IBPS Clerk flashcards
358 cards from 37 fact-checked topic notes · English
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Reading Comprehension — English Language · 7 cards
- Passage Types
- Factual/informational passages dominate (banking schemes, social welfare, environmental issues). Occasional narrative or opinion-based passages appear but are rare.
- Direct vs. Inference Questions
- Clerk Prelims heavily favors direct questions where the answer is stated explicitly in the passage. Inference questions (requiring you to conclude something unstated) are fewer and simpler than in PO.
- Question Categories
- Expect five main types—main idea/title, detail-based (fact retrieval), vocabulary (synonym/antonym in context), tone/attitude of author, and true/false statements.
- Contextual Vocabulary
- Word-meaning questions ask for the meaning as used in the passage, not the dictionary definition. A word like "check" might mean "verify" in one passage and "stop" in another.
- Elimination Strategy
- Options are often designed with one clearly wrong, two partially correct, and one fully correct answer. Eliminating the obviously wrong choices first saves time.
- Referencing Pronouns
- Questions often test whether you can identify what "it," "they," or "this" refers to in a sentence. Trace back to the nearest logical noun.
- Author's Tone
- Limited to simple tones at Clerk level—informative, critical, optimistic, concerned, neutral. Extreme tones (sarcastic, cynical) are rarely tested.
Cloze Test — English Language · 7 cards
- Context is king
- The correct answer must fit the meaning of the entire paragraph, not just the sentence containing the blank. Read at least one sentence before and after each blank.
- Grammar agreement
- The word must agree with the subject in number (singular/plural) and tense. A verb blank following "he" cannot be "are" or "were" if present tense is needed.
- Collocation awareness
- Some words naturally pair together (make a decision, not do a decision; heavy rain, not strong rain). Collocations often distinguish the correct answer from close alternatives.
- Tone consistency
- If the passage is formal, slang or casual words are wrong. If the passage discusses a problem, a word suggesting a solution may not fit unless the paragraph shifts direction.
- Transition signals
- Words like however, therefore, moreover, despite signal logical relationships. A blank following "however" likely needs a word that contrasts with the previous idea.
- Part of speech identification
- Determine whether the blank needs a noun, verb, adjective, adverb, or preposition. This eliminates 2–3 options immediately in many cases.
- Elimination strategy
- When unsure, remove options that are grammatically impossible or contextually absurd. Often, you can narrow down to two choices, then re-read for nuance.
Error Spotting — English Language · 12 cards
- Subject-Verb Agreement
- The verb must match the subject in number (singular/plural). Intervening phrases between subject and verb are designed to confuse you.
- Tense Consistency
- A sentence should maintain the same tense throughout unless there's a clear reason to shift. Watch for sudden switches from past to present.
- Pronoun-Antecedent Agreement
- Pronouns must match their antecedents in number and gender. "Each," "everyone," and "everybody" take singular pronouns.
- Correct Preposition Usage
- Many verbs and adjectives pair with specific prepositions. "Interested in" (not "interested for"), "consists of" (= is made up of; "consists in" = lies in).
- Article Rules
- Use "a" before consonant sounds, "an" before vowel sounds. Unique or superlative nouns take "the." Abstract/uncountable nouns often take no article.
- Parallel Structure
- Items in a list or comparison must follow the same grammatical form. "She likes reading, writing, and to swim" is incorrect.
- Correct Word Form
- Adjectives describe nouns; adverbs describe verbs. "He runs quick" should be "He runs quickly."
- Comparison Errors
- Use "than" with comparatives, not "to." Avoid double comparatives like "more better."
- Subject-Verb with "and"
- Wrong: Ram and Shyam is going · Correct: Ram and Shyam are going
- Subject-Verb with "or/nor"
- Wrong: Neither he nor they is · Correct: Neither he nor they are (verb follows nearest subject)
- Collective nouns
- Wrong: The team are playing well · Correct: The team is playing well
- Each/Every/Everyone
- Wrong: Everyone have arrived · Correct: Everyone has arrived
Sentence Improvement / Phrase Replacement — English Language · 12 cards
- Subject-Verb Agreement
- The verb must match the subject in number. Intervening phrases between subject and verb are common traps ("The list of items is ready" not "are ready").
- Tense Consistency
- A sentence should maintain logical tense flow. Mixing past and present without reason is the most common error pattern.
- Correct Preposition Usage
- Many verbs and adjectives take specific prepositions. "Comply *with*" not "comply to"; "different *from*" not "different than."
- Pronoun-Antecedent Agreement
- Pronouns must agree in number and gender with what they refer to. "Each student must bring his/her book" not "*their* book" (in formal usage).
- Parallelism
- Items in a list or comparison must follow the same grammatical structure. "She likes reading, writing, and *swimming*" not "to read, writing, and swim."
- Modifier Placement
- Adjectives and adverbs must be placed near what they modify. Misplaced modifiers create absurd meanings.
- Redundancy and Wordiness
- Phrases like "return back," "repeat again," "free gift" are redundant. The correct answer is always the more concise option.
- Correct Conjunction Usage
- Know the difference between "although/but," "not only...but also," "neither...nor," and when each applies.
- Subject-Verb with "one of"
- Wrong Usage: One of the boys are late · Correct Usage: One of the boys is late
- Collective nouns
- Wrong Usage: The team are playing well · Correct Usage: The team is playing well
- "Neither...nor" agreement
- Wrong Usage: Neither he nor I are wrong · Correct Usage: Neither he nor I am wrong
- Past perfect for earlier action
- Wrong Usage: He reached after she left · Correct Usage: He reached after she had left
Fill in the Blanks — English Language · 11 cards
- Context is king
- Every sentence contains clues — positive/negative tone, cause-effect relationships, contrast markers — that point toward the correct answer. Never guess without analyzing context first.
