for independent events)

Mistake 3: Counting 1 as a prime number

• Wrong thinking: Including 1 in primes when asked "prime number on a die"
• Correct fix: 1 is NOT prime. Primes on a die are 2, 3, 5 only (3 numbers)

Mistake 4: Forgetting to simplify the fraction

• Wrong thinking: Writing 4/12 as final answer
• Correct fix: Always reduce to lowest terms (4/12 = 1/3). Options are usually in simplest form

Mistake 5: Not reading "not" or "at least"

• Wrong thinking: Calculating P(blue) when asked for P(not blue)
• Correct fix: Underline key words in the question before solving

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Quick Reference

• P(E) = Favourable / Total — the only formula you truly need
• Die: 6 outcomes; primes = {2, 3, 5}; evens = {2, 4, 6}
• 2 Coins: 4 outcomes — HH, HT, TH, TT
• Deck of 52: 4 suits × 13 cards; 12 face cards; 4 aces
• Complement shortcut: P(at least one) = 1 − P(none)
• Answer check: If probability > 1 or < 0, you made a counting error

Mixture and Alligation

Overview

Mixture and Alligation is a high-scoring arithmetic topic in SBI Clerk Prelims. The concept helps you quickly find the ratio in which two ingredients at different prices (or concentrations) must be mixed to obtain a desired average price (or concentration).

The questions are typically straightforward—mixing two types of rice, replacing part of a solution, or finding the ratio of milk to water. Mastering the alligation rule gives you a shortcut compared to equation-based methods, which is crucial given the time pressure in Prelims.

The key skill to develop: identify the "cheaper," "dearer," and "mean" values, apply the cross-difference rule, and interpret the resulting ratio correctly.

Key Concepts

• Mixture: Combining two or more ingredients of different values (price, concentration, percentage) to form a new product with an intermediate value.
• Alligation Rule: When two ingredients are mixed, the ratio of their quantities equals the inverse ratio of their deviations from the mean value. This is the foundation of all mixture problems.
• Cheaper and Dearer: The ingredient with value below the mean is "cheaper"; the one above is "dearer." The mean must always lie between the two.
• Mean Price/Concentration: The resultant value of the mixture—this is what you're trying to achieve or what's given in the problem.
• Replacement Problems: When part of a mixture is removed and replaced with another substance, use the formula for repeated replacement to find the final concentration.
• The alligation cross method: Draw an X connecting cheaper-to-mean and dearer-to-mean, then take differences to get the ratio directly.

Formulas / Key Facts

The Alligation Rule

Quantity of Cheaper   Dearer Value − Mean Value
─────────────────── = ─────────────────────────
Quantity of Dearer    Mean Value − Cheaper Value

Visual Cross Method

Cheaper (C)                    Dearer (D)
         \                    /
          \                  /
           \                /
            Mean (M)
           /                \
          /                  \
    (D − M)                (M − C)

Ratio of Cheaper : Dearer = (D − M) : (M − C)

Repeated Replacement Formula When a vessel contains A litres of liquid and B litres is taken out and replaced with another liquid n times:

Final quantity of original liquid = A × (1 − B/A)ⁿ = A × ((A − B)/A)ⁿ

Key Facts to Remember

• The ratio gives Cheaper : Dearer (not the other way around)
• For percentage problems, treat percentages as values directly (e.g., 20% and 50% solutions)
• In replacement problems, the concentration decreases geometrically with each replacement
• If mixing in ratio a : b, the mean lies at (a × C + b × D)/(a + b)

Worked Examples

Example 1: Basic Price Mixing

Problem: In what ratio must rice at ₹40/kg be mixed with rice at ₹60/kg to get a mixture worth ₹45/kg?

Solution:

• Cheaper = 40, Dearer = 60, Mean = 45
• Cheaper : Dearer = (60 − 45) : (45 − 40) = 15 : 5 = 3 : 1

Answer: 3 : 1

Example 2: Concentration Problem

Problem: A vessel contains 80 litres of milk. 8 litres of milk is taken out and replaced with water. This process is repeated once more. Find the quantity of milk remaining.

Solution:

• Initial quantity (A) = 80 litres
• Quantity replaced each time (B) = 8 litres
• Number of operations (n) = 2

Using formula: Final milk = 80 × (1 − 8/80)² = 80 × (72/80)² = 80 × (9/10)² = 80 × 81/100 = 64.8 litres

Answer: 64.8 litres

Example 3: Finding the Mean

Problem: Two varieties of tea costing ₹80/kg and ₹100/kg are mixed in the ratio 3 : 2. Find the cost of the mixture per kg.

Solution:

• Cost of mixture = (3 × 80 + 2 × 100)/(3 + 2)
• = (240 + 200)/5
• = 440/5
• = ₹88/kg

Answer: ₹88 per kg

Example 4: Milk-Water Problem

Problem: A mixture contains milk and water in the ratio 5 : 3. If 16 litres of water is added, the ratio becomes 5 : 5. Find the initial quantity of milk.

Solution:

• Let initial milk = 5x, initial water = 3x
• After adding 16 litres water: milk = 5x, water = 3x + 16
• New ratio: 5x : (3x + 16) = 5 : 5 = 1 : 1
• Therefore: 5x = 3x + 16
• 2x = 16, so x = 8
• Initial milk = 5 × 8 = 40 litres

Answer: 40 litres

Common Mistakes

• Reversing the ratio: Students often write (M − C) : (D − M) instead of (D − M) : (M − C). Remember: the difference from the dearer gives the quantity of cheaper, not the other way around.
• Confusing what the ratio represents: The alligation ratio gives Cheaper quantity : Dearer quantity. Some students assign it to the wrong ingredients and get the inverse answer.
• Forgetting repeated replacement is multiplicative: In replacement problems, students sometimes subtract twice instead of using the exponential formula. Each replacement reduces the concentration by the same fraction, not the same amount.
• Not converting units properly: When mixing percentages with actual quantities, convert everything to the same unit (either all percentages or all absolute values) before applying alligation.
• Applying alligation when mean is outside the range: If the desired mean is less than both values or greater than both, mixing cannot achieve it. The mean must lie strictly between cheaper and dearer values.

Quick Reference

• Cheaper : Dearer = (Dearer − Mean) : (Mean − Cheaper)
• For replacement n times: Final = Initial × ((Total − Replaced)/Total)ⁿ
• The ratio from alligation is always Cheaper : Dearer—label carefully
• Mean value always lies between the two extremes
• For mixing in ratio a : b, Mean = (aC + bD)/(a + b)
• In percentage mixtures, treat percentages as direct values in the formula

Mensuration

Overview

Mensuration deals with the measurement of geometric shapes — calculating perimeter, area, surface area, and volume. The questions typically involve basic 2D shapes (rectangles, circles, triangles) and simple 3D solids (cubes, cylinders, cuboids).

Mastery of mensuration requires memorizing key formulas and applying them quickly. Unlike other arithmetic topics, there's little room for shortcuts — you either know the formula or you don't. The good news: the formulas are finite and the application is straightforward. Focus on speed and accuracy rather than complex problem-solving strategies.

Questions may test direct formula application with one or two calculation steps. Occasionally, you'll encounter problems combining two shapes (like a square inscribed in a circle) or requiring you to find dimensions before calculating area/volume.

Key Concepts

• Perimeter is the total boundary length of a 2D shape; Area is the space enclosed within that boundary.
• Surface Area of a 3D solid is the total area of all its faces; Volume is the space it occupies.
• For 3D solids, distinguish between Curved Surface Area (CSA) — only the curved portion — and Total Surface Area (TSA) — curved plus flat faces.
• When a shape is inscribed in another (e.g., circle in square), their dimensions share a relationship — identify the connecting element (diagonal, diameter, side).
• Units matter: Area uses square units (cm², m²), Volume uses cubic units (cm³, m³). Converting between units requires squaring or cubing the conversion factor.
• A hemisphere is half a sphere — its CSA excludes the flat circular base, while TSA includes it.
• For composite shapes, break them into standard shapes, calculate separately, then add or subtract as needed.

Formulas / Key Facts

2D Shapes

Key relationships:

• Diagonal of square = a√2
• Diagonal of rectangle = √(l² + b²)
• Circumference = π × diameter

3D Shapes

Slant height of cone: l = √(r² + h²)

Diagonal of cuboid: √(l² + b² + h²)

Worked Examples

Example 1: Finding Area from Perimeter

The perimeter of a rectangular field is 80 m. If the length is 10 m more than the breadth, find the area.

Solution:

• Let breadth = b, then length = b + 10
• Perimeter: 2(l + b) = 80 → l + b = 40
• Substituting: (b + 10) + b = 40 → 2b = 30 → b = 15 m
• Length = 25 m
• Area = 25 × 15 = 375 m²

Example 2: Volume of a Cylinder

A cylindrical tank has diameter 14 m and height 5 m. Find its volume. (Use π = 22/7)

Solution:

• Diameter = 14 m → Radius = 7 m
• Volume = πr²h = (22/7) × 7 × 7 × 5
• Volume = 22 × 7 × 5 = 770 m³

Example 3: Composite Shape

A square of side 14 cm has a circle of maximum possible size cut from it. Find the area of the remaining portion. (π = 22/7)

Solution:

• Maximum circle that fits → diameter = side of square = 14 cm
• Radius = 7 cm
• Area of square = 14² = 196 cm²
• Area of circle = (22/7) × 7² = 154 cm²
• Remaining area = 196 − 154 = 42 cm²

Common Mistakes

• Confusing radius and diameter → Always check what's given. Diameter = 2 × radius. Halve the diameter to get the radius when diameter is provided before applying formulas.
• Mixing up CSA and TSA → Read carefully whether the question asks for "curved surface" or "total surface." A closed cylinder's TSA includes two circular ends; CSA does not.
• Forgetting to square/cube when converting units → 1 m² = 10,000 cm² (not 100). 1 m³ = 1,000,000 cm³. Always square for area, cube for volume.
• Using wrong triangle area formula → For any triangle, area = ½ × base × height, where height is perpendicular to that base. For equilateral triangles only, use (√3/4)a².
• Miscalculating slant height vs vertical height in cones → Slant height (l) is the side length; vertical height (h) goes straight down. Related by l² = r² + h².

Quick Reference

• Square: Area = side², Diagonal = side × √2
• Circle: Area = πr², Circumference = 2πr
• Cylinder volume = πr²h; Cube volume = a³
• Sphere volume = (4/3)πr³; Hemisphere volume = (2/3)πr³
• TSA of cylinder = 2πr(r + h); CSA of cylinder = 2πrh
• Use π = 22/7 when radius/diameter is multiple of 7; else use 3.14

Partnership

Overview

Partnership is a fundamental arithmetic topic in SBI Clerk Prelims that tests your ability to distribute profits (or losses) among business partners based on their investments and time periods.

The concept mirrors real-world business scenarios where multiple people invest different amounts for varying periods, and profits must be divided fairly. Questions range from simple two-partner problems to slightly complex scenarios involving working and sleeping partners. Mastering partnership helps you tackle related topics like ratio-proportion and time-work more confidently.

