SBI Clerk flashcards
429 cards from 47 fact-checked topic notes · English
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All cards by topic
Reading Comprehension — English Language · 7 cards
- Passage-first vs Question-first approach
- For Clerk-level RC, read the passage once carefully before attempting questions. The passages are short enough that pre-reading questions wastes time.
- Question types fall into clear categories
- Direct/factual questions ask "what did the passage say," inference questions ask "what can we conclude," and vocabulary questions test word meanings in context.
- The answer is always in the passage
- Never bring outside knowledge. Even if you know something different about the topic, stick strictly to what the passage states.
- Tone and purpose matter
- Identify whether the author is positive, negative, neutral, critical, or appreciative. This helps answer main idea and inference questions.
- Elimination is your best friend
- In vocabulary and inference questions, eliminate options that contradict the passage or go beyond its scope.
- Keywords act as locators
- Names, dates, numbers, and capitalised words help you quickly locate the relevant paragraph when answering specific questions.
- "Not mentioned" is different from "false"
- Some options may be true in real life but not stated in the passage—these are incorrect choices.
Cloze Test — English Language · 12 cards
- 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.
- Typical question count
- 5–6 blanks per passage in SBI Clerk Prelims
- Time allocation
- 4–5 minutes for the entire cloze set
- Common themes
- Banking, economy, social welfare, technology, environment
- Option pattern
- Usually 5 options per blank (including "No change needed" sometimes)
- Elements tested
- Vocabulary (nouns, verbs, adjectives), prepositions, conjunctions
Error Spotting — English Language · 12 cards
- 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.)
- Agree with (person) / to (proposal)
- Agree for
- Consist of
- Consist in (different meaning)
- Different from
- Different than/to
- Prefer X to Y
- Prefer X than Y
Sentence Improvement / Phrase Replacement — English Language · 12 cards
- 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."
- Subject-Verb with "each"
- Wrong: Each of the boys were present · Correct: Each of the boys was present
- Tense shift error
- Wrong: He went to the market and buys vegetables · Correct: He went to the market and bought vegetables
- Preposition with "comply"
- Wrong: comply to the rules · Correct: comply with the rules
- Preposition with "congratulate"
- Wrong: congratulate for his success · Correct: congratulate on his success
Para Jumbles — English Language · 7 cards
- 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.
Sentence Rearrangement — English Language · 7 cards
- 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.
Fill in the Blanks — English Language · 7 cards
- 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.
Word Swap — English Language · 8 cards
- 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.
Synonyms and Antonyms — English Language · 7 cards
- 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."
Idioms and Phrases — English Language · 12 cards
- 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.
- A blessing in disguise
- Something good that initially seemed bad
- A piece of cake
- Very easy task
- Add fuel to the fire
- Worsen an already bad situation
- At the eleventh hour
- At the last possible moment
- Back to the drawing board
- Start over after failure
Spelling Check — English Language · 12 cards
- 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).
- Accommodation
- Accomodation
- Occurrence
- Occurence
- Separate
- Seperate
- Definitely
- Definately
Percentage — Numerical Ability · 12 cards
- 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%.
- x% of N = (x × N)/100
- Finding percentage of any number
- Percentage Change = [(New − Old)/Old] × 100
- Increase or decrease calculation
- Net change for a% and b% = a + b + ab/100
- Successive percentage changes
- If A is x% more than B, then B is [100x/(100+x)]% less than A
- Reversal problems
- If A is x% less than B, then B is [100x/(100−x)]% more than A
- Reversal problems
Tabular DI — Numerical Ability · 7 cards
- 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.
Simplification and Approximation — Numerical Ability · 8 cards
- 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.
Ratio and Proportion — Numerical Ability · 8 cards
- 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).
Bar Graph DI — Numerical Ability · 12 cards
- 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.
- Percentage increase
- [(Final − Initial) / Initial] × 100
- Percentage decrease
- [(Initial − Final) / Initial] × 100
- Percentage contribution
- [Value of part / Total] × 100
- Ratio
- Value A : Value B (simplify by HCF)
- Difference
- Value A − Value B
Number Series — Numerical Ability · 12 cards
- 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).
- Constant Addition
- How to Identify: Same difference throughout · Example: 5, 12, 19, 26 → difference is +7
- Constant Multiplication
- How to Identify: Same ratio throughout · Example: 3, 12, 48, 192 → ratio is ×4
- Increasing Difference
- How to Identify: Differences increase by fixed value · Example: 2, 4, 8, 14, 22 → differences: 2, 4, 6, 8
- Square Addition
- How to Identify: Add consecutive squares · Example: 1, 2, 6, 15, 31 → add 1, 4, 9, 16
Pie Chart DI — Numerical Ability · 11 cards
- 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.
- Degrees → Percentage
- (Angle / 360) × 100
- Percentage → Degrees
- (Percentage / 100) × 360
- Sector Value
- (Percentage / 100) × Total
- Sector Value (from angle)
- (Angle / 360) × Total
Quadratic Equations — Numerical Ability · 6 cards
- 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).
Profit and Loss — Numerical Ability · 7 cards
- 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.
Data Interpretation — Numerical Ability · 8 cards
- 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.
Line Graph DI — Numerical Ability · 7 cards
- 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.
Arithmetic — Numerical Ability · 8 cards
- 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.
Simple and Compound Interest — Numerical Ability · 9 cards
- 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.
- 5%
- 1.1025
- 10%
- 1.21
- 15%
- 1.3225
- 20%
- 1.44
Caselet DI — Numerical Ability · 7 cards
- 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.