- Tone matching
- If the sentence describes something negative (failure, decline, criticism), the blank likely needs a negative word. Positive contexts need positive words. Mismatched tone = wrong answer.
- Grammar filters first
- Before meaning, check if the blank needs a noun, verb, adjective, or adverb. This eliminates 1–2 options instantly in most questions.
- Collocations matter
- Certain words naturally pair together ("make a decision" not "do a decision"). Bank exams frequently test these fixed expressions.
- Double-blank strategy
- Both words must fit perfectly. If even one word in an option feels wrong, eliminate the entire option.
- Contrast and continuation markers
- Words like "although," "despite," "however" signal contrast (opposite ideas). Words like "moreover," "therefore," "consequently" signal continuation (similar ideas).
- Elimination over selection
- When unsure, eliminate clearly wrong options. Even removing two options improves your odds dramatically.
- Although, Despite, However
- Meaning: Contrast · Blank Direction: Opposite to main clause
- Therefore, Hence, Consequently
- Meaning: Result · Blank Direction: Same direction as cause
- Moreover, Furthermore, Additionally
- Meaning: Addition · Blank Direction: Same tone continues
- Rather than, Instead of
- Meaning: Replacement · Blank Direction: Opposite of what follows
Idioms, Phrases and Spelling — English Language · 12 cards
- Idiom = fixed expression with non-literal meaning.
- "Kick the bucket" means to die, not to physically kick anything. You cannot alter words or guess meaning from components.
- Phrase = group of words functioning as a unit.
- Phrases may be literal ("in the morning") or semi-idiomatic ("in the nick of time"). Exam questions often blur the line, so treat both as vocabulary items to memorise.
- Context determines correct idiom.
- Many idioms sound similar but differ in meaning—"a piece of cake" (easy task) vs "have your cake and eat it too" (want incompatible things).
- Spelling follows patterns, not strict rules.
- Learn pattern families: words ending in -ible vs -able, -ance vs -ence, -tion vs -sion. Exceptions exist.
- Homophones cause spelling errors in context.
- "Principal" vs "principle," "stationary" vs "stationery"—the word may be spelled correctly but wrong for the sentence.
- British spelling is standard for Indian bank exams.
- Use "colour" not "color," "honour" not "honor," "travelled" not "traveled."
- Accommodation
- Accomodation
- Occurrence
- Occurence
- Separate
- Seperate
- Definitely
- Definately
- Necessary
- Neccessary
- Receive
- Recieve
Word Usage / One-word Substitution — English Language · 12 cards
- Context is king
- The grammatically correct word must also fit the sentence's meaning. Always read the full sentence before choosing.
- Parts of speech matter
- Many errors come from confusing a noun with a verb or adjective. "Advice" is a noun; "advise" is a verb. Know which form the sentence needs.
- Confusables are predictable
- Exams recycle the same commonly confused pairs—stationary/stationery, principal/principle, emigrate/immigrate. Master the top 50 pairs.
- One-word substitutions follow patterns
- Words often share roots (e.g., "-cide" means killing, "-phobia" means fear). Learning roots helps you decode unfamiliar words.
- Collocations test natural English
- Some words simply "go together"—we say "make a decision" not "do a decision." Native-like combinations are tested indirectly.
- Elimination speeds you up
- If you're unsure, eliminate options that are clearly wrong in meaning or grammar, then choose from what remains.
- Affect (verb)
- Word 2: Effect (noun/verb) · Difference: Affect = to influence; Effect = result (noun) or to bring about (verb)
- Accept
- Word 2: Except · Difference: Accept = receive; Except = excluding
- Principal
- Word 2: Principle · Difference: Principal = head/main/capital; Principle = rule/belief
- Stationary
- Word 2: Stationery · Difference: Stationary = not moving; Stationery = paper/pens
- Compliment
- Word 2: Complement · Difference: Compliment = praise; Complement = complete
- Eminent
- Word 2: Imminent · Difference: Eminent = famous; Imminent = about to happen
Percentage — Numerical Ability · 12 cards
- Basic Definition
- Percentage means "per hundred." If 25 out of 100 students pass, the pass percentage is 25%. Formula: (Part / Whole) × 100.
- Fraction-Percentage Equivalence
- Every fraction has a percentage equivalent. Memorizing these (1/2 = 50%, 1/4 = 25%, 1/5 = 20%, etc.) eliminates calculation time.
- Percentage Change
- When a value increases or decreases, percentage change = (Change / Original) × 100. Always use the original value as the base, not the new value.
- Successive Percentage Change
- When two percentage changes occur one after another, they don't simply add up. Use the net effect formula: a + b + (ab/100).
- Percentage of a Percentage
- Finding "20% of 30% of 500" means multiplying sequentially: 0.20 × 0.30 × 500.
- Reverse Percentage
- If a value after 20% increase is 600, the original = 600 / 1.20 = 500. Work backward using multipliers.
- Base Matters
- "A is 25% more than B" and "B is 25% less than A" are NOT the same. The base changes the calculation entirely.
- 1/2
- Percentage: 50% · Fraction: 1/8 · Percentage: 12.5%
- 1/3
- Percentage: 33.33% · Fraction: 1/9 · Percentage: 11.11%
- 1/4
- Percentage: 25% · Fraction: 1/10 · Percentage: 10%
- 1/5
- Percentage: 20% · Fraction: 1/11 · Percentage: 9.09%
- 1/6
- Percentage: 16.67% · Fraction: 1/12 · Percentage: 8.33%
Tabular DI — Numerical Ability · 12 cards
- Table Structure
- Rows represent categories (people, years, cities, products) and columns represent attributes (values, quantities, percentages). Always read row and column headers first before attempting any question.