Key Concepts

• Basic Principle: Profit sharing ratio = Ratio of (Capital × Time) for each partner. If A invests ₹x for t₁ months and B invests ₹y for t₂ months, their profit ratio is x×t₁ : y×t₂.
• Simple Partnership: All partners invest for the same duration. Profit ratio equals the ratio of their capitals directly.
• Compound Partnership: Partners invest for different time periods. You must calculate Capital × Time for each partner before finding the ratio.
• Working Partner vs Sleeping Partner: A working partner manages the business and may receive a salary or extra share before profit distribution. A sleeping partner only contributes capital.
• Entry/Exit of Partners: When a partner joins mid-way or leaves early, calculate their contribution only for the months they were invested.
• Capital Changes During Year: If a partner adds or withdraws capital, treat each phase separately and sum up (Capital × Time) for all phases.
• Ratio Simplification: Always reduce the final ratio to its simplest form before calculating actual profit shares.

Formulas / Key Facts

Profit Share Formula: A's Share : B's Share = (A's Capital × A's Time) : (B's Capital × B's Time)

Individual Profit Calculation: A's Profit = (A's ratio part / Total ratio parts) × Total Profit

When Salary is Involved: Step 1: Deduct working partner's salary from total profit Step 2: Distribute remaining profit according to capital-time ratio

Equal Profit Condition: If profits are equal, then Capital₁ × Time₁ = Capital₂ × Time₂

Monthly Investment Calculation: When capital changes, Total Contribution = (C₁ × t₁) + (C₂ × t₂) + ...

Ratio of Investments When Profit Ratio is Given: If profit ratio and time are known, work backwards: Capital Ratio = Profit Ratio / Time Ratio

Worked Examples

Example 1: Simple Partnership A and B start a business with investments of ₹15,000 and ₹20,000 respectively. At the end of the year, total profit is ₹7,000. Find each partner's share.

Solution: Since both invest for the same period (1 year): Ratio of profits = 15,000 : 20,000 = 3 : 4 Total parts = 3 + 4 = 7 A's share = (3/7) × 7,000 = ₹3,000 B's share = (4/7) × 7,000 = ₹4,000

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Example 2: Compound Partnership A invests ₹12,000 for 8 months and B invests ₹9,000 for 12 months. If total profit is ₹6,300, find the difference between their shares.

Solution: A's contribution = 12,000 × 8 = 96,000 B's contribution = 9,000 × 12 = 1,08,000 Ratio = 96,000 : 1,08,000 = 8 : 9 Total parts = 17 A's share = (8/17) × 6,300 = ₹2,964.71 ≈ ₹2,965 B's share = (9/17) × 6,300 = ₹3,335.29 ≈ ₹3,335 Difference = (1/17) × 6,300 = ₹370.59 ≈ ₹371

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Example 3: Partner Joining Later A starts a business with ₹8,000. After 4 months, B joins with ₹12,000. At the end of the year, profit is ₹4,200. Find B's share.

Solution: A invests for 12 months, B invests for (12 - 4) = 8 months A's contribution = 8,000 × 12 = 96,000 B's contribution = 12,000 × 8 = 96,000 Ratio = 96,000 : 96,000 = 1 : 1 B's share = (1/2) × 4,200 = ₹2,100

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Example 4: With Salary Component A and B invest ₹5,000 and ₹6,000 respectively. A manages the business and gets ₹500 per month as salary. Annual profit is ₹8,800. Find A's total earning.

Solution: A's annual salary = 500 × 12 = ₹6,000 Remaining profit = 8,800 - 6,000 = ₹2,800 Investment ratio = 5,000 : 6,000 = 5 : 6 A's share from remaining = (5/11) × 2,800 = ₹1,272.73 ≈ ₹1,273 A's total earning = 6,000 + 1,273 = ₹7,273

Common Mistakes

• Ignoring time factor in compound partnership → Always check if investment durations differ. Even if not explicitly stated as "compound partnership," different entry/exit dates mean you must use Capital × Time.
• Using investment amounts directly as profit ratio → This works ONLY when all partners invest for equal time periods. Otherwise, multiply each investment by its respective time period first.
• Forgetting to deduct salary before profit distribution → When a working partner receives salary, subtract it from total profit first, then distribute the remainder according to the investment ratio.
• Calculating time incorrectly when partner joins later → If B joins after 4 months in a 12-month period, B's time is 8 months, not 4 months. Count from joining month to year-end.
• Not simplifying ratios → Large numbers like 96,000 : 1,08,000 should be simplified (8:9) to make calculations easier and reduce errors.

Quick Reference

• Profit Ratio = Capital₁ × Time₁ : Capital₂ × Time₂
• Same time period → Profit ratio equals capital ratio directly
• Partner joins after 'n' months → Their investment time = (12 - n) months
• Working partner's salary: deduct first, then distribute remaining profit
• Equal profits means equal (Capital × Time) products
• Always simplify ratios before calculating actual amounts

Number System

Overview

Mastering HCF/LCM, divisibility rules, and fraction-decimal conversions will significantly speed up your calculations across the entire Numerical Ability section.

This topic rewards memorization of key rules and patterns rather than complex problem-solving. Students who internalize divisibility tests and know standard fraction-decimal equivalents can solve these questions quickly, freeing up time for lengthier DI sets. The concepts here are straightforward but require consistent practice to achieve the speed needed for Prelims.

Key Concepts

• HCF (Highest Common Factor): The largest number that divides two or more numbers exactly. Also called GCD. Used when dividing things into equal groups or finding common measurements.
• LCM (Least Common Multiple): The smallest number that is divisible by two or more numbers. Used for problems involving repetition, cycles, or finding when events coincide.
• HCF × LCM = Product of two numbers: This relationship holds only for two numbers.
• Co-prime numbers: Two numbers with HCF = 1. Example: 8 and 15 are co-prime.
• Divisibility rules: Shortcuts to check if a number is divisible by 2, 3, 4, 5, 6, 8, 9, 11 without actual division.
• Fractions to decimals: Conversion requires either direct division or memorization of standard equivalents (1/8 = 0.125, 1/6 = 0.1666...).
• Types of fractions: Proper (numerator < denominator), Improper (numerator ≥ denominator), Mixed (whole + proper fraction).
• Recurring vs. terminating decimals: Decimals terminate when the denominator, in lowest terms, has only 2 and 5 as prime factors; otherwise, they recur.

Formulas / Key Facts

HCF and LCM:

• HCF × LCM = a × b (for two numbers a and b)
• HCF of fractions = HCF of numerators ÷ LCM of denominators
• LCM of fractions = LCM of numerators ÷ HCF of denominators

Divisibility Rules:

Standard Fraction-Decimal Conversions (memorize these):

• 1/2 = 0.5
• 1/3 = 0.333...
• 1/4 = 0.25
• 1/5 = 0.2
• 1/6 = 0.1666...
• 1/7 = 0.142857 (repeating)
• 1/8 = 0.125
• 1/9 = 0.111...
• 1/11 = 0.0909...
• 1/12 = 0.0833...

Worked Examples

Example 1: Finding HCF and LCM

Find HCF and LCM of 12 and 18.

Step 1: Prime factorization

• 12 = 2² × 3
• 18 = 2 × 3²

Step 2: HCF = Product of lowest powers of common primes

• HCF = 2¹ × 3¹ = 6

Step 3: LCM = Product of highest powers of all primes

• LCM = 2² × 3² = 36

Verification: HCF × LCM = 6 × 36 = 216 = 12 × 18 ✓

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Example 2: Application of HCF-LCM relationship

The HCF of two numbers is 8 and their LCM is 96. If one number is 24, find the other.

Using the formula: HCF × LCM = First number × Second number

• 8 × 96 = 24 × Second number
• 768 = 24 × Second number
• Second number = 768 ÷ 24 = 32

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Example 3: Divisibility check

Is 3,528 divisible by 8?

Rule for 8: Check last three digits

• Last three digits = 528
• 528 ÷ 8 = 66

Yes, 3,528 is divisible by 8.

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Example 4: HCF of fractions

Find HCF of 2/3, 4/5, and 6/7.

HCF of fractions = HCF of numerators ÷ LCM of denominators

• HCF of 2, 4, 6 = 2
• LCM of 3, 5, 7 = 105

HCF = 2/105

Common Mistakes

• Confusing HCF and LCM formulas for fractions → Remember: HCF uses HCF on top and LCM below; LCM uses LCM on top and HCF below. Think "opposite operations."
• Applying HCF × LCM = Product formula to three or more numbers → This formula works ONLY for exactly two numbers. For three numbers, you need a different approach.
• Forgetting to check both conditions for divisibility by 6 → A number must be divisible by BOTH 2 AND 3 to be divisible by 6. Checking only one condition leads to wrong answers.
• Mixing up divisibility rules for 4 and 8 → For 4: check last TWO digits. For 8: check last THREE digits. Associate 4 with 2 digits, 8 with 3 digits.
• Converting recurring decimals incorrectly → 0.333... equals 1/3, not 0.33. When comparing, either convert both to fractions or use sufficient decimal places.

Quick Reference

• HCF × LCM = Product (only for 2 numbers)
• Divisible by 3: digit sum divisible by 3
• Divisible by 4: last 2 digits divisible by 4
• Divisible by 8: last 3 digits divisible by 8
• Divisible by 11: (sum of odd-position digits) − (sum of even-position digits) divisible by 11
• 1/8 = 0.125, 1/6 = 0.1666..., 1/7 = 0.142857

Puzzles — Study Notes for SBI Clerk (Prelims)

Overview

These questions test your ability to organize scattered information, apply constraints logically, and arrive at a definite arrangement or comparison.

In SBI Clerk Prelims, puzzles remain at a moderate difficulty level. The key to scoring well is not brilliance but systematic practice — learning to extract conditions, build tables, and eliminate impossibilities step by step.

Mastering puzzles directly impacts your overall Reasoning score. A student who can confidently solve 2–3 puzzle sets in the exam gains a significant edge, as these questions come in clusters of 3–5 linked items.

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Key Concepts

• Single-variable vs Multi-variable: Single-variable puzzles have one attribute to arrange, like floors; multi-variable puzzles combine several (floor + department + age).
• Definite vs Indefinite Information: Start solving from definite clues (e.g., "A lives on floor 3") before tackling indefinite ones (e.g., "B lives above C").
• Positive and Negative Conditions: "A is on floor 5" is positive; "A is not on floor 5" is negative. Mark negatives with crosses (✗) in your table.
• Relative Positioning: Terms like "immediately above," "two floors below," "between X and Y" define relative positions. Distinguish between "above" (anywhere higher) and "immediately above" (exactly one floor higher).
• Boundary Constraints: In floor puzzles, the topmost and bottommost floors have special constraints — only one neighbor each.
• Either-Or Conditions: When a clue gives two possibilities, create branches and test which one leads to a valid solution without contradictions.
• Linked Clues: Often, two or three clues connect through a common person. Identify these chains to build larger portions of the arrangement.
• Elimination Method: When direct placement fails, list all possibilities and eliminate those violating any condition.

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Formulas / Key Facts

Critical Fact: Solving time target: 4–6 minutes per set (including all linked questions).

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Worked Examples

Example 1: Floor Puzzle

Problem: Six persons — P, Q, R, S, T, U — live on six floors numbered 1 (ground) to 6 (top).

• T lives on floor 4.
• Q lives three floors below P.
• R lives above T but not on the topmost floor.
• S does not live on floor 1 or 6.
• U lives below T.