Time and Work — Numerical Ability · 7 cards
- 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.
Permutation and Combination — Numerical Ability · 7 cards
- 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.
Time, Speed and Distance — Numerical Ability · 12 cards
- 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.
- Speed = Distance / Time
- Core formula—memorize all three rearrangements
- km/hr to m/s: multiply by 5/18
- 72 km/hr = 72 × 5/18 = 20 m/s
- m/s to km/hr: multiply by 18/5
- 25 m/s = 25 × 18/5 = 90 km/hr
- Relative speed (same direction) = S₁ − S₂
- Faster object catching up with slower
- Relative speed (opposite direction) = S₁ + S₂
- Objects approaching each other
Probability — Numerical Ability · 8 cards
- 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.
Mixture and Alligation — Numerical Ability · 6 cards
- 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.
Mensuration — Numerical Ability · 11 cards
- 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.
- Units matter
- Area uses square units (cm², m²), Volume uses cubic units (cm³, m³). Converting between units requires squaring or cubing the conversion factor.
- Square (side a)
- Perimeter: 4a · Area: a²
- Rectangle (l × b)
- Perimeter: 2(l + b) · Area: l × b
- Circle (radius r)
- Perimeter: 2πr · Area: πr²
- Triangle (sides a, b, c)
- Perimeter: a + b + c · Area: ½ × base × height
- Equilateral Triangle (side a)
- Perimeter: 3a · Area: (√3/4) × a²
- Right Triangle (legs a, b)
- Perimeter: a + b + √(a² + b²) · Area: ½ × a × b
- Parallelogram (base b, height h)
- Perimeter: 2(a + b) · Area: b × h
- Trapezium (parallel sides a, b; height h)
- Perimeter: a + b + c + d · Area: ½ × (a + b) × h
Partnership — Numerical Ability · 7 cards
- 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.
Number System — Numerical Ability · 9 cards
- 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.
- 11
- Difference of sum of alternate digits divisible by 11
Puzzles — Reasoning Ability · 12 cards
- 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.
- Floor Puzzle
- What to Determine: Who lives on which floor (numbered 1 to n) · Common Constraint Words: Above, below, immediately above, gap of two floors
- Day/Month Scheduling
- What to Determine: Who is assigned to which day or month · Common Constraint Words: Before, after, on Monday, not on adjacent days
- Box/Stack Puzzle
- What to Determine: Order of boxes from top to bottom · Common Constraint Words: On top of, below, immediately below, at the bottom
- Comparison Puzzle
- What to Determine: Rank persons by age, height, marks · Common Constraint Words: Older than, shorter than, between X and Y
Floor Puzzle — Reasoning Ability · 12 cards
- 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.
- Immediately above
- Exactly one floor higher (consecutive)
- Immediately below
- Exactly one floor lower (consecutive)
- Above
- Any higher-numbered floor
- Below
- Any lower-numbered floor
Linear Arrangement — Reasoning Ability · 12 cards
- 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).
- Total positions
- Equal to number of persons (n)
- "X is second to the left of Y"
- X's position = Y's position − 2
- "X is third to the right of Y"
- X's position = Y's position + 3
- "Exactly two persons between A and B"
- Gap of 2 positions → A and B are 3 positions apart
Seating Arrangement — Reasoning Ability · 11 cards
- 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.
- Linear facing North
- Left = West, Right = East
- Linear facing South
- Left = East, Right = West
- Circular facing center
- Clockwise = Left of the person
- Circular facing outside
- Clockwise = Right of the person
Circular Arrangement — Reasoning Ability · 8 cards
- 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.
Syllogism — Reasoning Ability · 11 cards
- 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.
- All A are B
- Standard Form: A ⊆ B · Venn Representation: Circle A inside Circle B
- No A is B
- Standard Form: A ∩ B = ∅ · Venn Representation: Circles don't touch
- Some A are B
- Standard Form: A ∩ B ≠ ∅ · Venn Representation: Circles partially overlap
- Some A are not B
- Standard Form: Part of A outside B · Venn Representation: A not fully inside B
Inequalities — Reasoning Ability · 12 cards
- 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.
- > with >
- Result: > · Definite?: Yes
- < with <
- Result: < · Definite?: Yes
- > with ≥
- Result: > · Definite?: Yes
- < with ≤
- Result: < · Definite?: Yes
- ≥ with ≥
- Result: ≥ · Definite?: Yes
Comparison Puzzle — Reasoning Ability · 7 cards
- 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.
Coding-Decoding — Reasoning Ability · 7 cards
- 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.
Blood Relations — Reasoning Ability · 12 cards
- 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.
- Sibling
- Brother or sister (same parents)
- Cousin
- Child of uncle or aunt
- Nephew
- Brother's or sister's son
- Niece
- Brother's or sister's daughter
- Father-in-law
- Spouse's father
Direction and Distance — Reasoning Ability · 7 cards
- 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.
Order and Ranking — Reasoning Ability · 7 cards
- 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.
Alphanumeric / Number Series — Reasoning Ability · 7 cards
- 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.
Alphabet Test / Word Formation — Reasoning Ability · 12 cards
- 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.
- Position from left
- A=1, B=2, ... Z=26
- Position from right
- A=26, B=25, ... Z=1
- Opposite letter position
- 27 - position
- Letters between two positions
- Larger position - Smaller position - 1
- nth letter to right of X
- Position of X + n