- Direct vs. Derived Data
- Direct data is given in the table; derived data must be calculated (totals, differences, ratios). Clerk questions mostly use direct data with simple one-step derivations.
- Percentage Calculation
- Converting raw numbers to percentages or finding what percentage one value is of another — the most common operation in Tabular DI.
- Ratio Comparison
- Questions often ask you to find ratios between two table values or compare ratios across rows/columns.
- Average Calculation
- Finding the average of a row, column, or specific cells. Remember: Average = Sum ÷ Count.
- Percentage Change
- (New − Old) ÷ Old × 100. Watch the direction — increase vs. decrease, and which year is the base.
- Approximation Skill
- When answer options are spread apart (e.g., 23%, 31%, 47%), approximate rather than calculate exact values. This saves time.
- Percentage
- Formula: (Part ÷ Whole) × 100 · Quick Tip: Convert to fraction first if numbers are friendly
- Ratio
- Formula: A : B = A/B · Quick Tip: Simplify by dividing both by GCD
- Average
- Formula: Sum of values ÷ Number of values · Quick Tip: Count items carefully
- Difference
- Formula: Larger − Smaller · Quick Tip: Read "by how much" questions carefully
- Total
- Formula: Sum of all relevant cells · Quick Tip: Ensure you include correct rows/columns
Ratio and Proportion — Numerical Ability · 12 cards
- Ratio
- is a comparison of two quantities by division. If A : B = 3 : 4, it means for every 3 units of A, there are 4 units of B. Ratios have no units—they are pure numbers.
- Proportion
- states that two ratios are equal. If A : B = C : D, then A, B, C, D are in proportion. This is written as A : B :: C : D.
- The "k-method"
- When A : B = 3 : 4, assume A = 3k and B = 4k, where k is a common multiplier. This converts ratios into actual values for calculation.
- Compound Ratio
- The compound ratio of (a : b) and (c : d) is (a × c) : (b × d). Used when two ratios combine multiplicatively.
- Duplicate and Triplicate Ratios
- Duplicate ratio of a : b is a² : b². Triplicate ratio is a³ : b³. Sub-duplicate is √a : √b.
- Componendo and Dividendo
- If a/b = c/d, then (a + b)/(a − b) = (c + d)/(c − d).
- Direct Proportion
- When two quantities increase or decrease together at the same rate (e.g., more items, more cost).
- Inverse Proportion
- When one quantity increases while the other decreases proportionally (e.g., more workers, less time).
- If A : B = a : b, then A = ak, B = bk
- Converting ratio to values
- Mean Proportional of a and b = √(a × b)
- Middle term when a : x = x : b
- Third Proportional to a, b = b²/a
- When a : b = b : x
- Fourth Proportional to a, b, c = (b × c)/a
- When a : b = c : x
Bar Graph DI — Numerical Ability · 7 cards
- Reading the scale correctly
- Always check the Y-axis scale and units (thousands, lakhs, crores). A misread scale destroys all your calculations.
- Single-bar vs Double-bar identification
- Single bars show one variable across categories; double bars show two variables side-by-side for each category, enabling direct comparison.
- Percentage calculation is king
- Most questions ask for percentage increase/decrease, percentage contribution, or percentage comparison between bars.
- Ratio questions compare two values
- When asked for ratio, simplify to lowest terms. Don't leave as decimals unless asked.
- Average calculation
- Sum of all bar values divided by number of bars. Watch for "average of selected years" vs "overall average."
- Difference-based questions
- These are fastest — pure subtraction. Prioritize them to save time.
- Approximate vs Exact
- Clerk Prelims often allows approximation. If options are spread apart (e.g., 45%, 52%, 61%, 73%), round aggressively.
Number Series — Numerical Ability · 8 cards
- Arithmetic Series (Constant Difference)
- Each term increases or decreases by the same fixed number. Example: 5, 8, 11, 14, ... (difference = +3).
- Geometric Series (Constant Ratio)
- Each term is multiplied or divided by the same number. Example: 3, 6, 12, 24, ... (ratio = ×2).
- Difference Series with Pattern
- The differences themselves form a pattern — increasing by a constant, following squares, or doubling. Example: 2, 3, 5, 8, 12, ... (differences: +1, +2, +3, +4).
- Square-Based Series
- Terms are perfect squares, or differences are perfect squares. Example: 1, 4, 9, 16, 25 (squares of 1, 2, 3, 4, 5).
- Cube-Based Series
- Terms are perfect cubes, or pattern involves adding/subtracting cubes. Example: 1, 8, 27, 64 (cubes of 1, 2, 3, 4).
- Alternating Operations
- Two different operations alternate. Example: ×2, +3, ×2, +3, ... giving 2, 4, 7, 14, 17.
- Prime Number Series
- Terms are consecutive primes or differences are primes. Example: 2, 3, 5, 7, 11, 13.
- Mixed Operation Series
- Each term involves a changing multiplier or addend. Example: ×1+1, ×2+2, ×3+3, etc.
Average — Numerical Ability · 7 cards
- Basic Average
- Sum of all observations divided by the number of observations. This is your default starting point for every problem.
- Sum = Average × Count
- Rearranging the formula lets you find total sum when average and count are known — critical for most exam questions.