Solution:

Step 1: Place definite information.

• T → Floor 4

Step 2: Apply "R lives above T but not on topmost."

• R can be on floor 5 only (floor 6 is topmost, ruled out).
• R → Floor 5

Step 3: "U lives below T" means U is on floor 1, 2, or 3.

Step 4: "S does not live on floor 1 or 6."

• S can be on floors 2, 3, or but floors 4 and 5 are taken.
• S → Floor 2 or 3

Step 5: "Q lives three floors below P."

• P is exactly three floors above Q. Remaining floors: 1, 2, 3, 6.
• Possible pairs: (Q on 1, P on 4) and (Q on 2, P on 5) are ruled out because floors 4 and 5 are taken; only (Q on 3, P on 6) is left.

If Q=3, P=6 → Remaining: 1, 2 for S and U. S ≠ 1, so S=2, U=1. Check: U=1 is below T=4. Valid!

Final Arrangement:

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Example 2: Day Scheduling

Problem: Five persons — A, B, C, D, E — have meetings on five consecutive days, Monday to Friday.

• B has a meeting on Wednesday.
• A has a meeting on the day immediately before C, but after D.
• E does not have a meeting on Monday or Friday.

Solution:

Step 1: B → Wednesday

Step 2: "A immediately before C, but after D" means D...A, C (in that order, with A and C on consecutive days).

Step 3: E ≠ Monday, E ≠ Friday → E is on Tuesday, Wednesday, or Thursday. But Wednesday = B. So E = Tuesday or Thursday.

Step 4: Fit D, A, C around these constraints.

• If E = Tuesday: Monday is D or part of D-A-C sequence.
  • D-A-C needs three days. Available: Mon, Thu, Fri.
  • D = Mon, A = Thu, C = Fri. Valid!
• Verify: E = Tuesday, B = Wednesday. All conditions hold. (If E = Thursday, the free days are Mon, Tue, Fri; the only consecutive pair is Mon-Tue, which would put A on Monday with no earlier day left for D — rejected.)

Answer: Mon=D, Tue=E, Wed=B, Thu=A, Fri=C

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Common Mistakes

• Confusing "above" with "immediately above": "X lives above Y" allows any floor higher than Y. "Immediately above" means exactly one floor higher. Fix: Underline the word "immediately" whenever you see it.
• Ignoring negative conditions midway: Students place persons but forget earlier "X ≠ floor 3" conditions. Fix: Mark all negatives with ✗ in your table before you start placing.
• Not testing both branches of either-or clues: When two possibilities exist, students assume one and proceed without verification. Fix: Quickly test the other branch if you hit a dead end.
• Miscounting gaps: "Two floors above" means a gap of one floor between them (e.g., floor 2 and floor 4). Fix: Use your fingers or draw lines to count physically.
• Starting with indefinite clues: Jumping to "A is above B" before using "C is on floor 5" wastes time. Fix: Always scan for definite placements first.

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Quick Reference

• Always draw a table first — floors as rows, persons to be filled.
• Mark all negative conditions (✗) before placing any person.
• Start from definite clues, then link relative clues to them.
• "Immediately" = exactly one position apart; "above/below" = anywhere in that direction.
• Target time: 4–6 minutes per puzzle set (3–5 questions).
• Check all conditions once after completing the arrangement — catches silly errors.

Floor Puzzle — Study Notes for SBI Clerk Prelims

Overview

Floor puzzles are a puzzle type in the Reasoning Ability section in SBI Clerk Prelims. In these problems, you are given a building with numbered floors (typically 5 to 8 floors) and a set of persons who live on different floors. Your task is to determine the correct floor assignment for each person based on the given clues.

These puzzles test your ability to organize information systematically, apply logical constraints, and eliminate impossible options. Some floor puzzles are "single-variable" — meaning you only need to assign persons to floors, without additional variables like profession, age, or department.

Success requires a calm, step-by-step approach. Students who rush often misread clues or lose track of possibilities. Building a clear table and working methodically will consistently yield correct answers.

Key Concepts

• Floor numbering convention: Unless stated otherwise, assume Floor 1 is the ground/bottom floor and the highest number is the topmost floor. Read the question stem carefully — some puzzles explicitly state the numbering direction.
• One person per floor: Unless stated otherwise, each floor has exactly one resident. If there are 6 persons and 6 floors, every floor is occupied.
• Definite vs. relative clues: Definite clues give exact positions ("P lives on Floor 3"). Relative clues give relationships ("Q lives immediately above R"). Always start with definite clues.
• "Above" vs. "Immediately above": "A lives above B" means A is on any higher floor than B (not necessarily adjacent). "A lives immediately above B" means A is exactly one floor higher — consecutive floors with no gap.
• "Between" interpretation: "C lives between D and E" means C is on a floor numerically between D and E, but D and E are not necessarily adjacent to C.
• Gap clues: "There are two floors between X and Y" means exactly two floors separate them (so X and Y are three floors apart in numbering).
• Negative clues: "M does not live on the topmost floor" or "N does not live immediately below O" — use these to eliminate options after placing others.
• Multiple possibilities: Sometimes early clues allow 2–3 arrangements. Carry forward all possibilities until a later clue eliminates one.

Formulas / Key Facts

Quick calculation: If "n floors between X and Y," then the floor difference = n + 1.

Worked Examples

Example Puzzle

Eight persons — P, Q, R, S, T, U, V, W — live on 8 floors of a building (Floor 1 to Floor 8, Floor 1 being the lowest).

Clues:

1. T lives on Floor 5.
2. There are two floors between T and P. P lives below T.
3. Q lives immediately above R.
4. S lives on the topmost floor.
5. U lives immediately above V. U lives below R.
6. W lives immediately below P.
7. R does not live on Floor 1.

Step-by-step solution:

Step 1: Start with definite clues.

• From Clue 1: T → Floor 5
• From Clue 4: S → Floor 8

Step 2: Apply gap clues.

• From Clue 2: Two floors between T and P, P below T.
  • T is on Floor 5. Two floors between means P is on Floor 5 − 3 = Floor 2.
  • P → Floor 2

Step 3: Apply "immediately" clues.

• From Clue 6: W immediately below P.
  • P is on Floor 2, so W → Floor 1.

Step 4: Work on Q-R pair.

• From Clue 3: Q immediately above R → Q and R are on consecutive floors (Q higher).
• From Clue 7: R is not on Floor 1.
• Remaining floors: 3, 4, 6, 7 (Floors 1, 2, 5, 8 are taken by W, P, T, S).
• Possible (R, Q) pairs: (3, 4), (4, 6 — not consecutive, invalid), (6, 7).
• Valid pairs: (R=3, Q=4) or (R=6, Q=7).

Step 5: Work on U-V pair.

• From Clue 5: U immediately above V → U and V are on consecutive floors, and U is below R.
• Remaining floors after placing Q-R will be 2 floors for U-V.

Case A: R=3, Q=4. Remaining: 6, 7 for U, V.

• U would be on Floor 6 or 7, which is above R (Floor 3), but U must be below R. Case A fails.

Case B: R=6, Q=7. Remaining: 3, 4 for U, V.

• U immediately above V: U=4, V=3. U (Floor 4) is below R (Floor 6). Case B works.

The key process is:

1. Build a table: Floors 1–8 as rows.
2. Fill definite clues first.
3. Apply gap/consecutive clues.
4. Test remaining possibilities.
5. Use negative clues to eliminate.

Final arrangement:

(Note: Always verify each clue against your final table.)

Common Mistakes

• Confusing "above" with "immediately above" → "Above" allows any higher floor; "immediately above" means exactly one floor higher. Read the exact wording.
• Miscounting "floors between" → "Two floors between X and Y" means 3-floor difference (e.g., Floor 2 to Floor 5), not 2-floor difference. Add 1 to the gap count.
• Forgetting floor direction → Always confirm whether Floor 1 is bottom or top. Misreading this inverts your entire solution.
• Not tracking multiple cases → When two arrangements are possible early on, students often pick one and ignore the other. Carry both cases forward until one is eliminated.
• Rushing negative clues → Clues like "P does not live on Floor 4" are useless initially but become decisive late. Revisit them after placing other persons.

Quick Reference

• Floor 1 = bottom unless stated otherwise.
• "n floors between" = (n + 1) floor difference.
• "Immediately above/below" = consecutive floors only.
• Start with definite positions, then gap clues, then negatives.
• One person per floor (unless stated otherwise).
• Always verify every clue against your final arrangement.

Linear Arrangement

Overview

Linear Arrangement is a topic in the SBI Clerk Prelims Reasoning section. These puzzles involve seating a group of persons (usually 5–8) in a straight line, where all face the same direction (typically North or South). The examiner provides indirect clues about relative positions, and your task is to determine the exact seating order.

Mastering linear arrangement builds the foundational logic needed for more complex puzzles like double-row and circular arrangements. Speed and accuracy here can secure easy marks if you develop a systematic approach.

The key challenge is translating verbal clues into a visual diagram quickly. Students who practice drawing neat lines and marking positions systematically outperform those who try to solve mentally.

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Key Concepts

• Single-row, single-direction: All persons sit in one straight line facing the same direction (North or South). This is simpler than double-row arrangements.
• Position numbering: Number positions 1 to n from left to right. When facing North, the left end is position 1; when facing South, interpret "left" and "right" from the person's perspective, which reverses the visual diagram.
• Immediate neighbour: Persons sitting directly next to each other with no gap. "A sits immediately to the left of B" means A is in position (B's position − 1).
• "X sits to the left/right of Y": This does NOT mean immediate neighbour—X is somewhere on the left/right side of Y with possible gaps.
• "Between" interpretation: "A sits between B and C" means B and C are on either side of A, but not necessarily immediate. Check if "immediately between" is specified.
• Definite vs. possible positions: Some clues fix positions absolutely; others give relative information. Start with definite clues, then layer conditional ones.
• Negative clues: "A does not sit at any end" or "B is not an immediate neighbour of C" eliminate possibilities—mark these as constraints.
• Ends and middle: Positions 1 and n are "ends." The middle position exists only when n is odd (e.g., position 4 in a 7-person row).

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Formulas / Key Facts

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Worked Examples

Example 1: Basic 5-Person Arrangement

Problem: Five persons P, Q, R, S, T sit in a row facing North.

• R sits at the extreme left end.
• Q sits second to the right of R.
• T is an immediate neighbour of Q.
• S does not sit at any end.

Solution:

Step 1: Draw positions 1–2–3–4–5 (left to right, facing North).

Step 2: R sits at extreme left → R is at position 1.

Step 3: Q is second to the right of R → Q is at position 1 + 2 = 3.

Position: 1   2   3   4   5
          R   _   Q   _   _

Step 4: T is an immediate neighbour of Q → T is at position 2 or 4.

Step 5: S does not sit at any end → S is not at position 1 or 5. Since position 1 is taken by R, S must be at 2, 3, or 4. Position 3 is Q's. So S is at 2 or 4.

Step 6: Remaining persons: S, T, and P for positions 2, 4, 5.

• T must be at 2 or 4 (neighbour of Q).
• S must be at 2 or 4 (not at ends).
• P takes whatever remains.

If T is at 2, S is at 4, P is at 5 → Valid. If T is at 4, S is at 2, P is at 5 → Valid.