- Weighted Average
- When groups have different sizes, you cannot simply average the averages. Multiply each group's average by its size, add them, then divide by total count.
- Effect of Adding a New Element
- If a new value is added and average increases by k, the new value = Old Average + k × (New Count).
- Effect of Removing an Element
- If one value is removed and average changes, the removed value = Old Average − (Change × New Count).
- Average of Consecutive Numbers
- For any arithmetic progression, the average equals the middle term (or average of two middle terms if count is even).
- Age-Based Problems
- When time passes, everyone's age increases equally. If average age of a group increases by t years, then t years have passed.
Pie Chart DI — Numerical Ability · 12 cards
- Full circle = 360° = 100%
- Every pie chart represents one complete whole. All sectors must add up to 360° or 100%.
- Degree to percentage conversion
- 1% = 3.6°, so to convert degrees to percentage, divide by 3.6. To convert percentage to degrees, multiply by 3.6.
- Sector value = (Sector % × Total) / 100
- This is your bread-and-butter formula. Always identify the total before calculating.
- Central angle interpretation
- If a sector is 72°, it represents 72/360 = 1/5 = 20% of the total.
- Comparing sectors
- The ratio of two sectors equals the ratio of their percentages (or degrees). No need to calculate absolute values for pure comparison.
- Combined sectors
- When a question asks about "A and B together," simply add their percentages before applying to the total.
- Successive pie charts
- When two pie charts share a category (e.g., income and expenditure), questions often ask for differences or ratios between the same category across charts.
- 36°
- Percentage: 10% · Fraction: 1/10
- 72°
- Percentage: 20% · Fraction: 1/5
- 90°
- Percentage: 25% · Fraction: 1/4
- 108°
- Percentage: 30% · Fraction: 3/10
- 120°
- Percentage: 33.33% · Fraction: 1/3
Quadratic Equations — Numerical Ability · 12 cards
- Standard form
- A quadratic equation is written as ax² + bx + c = 0, where a, b, c are constants and a ≠ 0.
- Roots
- The values of x (or y) that satisfy the equation. Each quadratic has exactly two roots (which may be equal or distinct).
- Sum of roots
- = -b/a; Product of roots = c/a. Use these to verify your factorization quickly.
- Factorization method
- Split the middle term into two parts whose product equals a × c and whose sum equals b.
- Sign convention for comparison
- After finding both roots of each equation, compare all possible pairs and decide the universal relationship.
- Answer options
- in IBPS exams typically are:
- "Cannot be established"
- If some pairs give x > y and others give x < y, the relationship is indeterminate.
- ax² + bx + c = 0
- Standard quadratic form
- Sum of roots = -b/a
- Quick verification after factorization
- Product of roots = c/a
- Helps confirm root signs (+/−)
- Discriminant = b² - 4ac
- If negative, no real roots (rare in Clerk exams)
- (x - p)(x - q) = 0 means roots are p and q
- Factorization outcome
Profit and Loss — Numerical Ability · 7 cards
- Cost Price (CP)
- is what you pay to acquire an item; Selling Price (SP) is what you receive when selling it. Profit or Loss is always calculated on CP.
- Profit occurs when SP > CP
- ; Loss occurs when SP < CP. The amount of profit or loss is simply the difference between SP and CP.
- Marked Price (MP)
- is the price tag on an item before any discount. The actual SP equals MP minus the discount given.
- Discount is always calculated on MP
- , while Profit/Loss percentage is always calculated on CP — mixing these bases is the most common error.
- Successive discounts
- are not additive. Two discounts of 10% and 20% do not equal 30%. They must be applied one after another on the reduced price.
- When CP and SP are given per unit
- , always ensure both refer to the same quantity before calculating profit/loss percentage.
- Break-even point
- means SP = CP, resulting in zero profit and zero loss.
Data Interpretation — Numerical Ability · 8 cards
- Tables
- present data in rows and columns; read row headers and column headers carefully before solving.
- Bar Graphs
- display quantities using rectangular bars; height/length represents magnitude. Watch for scale divisions on the y-axis—each small division may represent 10, 50, or 100 units.
- Pie Charts
- represent parts of a whole as sectors of a circle. The complete circle = 360° = 100%. Thus, 1% = 3.6°. Converting between percentage and degrees is essential.
- Line Graphs
- show trends over time using connected points. Focus on direction (increasing/decreasing) and magnitude of change between consecutive points.
- Percentage calculations
- dominate DI questions: percentage share, percentage change, and percentage comparison.
- Approximation
- is your best friend—round off values to nearest 5s or 10s when the question says "approximate" or options are well-separated.
- Ratio comparisons
- appear frequently: comparing two entities or finding which year/category has highest ratio.
- Average and total
- calculations: summing across rows/columns, finding mean values.
Line Graph DI — Numerical Ability · 12 cards
- Trend Identification
- A line moving upward indicates increase; downward indicates decrease; horizontal or flat indicates stability. Questions often ask "in which year was the maximum increase" — this means the steepest upward slope.
- Difference vs. Percentage Change
- Absolute difference = Value₂ − Value₁. Percentage change = [(Value₂ − Value₁) / Value₁] × 100. Don't confuse the two — questions specifically ask for one or the other.
- Reading Intermediate Values
- When a data point falls between gridlines, estimate carefully. If gridlines are at 100 and 150, a point halfway is 125.
- Multiple Lines
- With two or more lines (e.g., Company A vs. Company B), track each line separately. Questions may ask for the year when the difference was maximum or when values were equal.
- Cumulative vs. Individual Values
- Some graphs show cumulative data; most Clerk-level graphs show individual period values. Read the title and axis labels to confirm.