Two possible arrangements:

• R – T – Q – S – P
• R – S – Q – T – P

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Example 2: "Between" Clue

Problem: Six persons A, B, C, D, E, F sit facing South.

• B sits at one of the ends.
• Exactly two persons sit between B and D.
• A sits immediately to the right of D.
• C sits second to the left of A.

Solution:

Step 1: Positions 1–6 (left to right from our view). Since they face South, "right of D" from D's perspective is towards position numbers decreasing.

Wait—let's clarify: When facing South, the person's right corresponds to our left (viewer's left). So "A sits immediately to the right of D" means A is at (D's position − 1) from our diagram perspective.

Step 2: B is at position 1 or 6. Two persons between B and D → gap of 2 → B and D are 3 positions apart.

• If B at 1, D at 4.
• If B at 6, D at 3.

Step 3: A immediately to the right of D (i.e., A at D − 1):

• Case 1: D at 4 → A at 3.
• Case 2: D at 3 → A at 2.

Step 4: C is second to the left of A. ("Left of A" from A's perspective = our right.)

• Case 1: A at 3 → C at 3 + 2 = 5.
• Case 2: A at 2 → C at 2 + 2 = 4.

Step 5: Check Case 1: B at 1, A at 3, D at 4, C at 5. Remaining: E, F at 2 and 6.

1   2   3   4   5   6
B   ?   A   D   C   ?

E and F at 2 and 6 (no further constraint) → Valid.

Step 6: Check Case 2: B at 6, D at 3, A at 2, C at 4. Remaining: E, F at 1 and 5.

1   2   3   4   5   6
?   A   D   C   ?   B

Valid arrangement.

Answer: Two arrangements exist unless additional clues narrow it down.

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Common Mistakes

• Confusing "to the left of" with "immediately to the left of" → Always check if "immediately" is mentioned. Without it, there can be gaps between persons.
• Forgetting direction affects left/right → When persons face South, their right is the viewer's left. Draw the direction clearly and interpret clues from the person's viewpoint.
• Miscounting "between" → "Two persons between A and B" means A and B are 3 positions apart, not 2. Count the gap, not the positions.
• Not considering multiple cases → Many puzzles have 2 valid arrangements initially. Test all possibilities before answering specific questions.
• Ignoring negative clues → "A is not a neighbour of B" is a constraint. Mark it and verify your final arrangement against it.

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Quick Reference

• Number positions 1 to n; start with definite clues (end positions, exact placements).
• "Second to the right of X" = X's position + 2.
• "Between A and B" with k persons → A and B are (k + 1) positions apart.
• Facing North: person's left = our left. Facing South: person's left = our right.
• Always verify final arrangement against ALL clues, especially negative ones.
• Practice drawing the line diagram—never solve purely in your head.

Seating Arrangement

Overview

These problems test your ability to organize information systematically and draw logical conclusions from given conditions.

The topic divides into two main types: Linear Arrangement (persons sitting in a row) and Circular Arrangement (persons sitting around a table). Mastering this topic is non-negotiable; it's a reliable scoring area once you develop a systematic approach.

Success here depends on three skills: accurate diagram-making, careful clue interpretation, and methodical elimination. Students who rush through clues or draw messy diagrams lose marks to silly errors, not lack of understanding.

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Key Concepts

• Linear Arrangement: Persons sit in a single row. Critical question: Are they facing North or South? If not mentioned, assume facing North (left = West, right = East).
• Circular Arrangement: Persons sit around a round table. Key detail: Are they facing the center or facing outside? This reverses the meaning of "left" and "right."
• Definite vs. Conditional Clues: Start with definite clues (exact positions like "A sits at the left end") before processing conditional clues ("B sits to the left of C" without exact position).
• Immediate vs. Non-Immediate Neighbors: "A sits next to B" means they are adjacent. "A sits to the left of B" may or may not mean adjacent—check for words like "immediately."
• Multiple Possibilities: Sometimes clues allow 2-3 valid configurations. Mark both cases and eliminate using later clues.
• Direction Convention: In circular facing center—a person's left is your right when you look at them. In circular facing outside—a person's left is also your left.
• Counting Positions: In linear rows, count positions from Left End or Right End as specified. Position 1 from left end = leftmost seat.

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Key Facts to Remember

Must-Remember Points:

1. "Opposite" in circular = directly across the table (for 8 persons, 3 persons between them on either side)
2. "Second to the left" = skip one person, count two positions leftward
3. In a row of n persons, person at position k from left is at position (n-k+1) from right
4. "Neither A nor B sits at the end" = both are somewhere in the middle
5. "A and B are not neighbors" = at least one person sits between them

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Worked Examples

Example 1: Linear Arrangement

Problem: Five persons P, Q, R, S, T sit in a row facing North.

• R sits at the right end.
• Q sits second to the left of R.
• P is an immediate neighbor of Q.
• S does not sit at any end.

Find: Who sits at the left end?

Solution:

• Step 1: Draw 5 positions. R at right end → Position 5.
• Step 2: Q is second to left of R → Position 3.
• Step 3: P is immediate neighbor of Q → Position 2 or 4.
• Step 4: S doesn't sit at ends → S is in Position 2, 3, or 4. Position 3 is Q's. So S is at 2 or 4.
• Step 5: If P is at Position 2, then S must be at Position 4. T gets Position 1. ✓
• Step 6: If P is at Position 4, then S must be at Position 2. T gets Position 1. ✓

Both cases give T at Position 1 (left end).

Answer: T sits at the left end.

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Example 2: Circular Arrangement

Problem: Six persons A, B, C, D, E, F sit around a circular table facing the center.

• A sits second to the right of D.
• B sits opposite to A.
• C is an immediate neighbor of both A and D.
• E is not a neighbor of B.

Find: Who sits opposite to D?

Solution:

• Step 1: Place D anywhere (say at 12 o'clock position).
• Step 2: A is second to right of D → A at 8 o'clock.
• Step 3: B is opposite A → B at 2 o'clock.
• Step 4: C is neighbor of both A and D → C must be between them at 10 o'clock.
• Step 5: Remaining positions: 4, 6 o'clock for E and F.
• Step 6: E is not neighbor of B. B's neighbors are positions at 4 and 12. 12 is D. So 4 o'clock cannot be E → 4 o'clock = F, 6 o'clock = E.
• Step 7: D (12 o'clock) is opposite to 6 o'clock = E.

Answer: E sits opposite to D.

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Common Mistakes

• Ignoring facing direction → Students apply left-right rules for "facing center" when persons face outside. Always confirm direction before drawing.
• Treating "to the left" as "immediately to the left" → "A sits to the left of B" allows gap between them unless "immediately" is stated. Read clues word-by-word.
• Fixing positions too early → Placing a person definitively when the clue allows multiple spots leads to wrong diagrams. Keep options open with Case 1/Case 2 notation.
• Miscounting in circular → In circular, students often miscount "second to the right" because they forget to skip the immediate neighbor. Practice counting: immediate = 1, next = 2.
• Forgetting to verify → After completing the arrangement, not cross-checking all conditions. Spend 10 seconds verifying each clue against final diagram.

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Quick Reference

• Linear: Always note facing direction—it determines left/right meaning.
• Circular facing center: Person's right = your left when looking at them.
• Start with definite clues (end positions, exact placements) first.
• "Second to the right" = skip one, land on the second.
• "Opposite" in circular of n persons = n/2 positions away.
• When stuck, draw multiple cases and eliminate with remaining clues.

Circular Arrangement

Overview

Circular Arrangement is a core puzzle type in SBI Clerk Prelims Reasoning section. The puzzle involves seating persons around a round table and determining their positions based on given conditions.

What makes circular arrangement distinct from linear arrangement is the concept of relative positioning—there's no absolute "left end" or "right end." Every position is defined only in relation to other persons. Mastering this topic requires understanding facing direction (inward vs outward), clockwise vs anti-clockwise movement, and systematic elimination of possibilities.

The conditions are usually straightforward—immediate neighbors, second to the left/right, and opposite positions.

Key Concepts

• No fixed starting point: In a circle, any position can be your reference point. Pick one person from the strongest clue and fix them first.
• Facing direction matters: "Facing center" means the person looks inward; "facing outward" means they look away from center. This reverses left-right orientation.
• Clockwise = Left (when facing center): For a person facing the center, moving clockwise means moving to their left. Anti-clockwise means moving to their right.
• Clockwise = Right (when facing outward): For a person facing outward, clockwise becomes their right and anti-clockwise becomes their left.
• Immediate neighbor: The person sitting directly adjacent (one position away) on either side.
• "Second to the left": Skip one person and reach the second position in that direction. "Third to the right" means skip two persons.
• Opposite position: In a table of n persons, the opposite person sits n/2 positions away. In 8 persons, opposite = 4 positions away.
• Definite vs possible cases: Some clue sets produce multiple valid arrangements. Track all possibilities until later clues eliminate one.

Formulas / Key Facts

• Opposite position formula: In n persons, opposite person is at position n/2 away (works only for even n).
• Position count: "X is 3rd to the left of Y" means starting from Y, count 3 positions clockwise (if Y faces center).
• Total positions in circle: If 8 persons, positions are 1-8; each person has exactly 2 neighbors.
• Clockwise direction rule: When viewed from above, clockwise is the direction in which clock hands move.
• Symmetry principle: A circular arrangement has no unique starting point, so one arrangement and its rotation are considered the same.
• Neighbor identification: If A is 2nd to left of B, then B is 2nd to right of A (for same facing direction).
• Facing outward reversal: All left-right directions flip when a person faces outward compared to facing inward.

Worked Examples

Example 1: Basic Circular Arrangement

Problem: Eight persons A, B, C, D, E, F, G, H sit around a circular table facing the center.

• B sits second to the left of D
• F sits opposite to B
• A sits immediate right of F
• C sits second to the right of A
• E is not an immediate neighbor of C
• G sits opposite to A

Solution:

Step 1: Fix D at any position (say position 1). B is second to left of D → B at position 3.

Step 2: F is opposite to B. In 8 persons, opposite = 4 positions away. F at position 7.

Step 3: A is immediate right of F → A at position 6.

Step 4: G is opposite to A → G at position 2.

Step 5: C is second to right of A → move 2 seats anti-clockwise from A (5, 4) → C at position 4.

Step 6: Remaining seats 5 and 8 for E and H. E is not an immediate neighbor of C (seat 4), so E is not at 5 → E at 8, H at 5.

Final (seats 1 to 8): D, G, B, C, H, A, F, E.

Example 2: Mixed Facing Direction

Problem: Six persons P, Q, R, S, T, U sit around a circle. Some face center, some face outward.

• P faces outward and sits second to left of Q
• Q faces center
• R sits opposite to P and faces same direction as P
• S is immediate neighbor of both P and Q

Solution:

Step 1: Fix Q at position 1 (facing center). P is second to left of Q → P at position 3 (facing outward).

Step 2: R is opposite P. In 6 persons, opposite = 3 positions. R at position 6. R faces outward (same as P).

Step 3: S is neighbor of both P and Q. P at 3, Q at 1. Neighbors of P: positions 2 and 4. Neighbors of Q: positions 6 and 2.

Common neighbor position = 2. So S is at position 2.