- Average Calculation
- Sum of all values ÷ Number of periods. For 5 years of data, divide total by 5.
- Ratio Questions
- Express as a simplified fraction. If values are 450 and 300, ratio = 450:300 = 3:2.
- Percentage Increase
- [(New − Old) / Old] × 100
- Percentage Decrease
- [(Old − New) / Old] × 100
- Average
- Sum of all values ÷ Number of values
- Ratio
- A : B = A/B (simplify by HCF)
- Percentage of Total
- (Part / Total) × 100
Arithmetic — Numerical Ability · 8 cards
- Percentage is the foundation
- Almost every arithmetic topic—profit/loss, interest, partnership—uses percentage calculations. Master fraction-to-percentage conversions first.
- Ratio links quantities
- Ratios compare two quantities; proportions state that two ratios are equal. Always reduce ratios to simplest form before solving.
- Average = Sum ÷ Count
- The weighted average formula is essential when groups have different sizes.
- Profit/Loss is always on Cost Price
- Unless stated otherwise, profit% and loss% are calculated on CP, not SP.
- Interest problems differentiate SI and CI
- SI grows linearly; CI grows exponentially. For 2-year problems, CI – SI = P × (R/100)².
- Time and Work uses the "1/n" concept
- If A completes work in n days, A's one-day work = 1/n. Use LCM method for faster calculations.
- Speed, Time, Distance are inversely/directly related
- Distance = Speed × Time. Relative speed applies when objects move toward or away from each other.
- Alligation gives the mixing ratio
- It finds the ratio in which two items at different values must be mixed to get a desired average value.
Simple and Compound Interest — Numerical Ability · 7 cards
- Simple Interest (SI)
- charges interest only on the original principal. The interest remains constant each year.
- Compound Interest (CI)
- charges interest on both principal and accumulated interest. Interest grows each year because it's calculated on an increasing amount.
- The difference between CI and SI arises because CI adds previous years' interest to the principal.
- For year 1, SI = CI when interest is compounded annually.
- Rate and time must use the same unit.
- If rate is annual, time must be in years. Convert months to fractions of a year (6 months = 0.5 years).
- Effective rate for CI increases with compounding frequency.
- Half-yearly compounding at 10% p.a. means 5% for 6 months, applied twice.
- When CI is compounded annually, Amount = P(1 + R/100)ⁿ.
- This is the master formula from which CI is derived.
- For successive percentage increases, use the net effect formula.
- Two successive increases of R% each give net effect = 2R + R²/100 percent.
Time and Work — Numerical Ability · 7 cards
- Work as a measurable unit
- Assume total work = LCM of all given time periods. This converts fractions into whole-number efficiencies, making calculations faster.
- Efficiency = Work ÷ Time
- If A completes a job in 10 days and total work = 30 units, then A's efficiency = 3 units/day.
- Combined efficiency is additive
- When A and B work together, their combined rate = A's rate + B's rate. This is the heart of all "working together" problems.
- Inverse relationship
- Time and efficiency are inversely proportional. If A is twice as efficient as B, A takes half the time B takes for the same work.
- Work done = Efficiency × Days worked
- When workers join or leave midway, calculate each phase separately and sum up the work done.
- Negative efficiency for destroyers
- In problems where someone undoes work (like a leak in a tank), assign negative efficiency to that agent.
- Man-days concept
- Total work can be expressed as (number of workers) × (days) = constant. If 5 men finish in 10 days, total work = 50 man-days.
Permutation and Combination — Numerical Ability · 12 cards
- Fundamental Counting Principle
- If one task can be done in m ways and another in n ways, both tasks together can be done in m × n ways. This is the backbone of all counting problems.
- Factorial (n!)
- The product of all positive integers from 1 to n. Example: 5! = 5 × 4 × 3 × 2 × 1 = 120. Remember: 0! = 1 and 1! = 1.
- Permutation (ⁿPᵣ)
- Number of ways to arrange r items from n distinct items where order matters. Use when the problem asks about "arrangements," "sequences," or "positions."
- Combination (ⁿCᵣ)
- Number of ways to select r items from n distinct items where order doesn't matter. Use when the problem asks about "selecting," "choosing," or "forming groups."
- Permutation with Repetition
- When items can repeat, n choices for each of r positions gives nʳ arrangements.
- Combination with Constraints
- Problems often add conditions like "at least," "at most," or "exactly"—break these into cases and add/subtract accordingly.
- Symmetry Property
- ⁿCᵣ = ⁿCₙ₋ᵣ. Choosing 3 items from 10 equals choosing 7 items to leave behind.
- n! = n × (n-1) × (n-2) × ... × 1
- Meaning: Factorial of n · When to Use: Foundation for all P&C calculations
- ⁿPᵣ = n!/(n-r)!
- Meaning: Permutation formula · When to Use: Arrangements where order matters
- ⁿCᵣ = n!/[r!(n-r)!]
- Meaning: Combination formula · When to Use: Selections where order doesn't matter
- ⁿCᵣ = ⁿPᵣ/r!
- Meaning: Relation between P and C · When to Use: Quick conversion between the two
- ⁿC₀ = ⁿCₙ = 1
- Meaning: Boundary cases · When to Use: Selecting none or all items
Time, Speed and Distance — Numerical Ability · 7 cards
- The fundamental relationship
- Speed = Distance ÷ Time. This single formula, rearranged three ways, solves every basic TSD problem.
- Unit conversion is non-negotiable
- km/hr to m/s requires multiplying by 5/18; m/s to km/hr requires multiplying by 18/5. Mismatched units cause most calculation errors.
- Relative speed determines meeting/crossing problems
- When objects move in the same direction, subtract speeds; when moving in opposite directions, add speeds.
- Train problems always involve length
- Unlike cars, trains have significant length. The distance covered when crossing an object equals train length plus object length (if the object has length).
- Boats and streams split into upstream and downstream
- Downstream speed = boat speed + stream speed; upstream speed = boat speed − stream speed.
- Average speed is not the arithmetic mean
- For equal distances at different speeds, use the harmonic mean formula: 2ab/(a+b).
- Inverse proportionality
- For constant distance, speed and time are inversely proportional—double the speed means half the time.
Number System — Numerical Ability · 12 cards
- HCF (Highest Common Factor)
- The largest number that divides two or more numbers exactly. Used when you need to "reduce" or find the greatest common measure (e.g., cutting ropes into equal pieces).
- LCM (Least Common Multiple)
- The smallest number divisible by all given numbers. Used when events repeat or align (e.g., bells ringing together, circular track meetings).
- HCF × LCM = Product of two numbers
- This identity holds only for exactly two numbers—a frequent exam trap.
- Prime Factorization
- Express a number as a product of primes (e.g., 60 = 2² × 3 × 5). This unlocks HCF, LCM, and factor-count problems instantly.
- Divisibility Rules
- Shortcuts to check if a number divides another without actual division. Critical for simplification speed.
- Co-prime Numbers
- Two numbers with HCF = 1. If HCF(a, b) = 1, then LCM(a, b) = a × b.
- Surds
- Irrational roots that cannot be simplified to a rational number (e.g., √2, ∛5). Rationalization removes surds from denominators.
- Number of Factors Formula
- If N = p^a × q^b × r^c, then total factors = (a+1)(b+1)(c+1).
- HCF × LCM
- HCF(a,b) × LCM(a,b) = a × b (for two numbers only)
- LCM of fractions
- LCM of numerators ÷ HCF of denominators
- HCF of fractions
- HCF of numerators ÷ LCM of denominators
- Number of factors
- N = p^a × q^b → Factors = (a+1)(b+1)
Problems on Ages — Numerical Ability · 12 cards
- Present age is your base reference
- Unless stated otherwise, all ages mentioned are present ages. Past ages subtract years; future ages add years.
- "X years ago" means (Present Age − X)
- If Ravi is 30 now, his age 5 years ago was 30 − 5 = 25.
- "X years hence/later" means (Present Age + X)
- If Ravi is 30 now, his age 8 years hence will be 30 + 8 = 38.
- Age difference remains constant
- If A is 10 years older than B today, A will always be 10 years older than B—past, present, or future.
- Ratio of ages changes over time
- Unlike difference, the ratio between two persons' ages changes as years pass.
- When ages are in ratio, use a common multiplier
- If A:B = 3:2, let A = 3x and B = 2x. Solve for x using the other condition.
- Linear equations suffice for Clerk level
- Many problems solve with one variable and one equation.
- A is X years older than B
- A = B + X
- A is X times as old as B
- A = X × B
- Sum of ages is S
- A + B = S (or A + B + C = S)
- X years ago, A was Y times B
- (A − X) = Y × (B − X)
- X years hence, A will be Y times B
- (A + X) = Y × (B + X)
Puzzles — Reasoning Ability · 12 cards
- Single-variable focus
- Clerk puzzles typically assign one attribute (person to floor, person to day). PO-level multi-variable puzzles (person + department + city) are rare here.
- Start with definite clues
- Always begin with clues that give fixed positions ("A lives on floor 5" or "B's meeting is on Monday"). These anchor your arrangement.
- Negative clues come last
- Clues like "C does not live on floor 3" are useful only after you've placed other elements. Don't start with these.
- Ordinal positions matter
- "Above," "below," "immediately above," "between" — understand the difference. "Immediately above" means directly on top (no gap); "above" means anywhere higher.
- Count gaps carefully
- "Two persons live between A and B" means there are exactly 2 floors/positions separating them, so A and B are 3 positions apart.
- Use elimination grids
- For 6–8 person puzzles, maintain a simple grid marking confirmed positions with ✓ and eliminated positions with ✗.
- Watch for "either-or" scenarios
- When clues create two possible arrangements, note both and let later clues eliminate one.
- Floor numbering convention
- Unless stated otherwise, Floor 1 is the ground floor (bottom), and higher numbers go up.
- "A is immediately above B"
- A is exactly one floor above B (no gap)
- "A is above B"
- A is on any floor higher than B
- "Two persons between A and B"
- Exactly 2 floors/persons separate them
- "A is three floors above B"
- If B is on floor 2, A is on floor 5
Floor Puzzle — Reasoning Ability · 7 cards
- Floor numbering convention
- Unless stated otherwise, the ground floor is Floor 1, and floor numbers increase upward. Some puzzles explicitly state "ground floor is 0" — always check the question.
- Definite vs. conditional clues
- Definite clues give exact positions ("A lives on floor 3"). Conditional clues create dependencies ("B lives immediately above C"). Always process definite clues first.
- Immediately above/below
- This means consecutive floors with no gap. "A lives immediately above B" means if B is on floor 2, A is on floor 3.
- Above/below (not immediate)
- This allows any number of floors in between. "A lives above B" means A's floor number is greater than B's floor number.
- Gap-based clues
- "Two persons live between A and B" means there are exactly two floors (occupied by two other people) separating A and B.
- Negative clues
- "A does not live on the topmost floor" eliminates one possibility. Collect all negative clues to narrow down options.