Key insight: In exams, if constraints seem contradictory, you may have misread the direction. Always reread when stuck.

Common Mistakes

• Confusing left-right for outward-facing persons → Remember: For outward-facing, left and right are reversed. Draw an arrow showing where they're looking.
• Miscounting positions (off-by-one error) → Don't count the starting person. "Second to the left" = skip one, land on second.
• Assuming all face center unless stated → Read the problem stem carefully. "Some face center, some face outward" changes everything.
• Forgetting that opposite positions need even number of persons → Opposite is defined only when total persons are even. For odd numbers, there's no exact opposite.
• Starting with weak clues → Begin with clues that connect multiple persons or fix absolute relationships (like "opposite to" or "immediate neighbor").

Quick Reference

• Fix one person first; build around them.
• Facing center: clockwise = left; facing outward: clockwise = right.
• Opposite position = n/2 seats away (for n persons, n must be even).
• "2nd to the left" means count 2 positions clockwise (when facing center).
• Always draw the circle; never solve in your head.
• Check facing direction before applying left/right clues.

Syllogism — Study Notes for SBI Clerk Prelims

Overview

These questions test your ability to draw valid logical conclusions from two given statements using universal and particular quantifiers (All, Some, No, Only).

The good news: syllogism follows strict, predictable rules. Once you master the Venn diagram method, you can solve these questions quickly and accurately—often in under 30 seconds each. The challenge lies in avoiding over-conclusion (deriving more than what logically follows) and handling tricky "Only" statements correctly.

Master the basics thoroughly before attempting shortcuts.

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Key Concepts

• Universal Positive (A-type): "All A are B" — Every member of A belongs to B. A is completely inside B.
• Universal Negative (E-type): "No A is B" — Not a single member of A belongs to B. A and B don't overlap at all.
• Particular Positive (I-type): "Some A are B" — At least one member of A belongs to B. Partial overlap exists.
• Particular Negative (O-type): "Some A are not B" — At least one member of A does not belong to B.
• "Only A are B" = "All B are A": This is a critical conversion. "Only teachers are graduates" means "All graduates are teachers."
• Definite vs Possibility conclusions: A definite conclusion must be true in ALL valid Venn diagrams. A possibility conclusion is true if it holds in AT LEAST ONE valid diagram.
• Complementary pairs: "Some A are B" and "No A is B" are complementary—exactly one must be true. Similarly, "All A are B" and "Some A are not B" are complementary.

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Formulas / Key Facts

Conversion Rules:

• "All A are B" → "Some B are A" (valid)
• "All A are B" → "All B are A" (NOT valid)
• "No A is B" → "No B is A" (valid)
• "Some A are B" → "Some B are A" (valid)
• "Some A are not B" → Cannot be converted

Important Derivations:

• "All A are B" + "All B are C" → "All A are C" and "Some C are A"
• "All A are B" + "No B is C" → "No A is C"
• "Some A are B" + "All B are C" → "Some A are C"
• "Some A are B" + "Some B are C" → No definite conclusion

Remember: Two particular statements (Some + Some) or two negative statements (No + No) give NO definite conclusion.

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Worked Examples

Example 1: Basic Two-Statement Problem

Statements:

1. All books are pens.
2. All pens are erasers.

Conclusions: I. All books are erasers. II. Some erasers are books. III. All erasers are pens.

Solution: Draw Venn diagram: Books (innermost) → Pens (middle) → Erasers (outermost)

• Conclusion I: Books ⊆ Pens ⊆ Erasers, so Books ⊆ Erasers. TRUE
• Conclusion II: Since all books are erasers, at least some erasers are books. TRUE
• Conclusion III: Erasers is the largest set; not all erasers need be pens. FALSE

Answer: Only I and II follow.

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Example 2: With Negative Statement

Statements:

1. All cats are dogs.
2. No dog is a rat.

Conclusions: I. No cat is a rat. II. Some dogs are cats.

Solution: Draw: Cats inside Dogs; Rats completely separate from Dogs.

• Conclusion I: Cats ⊆ Dogs, and Dogs ∩ Rats = ∅, so Cats ∩ Rats = ∅. TRUE
• Conclusion II: Since all cats are dogs, some dogs are definitely cats. TRUE

Answer: Both I and II follow.

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Example 3: Possibility Question

Statements:

1. Some apples are oranges.
2. All oranges are bananas.

Conclusions: I. All apples being bananas is a possibility. II. Some bananas are apples.

Solution: "Some apples are oranges" means partial overlap. Those overlapping apples are inside bananas (since all oranges are bananas).

• Conclusion I: In one valid diagram, the apple circle could be entirely inside bananas. So possibility exists. TRUE
• Conclusion II: The apples that are oranges are definitely bananas. So some bananas are apples. TRUE (Definite)

Answer: Both follow.

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Common Mistakes

• "All A are B" means "All B are A" → WRONG. "All A are B" only guarantees "Some B are A." Always remember A is the subset, not B.
• Drawing only one Venn diagram → WRONG when checking definite conclusions. A conclusion is definite only if it's true in EVERY possible valid diagram. Draw multiple configurations.
• Confusing "Only" with "All" → "Only A are B" means "All B are A," not "All A are B." Flip the subject and predicate.
• Concluding from two particular statements → "Some A are B" + "Some B are C" does NOT guarantee "Some A are C." The overlapping B members might be different.
• Ignoring complementary pair logic → In "either-or" type answers, check if two conclusions are complementary (one must be true). Example: "Some A are B" and "No A is B" — exactly one is always true.
• Treating possibility as certainty → "Some A may be B" is NOT the same as "Some A are B." Possibility only requires one valid diagram where it holds.

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Quick Reference

• All A are B → Some B are A (always valid conversion)
• No A is B = No B is A (symmetric relationship)
• Only A are B = All B are A (swap and change to All)
• Two negatives or two particulars = No definite conclusion
• Possibility = True in at least one valid diagram; Definite = True in all valid diagrams
• Complementary pairs: (All, Some...not) and (Some, No) — one must be true

Inequalities

Overview

Inequalities is a topic in SBI Clerk Prelims Reasoning section. Questions test your ability to interpret relationship symbols (>, <, =, ≥, ≤) between elements and derive valid conclusions.

This topic comes in two forms: Direct Inequalities (symbols given as-is) and Coded Inequalities (symbols replaced by codes like @, #, $, %). Mastering the logical chain rules and recognizing invalid combinations is the key to accuracy. Since there's no calculation involved, this is pure logic — ideal for quick marks.

Key Concepts

• Basic Symbols: > means "greater than", < means "less than", = means "equal to", ≥ means "greater than or equal to", ≤ means "less than or equal to".
• Definite vs. Indefinite Relationships: A conclusion is definite only when all connecting symbols point in the same direction (all left-pointing or all right-pointing). Mixed directions yield no definite relationship.
• Chain Rule: You can combine relationships only when elements share a common link. For A > B ≤ C, the relationship between A and C is indefinite because > and ≤ conflict.
• Either-Or Conclusions: When two conclusions are individually false but together cover all possibilities (one uses > and other uses =, or one uses < and other uses =), "either-or" applies.
• Priority of Definite Symbol: In a chain running one way, one strict link (> or <) makes the result strict; the result is ≥ (or ≤) only when every link is ≥ (≤) or =.
• Complementary Pairs: > and ≤ are complementary (opposite). Similarly, < and ≥ are complementary. A relationship must be one or the other.
• Coded Inequality Decoding: Always write out the code key first. Convert coded statements to standard symbols before analyzing.

Formulas / Key Facts

Must-Remember Rules:

1. Same direction symbols → Definite conclusion possible
2. Opposite direction symbols → No definite conclusion
3. "Either-or" applies when both individual conclusions are false but are complementary
4. Always trace the chain from the first element to the last element mentioned in the conclusion
5. For coded inequalities, decode ALL symbols before attempting any question

Worked Examples

Example 1: Direct Inequality

Statement: P > Q ≥ R = S < T

Conclusions: I. P > S II. T > Q

Solution:

For I (P > S): Trace P → Q → R → S P > Q ≥ R = S All symbols point in the same direction (left to right: P is greater) P > Q ≥ R = S → P > S is TRUE

For II (T > Q): Trace T → S → R → Q T > S = R ≤ Q From T's perspective: T > S = R, then R ≤ Q Directions conflict (> then ≤) → T > Q is NOT DEFINITE

Answer: Only conclusion I follows.

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Example 2: Coded Inequality

Code: @ means >, # means <, $ means =, % means ≥, & means ≤

Statement: A @ B $ C # D % E

Decode first: A > B = C < D ≥ E

Conclusions: I. A > C II. E < B

Solution:

For I (A > C): A > B = C → A > C is TRUE

For II (E < B): Trace E → D → C → B E ≤ D > C = B Directions: ≤ then > then = → Mixed directions E < B is NOT DEFINITE

Answer: Only conclusion I follows.

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Example 3: Either-Or Case

Statement: M ≥ N = O ≤ P

Conclusions: I. M > P II. M = P

Solution:

Trace M → N → O → P: M ≥ N = O ≤ P Directions: ≥ then = then ≤ → Opposite directions (≥ vs ≤)

M > P → Not definite (FALSE) M = P → Not definite (FALSE)

But together, M ≥ P or M ≤ P must be true. Since we have M ≥ N = O and O ≤ P, the only certainty is M could be >, =, or < compared to P.

Wait — let's check: These conclusions are M > P and M = P. Together they make M ≥ P. But the chain doesn't guarantee M ≥ P.

Either-or does NOT apply here because M could also be < P.

Answer: Neither conclusion follows.

Common Mistakes

• Ignoring direction conflicts → Students assume A > B < C means A > C. Fix: Check if all symbols point the same way; opposite symbols = no conclusion.
• Confusing ≥ and > → Writing "A > B" when chain shows "A ≥ B". Fix: The result includes the "=" possibility only when no link is strict (every link is ≥ or =).
• Applying either-or incorrectly → Using either-or when conclusions aren't complementary. Fix: Either-or works only for the same pair when the two conclusions together cover every case: complementary pairs (> with ≤, < with ≥), or > with = (< with =) when the chain gives ≥ (≤).
• Decoding errors in coded inequalities → Misremembering which symbol means what. Fix: Write the code key on rough sheet before solving. Never decode mentally.
• Reversing the chain direction → Checking Q > P when asked about P > Q. Fix: Always trace FROM the first element TO the second element as written in the conclusion.

Quick Reference

• Same direction symbols = Definite conclusion possible
• Opposite/mixed directions = No definite relationship
• Either-or = Both false individually + complementary pair
• Decode first, solve later (for coded inequalities)
• ≥ combines with ≥, >, or = to stay definite; breaks with < or ≤
• Trace conclusion elements in exact order given

Comparison Puzzle

Overview

Comparison puzzles test your ability to arrange people or objects based on relative comparisons—who is taller, older, scored more marks, or weighs more. Instead of giving exact values, the question provides statements like "A is shorter than B" or "C scored more than D but less than E." Your task is to deduce a complete ranking from these scattered clues.

They're considered moderate difficulty—easier than seating arrangements but trickier than direct inequalities. Mastering this topic gives you quick, accurate marks because the logic is straightforward once you develop a systematic approach.

The key skill here is translating verbal comparisons into a consistent notation (greater-than/less-than symbols) and building a single ordered chain. Speed comes from practice and avoiding the trap of re-reading statements multiple times.

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Key Concepts

• Relative ranking, not absolute values: You're finding positions (1st, 2nd, 3rd), not actual heights or ages. "A is taller than B" means A ranks higher than B in the height order.
• Consistent direction: Always convert statements to one direction—either "greater than" (>) or "less than" (<). Mixing directions causes confusion. Pick one and stick to it throughout a problem.
• Transitive property: If A > B and B > C, then A > C. This is the backbone of comparison puzzles—use it to connect disconnected clues.
• Anchor elements: Look for people who appear in multiple comparisons. They act as bridges connecting different parts of the chain.
• Boundary markers: Identify who is "tallest" or "shortest" first. Statements like "No one is taller than X" or "Y scored the least" lock positions immediately.
• Handling ties: Unless explicitly stated ("A and B scored equal marks"), assume no ties exist.
• Negative statements matter: "A is not the tallest" eliminates one possibility. "Only two people are shorter than B" fixes B's position precisely.

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Formulas / Key Facts

• Standard notation: Use > for "more than/taller than/older than" and < for "less than/shorter than/younger than."
• "Only n people" clue: "Only 2 people are taller than X" means X is in position 3 from the top (2 people above X).
• "As many above as below": If equal number of people rank above and below X, then X is in the middle position. For 7 people, X is 4th.
• Difference clues: "A is 3 positions above B" means if B is 6th, A is 3rd.
• Combining chains: When you have A > B > C and D > B > E, merge them at the common element (B) to form: A/D > B > C/E, then resolve A vs D and C vs E using other clues.
• Total positions = Total people: In a comparison of 6 people, ranks are 1 through 6 with no gaps.

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Worked Examples

Example 1: Height Comparison

Question: Six friends—P, Q, R, S, T, U—have different heights. R is taller than Q but shorter than P. S is the tallest. T is taller than U but shorter than Q. Only three people are shorter than R. Who is the shortest?

Solution:

Step 1: Convert each statement to > notation.

• R > Q, P > R → P > R > Q
• S is tallest → S is at position 1
• T > U, Q > T → Q > T > U

Step 2: Combine chains using common elements.

• Chain 1: P > R > Q
• Chain 2: Q > T > U
• Combined: P > R > Q > T > U

Step 3: Apply "only three shorter than R."

• Three people below R means R is 4th from bottom, i.e., position 3 from top (in 6 people).
• Current chain: P > R > Q > T > U (5 people)
• S is tallest, so: S > P > R > Q > T > U

Step 4: Verify R's position.

• S(1) > P(2) > R(3) > Q(4) > T(5) > U(6)
• People shorter than R: Q, T, U = 3 people. This matches the clue.

Step 5: Final order.

• S is 1st. P > R > Q and Q > T > U gives: P > R > Q > T > U
• Insert S at top: S > P > R > Q > T > U
• R is 3rd; people shorter than R = Q, T, U = 3 people.
• Final order: S > P > R > Q > T > U, and U is shortest.

Answer: U is the shortest.

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Example 2: Marks Comparison

Question: Among five students A, B, C, D, E, each scored different marks. B scored more than C. A scored less than D but more than B. E scored the least. Who scored the highest?

Solution:

Step 1: Convert to symbols.

• B > C
• D > A > B
• E is last (lowest scorer)

Step 2: Build the chain.

• D > A > B > C
• E is at the bottom

Step 3: Where does E fit?

• Since E scored least: D > A > B > C > E

Step 4: Answer.

• Highest scorer: D

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Common Mistakes

• Reversing the direction mid-problem: You read "A is shorter than B" and write A > B (thinking A's rank is higher). Fix: Decide upfront—if comparing heights, taller = higher rank, so B > A.
• Ignoring "only" in clues: "Only 3 people are older" is different from "3 people are older." "Only" often implies exactly that number. Fix: Treat "only n" as a precise count.
• Not merging chains at common elements: You solve two separate chains but forget to combine them using a shared person. Fix: Always look for overlapping names and connect chains.
• Misreading superlatives: "A is not the tallest" doesn't mean A is shortest—it just eliminates position 1 for A. Fix: Cross out one possibility, don't assume the opposite extreme.
• Skipping verification: You build a chain and move to questions without checking if it satisfies all clues. Fix: Spend 10 seconds re-reading each clue against your final order.

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Quick Reference

• Convert all statements to one direction (> or <) immediately.
• "Only n people above X" → X is at position (n + 1).
• Find boundary elements (tallest/shortest) first—they anchor your chain.
• Merge chains at common names using transitivity.
• No ties unless explicitly stated.
• Always verify final order against every clue before answering questions.

Coding-Decoding

Overview

This topic tests your ability to identify hidden patterns in how letters, numbers, or symbols are transformed according to a specific rule. The examiner encodes a word using a particular logic, and you must crack that logic to decode new words or find the code for given words.

The beauty of this topic lies in its predictability—once you recognize the pattern type, solving becomes mechanical. However, the trap is overthinking simple patterns or missing subtle variations. Mastering coding-decoding requires pattern recognition speed rather than complex reasoning, making it an easy scoring area if you practice the common types systematically.

For SBI Clerk level, expect straightforward single-rule or two-rule patterns. The questions are designed to be solved in 30–45 seconds each, so quick identification of the coding logic is essential.

Key Concepts

• Letter Shifting: Each letter moves forward or backward in the alphabet by a fixed number (e.g., A→C means +2 shift). The shift can be uniform or positional (1st letter +1, 2nd letter +2, etc.).
• Reverse Order Coding: The letters of the word are simply written in reverse order, sometimes combined with a shift.
• Opposite Letter Coding: Each letter is replaced by its opposite in the alphabet (A↔Z, B↔Y, C↔X). Remember: Letter + Opposite = 27.
• Position-Based Coding: Letters are replaced by their alphabetical position numbers (A=1, B=2... Z=26) or vice versa.
• Symbol/Number Substitution: Letters are replaced by symbols or numbers following a consistent pattern across all given examples.
• Vowel-Consonant Rules: Different rules apply to vowels and consonants—vowels might shift +1 while consonants shift -1.
• New Pattern Coding: A sentence-based format where you deduce word-code pairs by comparing multiple coded sentences to find common elements.

Formulas / Key Facts

Alphabet Position Reference (memorize this):

• A=1, B=2, C=3... L=12, M=13, N=14... Z=26
• Quick check: E=5, J=10, O=15, T=20

Opposite Letter Pairs (sum = 27):

• A↔Z, B↔Y, C↔X, D↔W, E↔V, F↔U, G↔T, H↔S, I↔R, J↔Q, K↔P, L↔O, M↔N

EJOTY Technique: E=5, J=10, O=15, T=20, Y=25 — use these as reference points to quickly find any letter's position.

Forward/Backward Shift Rule: If shifting forward from Z, continue from A (cyclic). Z+2 = B.

Pattern Identification Order: First check reversal → then opposite letters → then uniform shift → then positional shift → then vowel/consonant rules.

Sentence Coding Logic: If two sentences share one common word and one common code, that code represents that word.

Worked Examples

Example 1: Letter Shifting

If COME is coded as DPNF, how is BACK coded?

Step 1: Compare each letter pair

• C→D (+1), O→P (+1), M→N (+1), E→F (+1)

Step 2: Pattern identified — each letter shifts +1

Step 3: Apply to BACK

• B+1=C, A+1=B, C+1=D, K+1=L

Answer: CBDL

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Example 2: Opposite Letter Coding

If TIGER is coded as GRTVI, how is LION coded?

Step 1: Check each letter

• T(20)→G(7): 20+7=27 ✓ (opposites)
• I(9)→R(18): 9+18=27 ✓
• G(7)→T(20): 7+20=27 ✓
• E(5)→V(22): 5+22=27 ✓
• R(18)→I(9): 18+9=27 ✓

Step 2: Pattern — opposite letters

Step 3: Apply to LION

• L(12)→O(15)? Yes, 12+15=27. Opposite of L(12) is O(15)? Check: 12+15=27 ✓
• L→O, I→R, O→L, N→M

Answer: ORLM

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Example 3: New Pattern (Sentence-Based)

Given:

• 'sky is blue' → 'ra ta na'
• 'blue is bright' → 'na pa ta'
• 'bright sky high' → 'pa sa ra'

What is the code for 'blue'?

Step 1: Compare sentences 1 and 2

• Common words: 'is', 'blue'
• Common codes: 'na', 'ta'

Step 2: Compare sentences 2 and 3

• Common word: 'bright'
• Common code: 'pa'
• So 'bright' = 'pa'

Step 3: From sentence 2, remaining after removing 'bright/pa':

• 'blue is' = 'na ta'

Step 4: Compare sentences 1 and 3

• Common word: 'sky'
• Common code: 'ra'
• So 'sky' = 'ra'

Step 5: From sentence 1, removing 'sky/ra':

• 'is blue' = 'ta na'
• But 'is' and 'blue' both appear only in sentences 1 and 2, and so do 'ta' and 'na', so these sentences cannot tell which of the two codes is 'blue'

Answer: Cannot be determined ('na' or 'ta')

Common Mistakes

• Assuming uniform shift without checking all letters → Always verify the pattern holds for every letter in the given example before applying.
• Forgetting cyclic nature of alphabet → When Z+3 is needed, count Z→A→B→C, answer is C, not stuck at Z.
• Confusing opposite letter calculation → Don't subtract from 26; the sum of positions equals 27. Opposite of C(3) is X(24) because 3+24=27.
• Rushing sentence-based coding → Carefully track which words appear in which sentences. Make a small table: write words in rows, sentences in columns, tick marks for presence.
• Ignoring reversal before shift → Some codes first reverse the word, then apply a shift. If direct shift doesn't work, try reverse+shift.

Quick Reference

• Opposite letters always sum to 27: A(1)+Z(26)=27
• EJOTY: E=5, J=10, O=15, T=20, Y=25 — your anchor points
• First check: Is it simply reversed? Then check opposite letters. Then check shifts.
• Positional shift pattern: 1st letter +1, 2nd letter +2, 3rd letter +3...
• Sentence coding: Find common word between two sentences = find common code
• When stuck, write out both alphabets (A-Z and Z-A) on rough sheet for quick reference

Blood Relations

Overview

The questions test your ability to decode family relationships from verbal descriptions or coded statements. Mastering this topic requires understanding standard relationship terms and building quick mental family trees.

The challenge lies not in complex logic but in careful reading—many students lose marks by confusing maternal/paternal sides or misreading "pointing to a photograph" statements. Since these questions have definitive answers once the tree is correctly drawn, they offer reliable marks if you practice the standard patterns.

Success demands two skills: memorizing the relationship matrix (who is what to whom) and developing a consistent notation system for sketching family trees rapidly during the exam.