- Either-or situations
- When a clue creates two possibilities, make temporary cases (Case 1, Case 2) and test which one survives all conditions.
Linear Arrangement — Reasoning Ability · 8 cards
- Single-row setup
- All persons sit in one straight line. Positions are numbered left to right (Position 1 = leftmost, Position 7 = rightmost for 7 persons).
- Direction convention
- When all face North, "left" means towards Position 1 and "right" means towards higher position numbers. When all face South, left-right reverses on your diagram.
- Immediate neighbor
- Person sitting directly adjacent (one position gap = 0 persons between).
- "Between" interpretation
- "B sits between A and C" means A and C are on opposite sides of B, but not necessarily immediate neighbors unless specified.
- "X sits second to the left of Y"
- Count two positions from Y towards the left. X occupies that position.
- Definite vs. conditional clues
- Start with definite clues (exact positions) before tackling relative clues (A is to the left of B, without specific distance).
- Negative clues
- "A does not sit at any extreme end" eliminates two positions immediately—use these to narrow down.
- Multiple possibilities
- Some clue sets allow two valid arrangements. Track both until a later clue eliminates one.
Day / Month Scheduling — Reasoning Ability · 12 cards
- Fixed vs. Conditional Clues
- Fixed clues give absolute positions ("P works on Monday"). Conditional clues depend on other placements ("Q works immediately after R"). Always start with fixed clues.
- Gap-Based Conditions
- "Two days gap" means two empty slots between them. "A works two days after B" means if B is Monday, A is Wednesday (count forward, skip one day).
- Immediately Before/After
- No gap—consecutive days. "X immediately before Y" means X on Tuesday → Y on Wednesday.
- Either-Or Conditions
- "P works either on Monday or Friday" creates two scenarios. Note both possibilities and eliminate one using other clues.
- Negation Clues
- "R does not work on Wednesday" eliminates one cell—mark with '×' and move on.
- Week Structure
- Monday to Sunday = 7 days. Some puzzles use Monday to Friday (5 days) or Saturday to Friday (7 days). Check the boundary carefully.
- Month Structure
- January to December = 12 months, but Clerk puzzles usually use 6–7 consecutive months (e.g., March to September). Note the sequence order.
- "A works immediately after B"
- A's day = B's day + 1
- "A works immediately before B"
- A's day = B's day − 1
- "Two days gap between A and B"
- Difference = 3 days (two slots empty between them)
- "A works two days after B"
- A's day = B's day + 2
- "A works on one of the days after B"
- A comes later in the week than B
Seating Arrangement — Reasoning Ability · 12 cards
- Linear Arrangement
- Persons sit in a single row, all facing the same direction (usually North or South). Left-right relationships are critical. "To the left of X" means towards X's left hand.
- Circular Arrangement
- Persons sit around a round table. Two sub-types exist—facing the centre (common at Clerk level) and facing outward. The direction of left/right reverses when facing outward.
- Immediate vs Non-immediate Neighbours
- "A sits next to B" means they are adjacent. "A sits to the left of B" (without "immediate") may mean anywhere to B's left, not necessarily adjacent.
- Fixed Position Clues
- Statements like "A sits at one of the ends" or "B sits exactly in the middle" are anchor points—start your arrangement with these.
- Relative Position Clues
- "A is two places to the right of B" or "There are three persons between A and B"—these define distance but need an anchor to place absolutely.
- Negative Clues
- "A does not sit next to B" or "C is not at any end"—use these to eliminate possibilities after placing other persons.
- Multiple Possibilities
- Sometimes initial clues create two or more possible arrangements. Carry forward both until a later clue eliminates one.
- Linear facing North
- Left of a person = West side; Right = East side
- Linear facing South
- Left of a person = East side; Right = West side
- Circular facing centre
- Clockwise = Left of a person; Anti-clockwise = Right
- Circular facing outward
- Clockwise = Right of a person; Anti-clockwise = Left
- "Between A and B"
- Does not include A and B themselves
Circular Arrangement — Reasoning Ability · 7 cards
- Circular has no fixed reference point
- Unlike linear rows, you can place any person anywhere initially. Fix one person's position, then build others relative to them.
- Facing Center vs Facing Outward
- When facing center, the person's left is clockwise from your viewing perspective. When facing outward, left becomes anticlockwise. This single rule causes maximum confusion.
- "Immediate left/right" means adjacent
- No gap between the two persons. "Second to the left" means one person sits between them.
- Counting direction matters
- Count positions in the direction specified (left or right of a person), not your viewing direction.
- Opposite positions
- In an 8-person circle, opposite means 4 positions away. In a 6-person circle, opposite means 3 positions away. Formula: n/2 positions away for even n.
- Definite vs Conditional clues
- Start with clues that give exact positions ("A sits second to the left of B"). Save clues with "or" conditions for later verification.
- Neighbour means immediate neighbour
- "A and B are neighbours" means they sit adjacent to each other.
Box / Stack Puzzle — Reasoning Ability · 7 cards
- Stack structure
- Boxes are arranged in a single vertical column. Position 1 is the bottom; the highest number is the top (or vice versa — read the question to confirm).
- "Above" vs "Immediately above"
- "A is above B" means A is anywhere higher than B (either directly on B or with boxes in between). "A is immediately above B" means A sits directly on B with no box in between.
- Negative clues narrow options
- Clues like "C is not at the top" or "D is not immediately below E" eliminate specific cells.
- Anchor clues first
- Start with definite clues — "F is at the bottom" or "G is second from top" — to fix reference points.
- Work both ends
- Often the top and bottom positions get fixed early; fill middle slots by elimination.