Key Concepts

• Generation Levels: Family members exist at different generations. Parents are one level above you (+1), grandparents two levels up (+2), children one level below (−1), and so on. Siblings are at the same level (0).
• Two Family Sides: Maternal relations come through mother's side; paternal relations come through father's side. Uncle can mean father's brother (paternal) or mother's brother (maternal)—context determines which.
• The Pointing Trap: "A pointing to B says..." questions may ask the relationship of B to A or of A to B. Read the final question carefully.
• Only Child / Single Parent Clues: Statements like "X is the only son" or "Y has no siblings" eliminate possibilities and simplify the tree.
• In-Laws: Spouse relationships create in-laws. Your spouse's father is your father-in-law; your brother's wife is your sister-in-law.
• Gender Indicators: Words like son, daughter, brother, sister, nephew, niece, husband, wife directly indicate gender. Words like cousin, sibling, child, parent are gender-neutral.
• Coded Blood Relations: Some questions replace relationship words with symbols (e.g., A + B means A is father of B). Decode the legend first, then build the tree.

Key Facts

Quick Gender Reference:

• Male: father, son, brother, husband, nephew, uncle, grandfather
• Female: mother, daughter, sister, wife, niece, aunt, grandmother
• Neutral: parent, child, cousin, sibling, spouse

Worked Examples

Example 1: Direct Statement Type

Question: A is the father of B. C is the daughter of B. D is the wife of A. How is D related to C?

Solution:

• Step 1: A is father of B → B is A's child
• Step 2: D is wife of A → D is B's mother
• Step 3: C is daughter of B → C is grandchild of A and D
• Step 4: D to C relationship → D is C's grandmother

Answer: D is the grandmother of C.

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Example 2: Pointing to Photograph Type

Question: Pointing to a photograph, Ramesh said, "She is the daughter of the only son of my grandfather." How is the girl in the photograph related to Ramesh?

Solution:

• Step 1: Ramesh's grandfather's only son → Ramesh's father (since "only son" means no uncles)
• Step 2: Daughter of Ramesh's father → Ramesh's sister

Answer: The girl is Ramesh's sister.

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Example 3: Coded Blood Relations

Question: If A + B means A is the mother of B, A − B means A is the brother of B, A × B means A is the father of B, then what does P × Q + R − S mean?

Solution:

• Step 1: Decode left to right
• P × Q → P is father of Q
• Q + R → Q is mother of R
• R − S → R is brother of S
• Step 2: Build the tree:
  • P (male) is the father of Q (female)
  • Q is mother of R and S
  • R is male (brother), S's gender unknown
• Step 3: P is the maternal grandfather of both R and S

Answer: P is the maternal grandfather of S, and S is P's grandchild.

Common Mistakes

Confusing "pointing to" direction → In "A pointing to B says...", the question may ask about B's relation to A or A's relation to B. Students often reverse this. Fix: Identify who is pointing and who is being pointed to before solving.

Assuming gender without evidence → "A is the child of B" doesn't tell you A's gender. Students assume male by default. Fix: Mark unknown genders with a question mark and wait for more clues.

Missing "only" qualifiers → "Only son" means no brothers exist; "only child" means no siblings at all. Ignoring these words creates phantom family members. Fix: Circle words like "only," "no other," "single" when reading.

Confusing maternal/paternal → Mother's brother is maternal uncle, not paternal. Students mix these up, especially under time pressure. Fix: Write M or P next to each relation as you build the tree.

Jumping to conclusions in coded problems → Students decode symbols mentally without writing, then make errors. Fix: Always write out the meaning of each symbol before building the tree.

Quick Reference

• Draw the tree vertically: grandparents on top, grandchildren at bottom
• Use symbols: □ for male, ○ for female, — for marriage, | for parent-child
• "Only son/daughter" eliminates siblings on that side
• In pointing questions: check whether the question asks the pointed person's relation to the speaker or the speaker's relation to that person
• Spouse's parent = your in-law; sibling's spouse = your in-law
• When stuck, work backward from what you need to find

Direction and Distance

Overview

These problems test your spatial reasoning ability — tracking a person's movements through compass directions and calculating final positions or shortest distances.

The topic requires no complex formulas, just a clear mental picture of the compass and systematic tracking of movements. Students who master the basic compass layout and develop a habit of drawing quick diagrams can solve these questions in under 60 seconds, making it an excellent time-saver in the exam.

Success here depends on two skills: knowing direction changes (left/right turns from any starting direction) and applying the Pythagorean theorem for shortest distance. Both are straightforward once you build the right mental framework.

Key Concepts

• The Eight-Point Compass: North, South, East, West are cardinal directions. Northeast, Northwest, Southeast, Southwest are intermediate directions at 45° angles.
• Opposite Directions: North↔South, East↔West, NE↔SW, NW↔SE. If someone faces North and turns 180°, they face South.
• Right Turn Rule: Turning right from any direction moves you clockwise — North→East→South→West→North.
• Left Turn Rule: Turning left moves you anticlockwise — North→West→South→East→North.
• Shortest Distance: The straight-line distance between start and end points, calculated using the Pythagorean theorem when movements form a right angle.
• Shadow and Sun Direction: Before noon, shadows fall towards West (sun in East). After noon, shadows fall towards East (sun in West). At noon, shadows are shortest, falling towards the North in India.
• Displacement vs Distance Travelled: Total distance is the sum of all movements. Displacement (shortest distance) is the direct line from start to finish.

Formulas / Key Facts

Shortest Distance Formula (Right-angled path): Shortest Distance = √(horizontal distance² + vertical distance²)

90° Turn Conversions:

• Facing North + Right turn = Facing East
• Facing North + Left turn = Facing West
• Facing East + Right turn = Facing South
• Facing East + Left turn = Facing North
• Facing South + Right turn = Facing West
• Facing South + Left turn = Facing East
• Facing West + Right turn = Facing North
• Facing West + Left turn = Facing South

45° Turn Results:

• North + 45° Right = Northeast
• North + 45° Left = Northwest

Shadow Rules:

• Sunrise (6 AM): Sun in East, shadow towards West
• Sunset (6 PM): Sun in West, shadow towards East
• Shadow points towards you = You face the sun's direction

Key Distances:

• √2 ≈ 1.41, √3 ≈ 1.73, √5 ≈ 2.24 (useful for quick calculations)

Worked Examples

Example 1: Basic Direction Tracking

Ravi starts from point A, walks 5 km North, turns right and walks 3 km, then turns right again and walks 5 km. In which direction is he from point A?

Solution:

• Start at A, walk 5 km North → reaches B
• Turn right (now facing East), walk 3 km → reaches C
• Turn right (now facing South), walk 5 km → reaches D

Draw this: The 5 km North and 5 km South cancel out vertically. He is now directly East of A.

Answer: East

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Example 2: Shortest Distance Calculation

Priya walks 8 km East from her house, then turns left and walks 6 km. What is the shortest distance between her current position and her house?

Solution:

• Walks 8 km East (horizontal movement)
• Turns left from East = faces North
• Walks 6 km North (vertical movement)

The path forms a right angle. Shortest distance = √(8² + 6²) = √(64 + 36) = √100 = 10 km

Answer: 10 km

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Example 3: Shadow-Based Direction

One morning, Ajay was walking. His shadow fell to his right. Which direction was he facing?

Solution:

• Morning = Sun in East
• Shadow falls opposite to sun = Shadow towards West
• If shadow is to his right, West is on his right
• When West is on your right, you are facing South

Answer: South

Common Mistakes

Mistake 1: Confusing left/right turns with compass directions Wrong thinking: "Turn right means go East" Correct fix: Right turn is relative to current facing direction. If facing South and turning right, you now face West, not East.

Mistake 2: Forgetting to track net displacement Wrong thinking: Adding all distances without considering opposite movements cancel out Correct fix: Calculate net North-South displacement separately from net East-West displacement, then apply Pythagorean theorem.

Mistake 3: Shadow direction errors Wrong thinking: "Shadow falls towards the sun" Correct fix: Shadow falls opposite to the sun. Morning sun in East means shadow towards West.

Mistake 4: Mixing up 45° and 90° turns Wrong thinking: Treating "turns slightly right" same as "turns right" Correct fix: A 45° turn from North-right gives Northeast, while a 90° turn gives East. Read the question carefully for turn angles.

Mistake 5: Not drawing diagrams Wrong thinking: Solving mentally to save time Correct fix: A quick sketch takes 10 seconds but prevents errors. Always draw for problems with 3+ movements.

Quick Reference

• Compass clockwise: N → NE → E → SE → S → SW → W → NW → N
• Right turn = Clockwise 90°; Left turn = Anticlockwise 90°
• Shortest distance = √(x² + y²) where x and y are net perpendicular displacements
• Morning shadow points West; Evening shadow points East
• Always draw a rough diagram — start with North pointing up
• 3-4-5, 5-12-13, 8-15-17 are common Pythagorean triplets in exams

Order and Ranking

Overview

The concept is straightforward: you're given information about a person's position in a row, queue, or list (from top/bottom, left/right, or both ends), and you must determine total count, exact position, or number of persons between two individuals.

This topic requires zero formulas beyond one core relationship and tests your ability to avoid silly mistakes under time pressure. Students who master the single governing equation and practice visualizing positions can solve these questions in under 30 seconds each. The key challenge isn't complexity—it's careful reading of whether ranks are "from the top" or "from the bottom" and whether positions are being interchanged.

Key Concepts

• Single-direction position: When only one position (from left/top OR right/bottom) is given, you cannot determine total count without additional information.
• Dual-direction relationship: Total = Position from Left + Position from Right − 1. This works because the person is counted in both positions, so we subtract 1 to avoid double-counting.
• Position interchange: When two people swap places, their NEW positions become each other's OLD positions. Track carefully what changes and what stays constant.
• Persons between two individuals: If Person A is at rank X and Person B is at rank Y (where X < Y), then persons between them = Y − X − 1.
• Same position from both ends: If a person's rank from top equals rank from bottom, then Total = 2 × Rank − 1 (the person sits exactly in the middle).
• "From the left" vs "From the right": These are interchangeable with "from top/bottom" or "from start/end"—the logic remains identical.
• Consecutive vs Non-consecutive: When told "A and B are consecutive," the gap between them is 0. Otherwise, calculate using the between-formula.

Formulas / Key Facts

Total persons in a row: Total = Position from Left + Position from Right − 1

Persons between two people: Between = |Position of A − Position of B| − 1

When positions are interchanged: New position of A = Old position of B New position of B = Old position of A

Middle position (odd total): Middle Rank = (Total + 1) ÷ 2

If rank from both ends is equal: Total = 2 × Rank − 1

Minimum possible total (when "or more" situations arise): Consider both possible arrangements and take the one that fits all conditions.

Worked Examples

Example 1: Basic Position Calculation

Ravi is 15th from the left end and 20th from the right end of a row. How many persons are in the row?

Solution:

• Position from left = 15
• Position from right = 20
• Total = 15 + 20 − 1 = 34 persons

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Example 2: Persons Between Two People

In a row of 40 students, Meena is 14th from the left and Seema is 18th from the right. How many students are between them?

Solution:

• Meena's position from left = 14
• Seema's position from left = 40 − 18 + 1 = 23
• Persons between = 23 − 14 − 1 = 8 students

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Example 3: Position Interchange

In a row, Amit is 12th from the left and Vijay is 18th from the right. If they interchange their positions, Amit becomes 25th from the left. Find the total number of persons.

Solution:

• After interchange, Amit takes Vijay's old position
• Amit's new position from left = 25 = Vijay's old position from left
• Vijay's old position is also 18th from right (given)

Total = 25 + 18 − 1 = 42 persons

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Example 4: Finding Persons in Middle

In a class, Rahul ranks 9th from top and 38th from bottom. How many students are in the class?

Solution: Total = 9 + 38 − 1 = 46 students

Common Mistakes

• Forgetting to subtract 1: Students often add both positions without subtracting 1, double-counting the person. → Always apply: Total = Left + Right − 1.
• Confusing "between" with "including": If asked "how many between A and B," don't count A and B themselves. → Between = |Difference| − 1.
• Misreading interchange problems: After interchange, each person takes the OTHER's position, not some new position. → Track: A goes to B's spot, B goes to A's spot.
• Not converting directions: When one position is from left and another from right, convert both to the same direction before calculating "between." → Right position = Total − Left position + 1.
• Assuming insufficient data is sufficient: A single position (only "from left") cannot determine total count. → Need position from both ends OR total given.

Quick Reference

• Total = Left Position + Right Position − 1
• Between A and B = |Position A − Position B| − 1
• Convert Right to Left: Left Position = Total − Right Position + 1
• Interchange: A's new spot = B's old spot (and vice versa)
• Same rank from both ends means person is in exact middle
• Always double-check "from top" vs "from bottom" in the question

Alphanumeric / Number Series

Overview

Alphanumeric and Number Series questions test your ability to identify patterns in sequences of numbers, letters, or symbols.

These questions come in two main formats: find the missing term (what comes next or fills a blank) and find the wrong term (identify the element that breaks the pattern). The difficulty level stays moderate—patterns are usually based on basic arithmetic operations, letter positions, or simple symbol rules. Speed matters here because these questions can be solved quickly once you spot the pattern, freeing up time for complex puzzles.

Success requires memorizing the alphabet position values (A=1, B=2... Z=26), recognizing standard number patterns instantly, and practicing mixed alphanumeric sequences where letters and numbers follow connected or independent rules.

Key Concepts

• Letter Position Values: Every letter has a numeric position (A=1, B=2, C=3... Z=26). Patterns often add, subtract, or skip based on these values. Know that M=13 (middle) and common letters like E=5, J=10, O=15, T=20.
• Number Series Patterns: Common operations include constant difference (arithmetic), constant ratio (geometric), squares/cubes, prime numbers, Fibonacci-style (sum of previous two), and alternating operations.
• Difference of Differences: When first-level differences aren't constant, check if the differences between differences form a pattern. This reveals quadratic or accelerating series.
• Alternating Series: Two independent series may be interleaved at odd and even positions. Separate them and analyze individually.
• Mixed Alphanumeric Rules: In sequences like A2, D5, G8, letters and numbers may follow the same skip pattern (+3 each) or completely independent patterns.
• Symbol Series: Symbols rotate through a fixed set or change based on position rules. Count the symbols and track which one appears where.
• Wrong Number Identification: One term breaks an otherwise consistent pattern. Test each term by checking if removing it restores the pattern.

Formulas / Key Facts

Alphabet Position Reference (memorize these anchors):

• A=1, E=5, I=9, J=10, M=13, N=14, O=15, T=20, Z=26

Common Number Patterns:

• Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
• Cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000
• Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31
• Fibonacci: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55
• Triangular: 1, 3, 6, 10, 15, 21, 28, 36

Operation Patterns to Check:

• ×2, ×3 (geometric)
• +2, +4, +6 (increasing addition)
• ×1+1, ×2+2, ×3+3 (hybrid)
• Alternating +/− or ×/÷

Letter Skip Formula: If pattern skips by k, next letter = current position + k (mod 26 if crossing Z)

Worked Examples

Example 1: Number Series (Find Missing Term) Series: 2, 6, 18, 54, ?

Step 1: Check differences: 6−2=4, 18−6=12, 54−18=36 (not constant) Step 2: Check ratios: 6÷2=3, 18÷6=3, 54÷18=3 (constant ratio of 3) Step 3: Pattern is ×3 Step 4: Next term = 54 × 3 = 162

Example 2: Letter Series Series: B, E, H, K, ?

Step 1: Convert to positions: B=2, E=5, H=8, K=11 Step 2: Find differences: 5−2=3, 8−5=3, 11−8=3 (constant +3) Step 3: Next position = 11 + 3 = 14 Step 4: Position 14 = N

Example 3: Alphanumeric Series Series: A1, C4, E9, G16, ?

Step 1: Separate letters: A, C, E, G → positions 1, 3, 5, 7 → pattern is +2 Step 2: Separate numbers: 1, 4, 9, 16 → these are 1², 2², 3², 4² Step 3: Next letter position = 7 + 2 = 9 = I Step 4: Next number = 5² = 25 Answer: I25

Example 4: Wrong Term Identification Series: 3, 7, 15, 31, 61, (find wrong term)

Step 1: Check pattern assumption: ×2+1 Step 2: Verify: 3×2+1=7 ✓, 7×2+1=15 ✓, 15×2+1=31 ✓, 31×2+1=63 ✗ (given 61) Step 3: Wrong term = 61 (should be 63)

Common Mistakes

• Assuming constant difference without checking: Students see 2, 5, 10 and assume +3, +5 pattern, missing that it could be n² + 1 series (1+1, 4+1, 9+1). → Always verify your pattern holds for ALL given terms before answering.
• Forgetting alphabet wraps around: After Z comes A again. If you're at position 24 (X) and add 5, you get 29, which equals 29−26=3=C, not some invalid letter. → Subtract 26 when position exceeds 26.
• Treating mixed series as one pattern: In A3, B5, C7, students might look for a combined rule when letters (+1 each) and numbers (+2 each) follow independent patterns. → Separate components first, analyze each, then combine.
• Rushing wrong-term questions: Students often stop checking after finding the pattern works for the first few terms. → Test EVERY term against your pattern—the wrong one could be anywhere.
• Confusing opposite letter positions: Students mix up that opposite letters sum to 27 (A+Z=1+26=27), not 26. → For opposite letter questions: opposite of letter at position n is at position 27−n.

Quick Reference

• Alphabet anchors: A=1, E=5, J=10, M=13, O=15, T=20, Z=26
• First check: constant difference → constant ratio → squares/cubes → alternating series
• Two-level difference: if differences aren't constant, take differences of differences
• Mixed alphanumeric: split letters and numbers, solve separately
• Wrong term: verify pattern against every term, not just consecutive pairs
• Letter wrap: position > 26 means subtract 26 to find actual letter

Alphabet Test / Word Formation

Overview

These are quick-solving questions designed to test your familiarity with the English alphabet's positional values and your ability to manipulate letters under given conditions.

This topic rewards students who have internalized the alphabet positions (A=1 through Z=26) and can quickly count letters, identify patterns, and form meaningful words. Since these questions carry the same marks as complex puzzles but take far less time, mastering them gives you crucial extra minutes for harder sections.

The two main question types are: (1) Alphabet-based problems involving position finding, letter counting between words, and opposite letter identification; (2) Word formation problems where you rearrange selected letters from a given word to form a meaningful English word.

Key Concepts

• Alphabet Position Values: A=1, B=2, C=3... M=13, N=14... Z=26. The midpoint falls between M(13) and N(14). Memorize these anchor points: E=5, J=10, O=15, T=20, Y=25.
• Opposite Letters: Letters equidistant from both ends sum to 27. Opposite of any letter = 27 minus its position. Example: D(4) ↔ W(23), since 4+23=27.
• Left-Right Counting: "nth letter to the left of X" means count n positions backward from X. "nth letter to the right of X" means count n positions forward.
• Letter Counting Between Positions: Letters between positions P1 and P2 = |P2 - P1| - 1. Example: Between D(4) and H(8) = 8-4-1 = 3 letters (E, F, G).
• Word Formation Logic: When asked to form a meaningful word from selected letters, first list all given letters, then mentally rearrange to identify common English words.
• Vowel-Consonant Identification: Vowels are A, E, I, O, U (positions 1, 5, 9, 15, 21). All others are consonants.
• Alphabetical/Reverse Order Arrangement: Alphabetical means A→Z order; reverse alphabetical means Z→A order. Know how to quickly sort a small set of letters.

Formulas / Key Facts

Quick Position Memory Aid:

• EJOTY = 5, 10, 15, 20, 25 (multiples of 5)
• Opposite pairs: A↔Z, B↔Y, C↔X, D↔W, E↔V, F↔U, G↔T, H↔S, I↔R, J↔Q, K↔P, L↔O, M↔N

Worked Examples

Example 1: Position-Based Question

If the letters of the word CAUTION are arranged alphabetically, which letter will be third from the right?

Step 1: List letters: C, A, U, T, I, O, N

Step 2: Arrange alphabetically: A, C, I, N, O, T, U

Step 3: Third from right: Count from U (1st), T (2nd), O (3rd)

Answer: O

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Example 2: Word Formation

If from the word TRADITIONAL, the 2nd, 3rd, 5th and 10th letters are taken, which meaningful word can be formed?

Step 1: Identify positions in TRADITIONAL

• T(1), R(2), A(3), D(4), I(5), T(6), I(7), O(8), N(9), A(10), L(11)

Step 2: Extract required letters: 2nd=R, 3rd=A, 5th=I, 10th=A

Step 3: Letters available: R, A, I, A

Step 4: Rearrange to form meaningful word: ARIA (a melody for single voice)

Answer: ARIA

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Example 3: Letter Counting

How many letters are there between the 8th letter from left and 7th letter from right in the word PERMANENT?

Step 1: Word PERMANENT has 9 letters

• P(1), E(2), R(3), M(4), A(5), N(6), E(7), N(8), T(9)

Step 2: 8th from left = N (position 8)

Step 3: 7th from right = R (position 9-7+1 = 3)

Step 4: Letters between position 3 and position 8 = 8-3-1 = 4 letters (M, A, N, E)

Answer: 4

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Example 4: Opposite Letter

What is the opposite letter of the letter which is 5th to the right of M?

Step 1: M = position 13

Step 2: 5th to right of M = 13+5 = 18 = R

Step 3: Opposite of R = 27-18 = 9 = I

Answer: I

Common Mistakes

• Confusing "between" and "from-to" → "Letters between D and H" excludes both D and H. Students often count D or H, getting 4 or 5 instead of 3. Always use formula: larger - smaller - 1.
• Left-right direction reversal → "3rd to the left of K" means going backward (K→J→I→H), not forward. Visualize physically moving left on a written alphabet line.
• Position from right miscalculation → For a word with n letters, position from right = n - position from left + 1. Students often subtract without adding 1.
• Forgetting original word order in word formation → When extracting the "3rd and 5th" letters, count from the original word as given, not after any rearrangement mentioned earlier in the question.
• Missing meaningful words → In word formation, students sometimes miss less common but valid words. If RAIN, ARIA, or similar uncommon words are possible, consider them. However, exams typically use common English words.
• Opposite letter calculation error → Students sometimes add positions instead of subtracting from 27. Remember: A(1)+Z(26)=27, so any pair must sum to 27.

Quick Reference

• EJOTY: E=5, J=10, O=15, T=20, Y=25 — your anchor positions
• Opposite letter = 27 minus position (D↔W, G↔T, M↔N)
• Letters between = bigger position - smaller position - 1
• Position from right in n-letter word = n - left position + 1
• Always re-read whether question asks "from left" or "from right"
• In word formation, list extracted letters and try common word patterns (4-letter words ending in common suffixes)