- One variable only
- At Clerk level, you typically handle just position. If a second variable (colour, size) appears, treat it as a simple mapping after fixing positions.
- Check consistency
- After filling all slots, re-read every clue to ensure no contradiction.
Syllogism — Reasoning Ability · 12 cards
- Statements establish relationships between two groups
- using quantifiers. Think of each group as a circle, and the quantifier tells you how these circles overlap.
- Four standard quantifiers
- exist: All (complete inclusion), Some (partial overlap), No (complete exclusion), and Some not (partial exclusion).
- "All A are B" does not mean "All B are A."
- Direction matters—if all dogs are animals, it doesn't mean all animals are dogs.
- "Some" implies at least one, possibly all.
- When a statement says "Some A are B," it means one or more A could be B, including the possibility that all A are B.
- "No" is a complete denial
- and works both ways. "No A is B" automatically means "No B is A."
- Conclusions must be 100% certain
- from the given statements. If a conclusion is only sometimes true, it does not follow.
- Venn diagrams are the most reliable solving method
- for beginners. Draw circles representing groups and shade/overlap them according to statements.
- Complementary pairs
- If "Some A are B" is false, then "No A is B" is true, and vice versa.
- All A are B
- Some B are A (valid)
- Some A are B
- Some B are A (valid)
- No A is B
- No B is A (valid)
- Some A are not B
- No valid conversion
Direction and Distance — Reasoning Ability · 7 cards
- Eight Cardinal and Ordinal Directions
- North, South, East, West are the four main directions. Northeast, Northwest, Southeast, Southwest lie at 45° between them. Always orient your diagram with North at the top.
- Clockwise vs Anti-clockwise Turns
- Turning right means moving clockwise (N→E→S→W→N). Turning left means moving anti-clockwise (N→W→S→E→N). A 90° right turn from East points you South.
- Opposite Directions
- North↔South, East↔West, Northeast↔Southwest, Northwest↔Southeast. If someone faces North and turns 180°, they face South.
- Shadow-based Direction
- Morning sun rises in East, so shadows fall West. Evening sun sets in West, so shadows fall East. At noon, shadows are minimal (directly under or towards North in Northern Hemisphere).
- Displacement vs Total Distance
- Total distance is the sum of all path lengths. Displacement (shortest distance) is the straight line from start to end point.
- Pythagorean Theorem for Shortest Distance
- When net North-South movement and net East-West movement form a right angle, shortest distance = √(horizontal² + vertical²).
- Same-line Movements Cancel or Add
- Moving 5 km North then 3 km South gives net 2 km North. Moving 5 km North then 3 km North gives net 8 km North.
Order and Ranking — Reasoning Ability · 12 cards
- Position from opposite ends
- If you know position from one end, position from other end = Total – Given position + 1.
- Finding total when both positions are given
- Total = Position from left + Position from right – 1. The "–1" accounts for counting the person twice.
- When positions change after interchange
- Track each person separately. If A and B swap, A takes B's original position and vice versa.
- "Between" vs "From"
- "5 persons between A and B" means 5 people in the gap (total span = 7 including A and B). "A is 5th from left" means A occupies position 5.
- Left-Right / Top-Bottom convention
- Left and Top are position 1 side. Right and Bottom are the "other end" side.
- Minimum vs Exact total
- If a question says "at least," find the minimum possible value. If positions can overlap (the person counted from the left stands to the right of the person counted from the right), total is smaller.
- Two people, same row
- When given positions of two different people, consider whether they could be the same person, or if one is to the left/right of the other.
- Position from right when left position is known
- Right = Total – Left + 1
- Position from left when right position is known
- Left = Total – Right + 1
- Total persons (both positions of same person given)
- Total = Left + Right – 1
- Persons between A and B
- Between = Difference of positions – 1
- Minimum total (two people, positions may overlap)
- Larger of the two given positions
Alphabet Test — Reasoning Ability · 7 cards
- Forward Position
- A=1, B=2, C=3... Z=26. Memorize the positions of key letters: E=5, J=10, O=15, T=20, Y=25.
- Backward Position (EJOTY reverse)
- Z=1, Y=2, X=3... A=26. The formula is: Backward position = 27 - Forward position.
- Opposite Letters
- Letters equidistant from both ends form pairs summing to 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.
- Left-Right Convention
- "Left of" means toward A; "Right of" means toward Z. In the sequence A-B-C-D, B is to the left of D.
- Meaningful Word Formation
- Rearranging given letters (usually 4-6) to form valid English words, then answering based on specific positions.
- Letter Series/Patterns
- Identifying the logic in letter sequences—skipping letters, alternating directions, or combining with numbers.
- Middle Letter Identification
- For odd-numbered letter groups, the middle letter is at position (n+1)/2 from either end.
Data Sufficiency — Reasoning Ability · 8 cards
- The question stem is incomplete information.
- It presents a scenario but lacks enough data to reach a definite answer on its own.
- Each statement provides additional clues.
- You must check whether Statement I alone, Statement II alone, both together, or neither can answer the question.
- You are not asked to find the answer — only whether it CAN be found.
- Stop once you know sufficiency; don't solve further.
- Statements are independent.
- When testing Statement I, ignore Statement II completely, and vice versa.
- "Both together" means combining I and II.
- Only choose this if neither alone works but together they do.
- Uniqueness matters.
- If a statement leads to multiple possible answers (ambiguity), it is NOT sufficient.
- Common underlying topics
- Blood relations, direction-distance, ranking, coding, age problems, and simple arithmetic.
- Standard answer choices follow a fixed pattern
- memorise the framework to save reading time.