Aptitude Preparation for Placements: Topics, Shortcuts and a 30-Day Plan

For most freshers, the aptitude test is the first round that can end a placement drive. Mass recruiters like TCS, Infosys, Wipro, Accenture, Cognizant and Capgemini screen many thousands of applicants with an online test, and the aptitude section filters out a large share before any interviewer sees a resume. The maths is not hard. What fails people is not knowing the fast method, running out of time, or never having practised under a clock.

This guide is built to be used, not read once. Each quant topic below comes with the shortcut and a worked example. Do the examples with a pen before looking at the solution. Then follow the 30-day plan.

How Placement Aptitude Tests Work

A few structural facts change how you should prepare:

• Sectional timers. Many tests lock each section with its own timer. You cannot borrow time from verbal to finish quant, so each section needs its own pacing.
• Sectional cut-offs. Scoring very high in quant does not rescue a low verbal score if there is a per-section cut-off. Do not neglect your weakest section.
• Adaptive tests. Some assessment platforms (AMCAT is a well-known example) adapt difficulty to your answers: early questions matter more, and you usually cannot go back.
• No calculator. Most tests provide an on-screen calculator only in specific sections or not at all. Mental arithmetic speed is part of the test.
• Negative marking. Many recent mass-recruiter tests have been reported without negative marking, which means you should never leave a question blank. Always read the instructions, because this varies.

TCS, Infosys, Accenture and Other Test Patterns

The table below summarizes the commonly reported structure of recent drives. Exact section names, question counts and timings change between hiring seasons and between campus and off-campus drives, so always confirm against the official notification for your drive.

Our company guides go deeper on each: TCS, Infosys, Accenture and Capgemini.

Aptitude Topics in Priority Order

Not all topics appear equally often. Based on the syllabus outlines published by recruiters and the topics that recur in practice sets, prepare in this order. Tier 1 topics are almost guaranteed; Tier 3 appear occasionally.

Quantitative Aptitude Shortcuts with Worked Examples

Every shortcut here is derived from the underlying concept, which is why it works. Understand the derivation once and you will remember it in the exam.

Percentages: successive changes

Two successive changes of a% and b% give a net change of a + b + ab/100 percent (use negative values for decreases). This comes from (1 + a/100)(1 + b/100) - 1.

Example: A phone's price rises 20% and then falls 20%. Net change = 20 - 20 + (20 × -20)/100 = -4%. It does not return to the original price; it ends 4% lower.

Fraction table to memorize: 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 = 16.67%, 1/7 ≈ 14.29%, 1/8 = 12.5%, 1/9 ≈ 11.11%, 1/11 ≈ 9.09%, 1/12 ≈ 8.33%. Converting "12.5% off" to "one-eighth off" turns many questions into one-step mental maths.

Profit and loss

Profit % is always on cost price unless stated otherwise. Selling price = CP × (100 + profit%)/100.

Classic trap: Two items are each sold for ₹1,200, one at a 20% profit and one at a 20% loss. Is there an overall profit or loss? When two items are sold at the same SP, one at x% gain and one at x% loss, there is always a net loss of x²/100 percent = 400/100 = 4%. Check: CP1 = 1200/1.2 = 1000, CP2 = 1200/0.8 = 1500, total CP 2500, total SP 2400, loss 100 = 4% of 2500.

Dishonest shopkeeper: A trader sells at cost price but uses a 900 g weight for 1 kg. Gain % = (error / true value given) × 100 = 100/900 × 100 ≈ 11.11%.

Time and work: the LCM method

Instead of fractions, assume the total work equals the LCM of the given days. Each person's daily output becomes a whole number.

Example: A finishes a job in 12 days and B in 18 days. How long together? LCM(12, 18) = 36 units. A does 36/12 = 3 units a day, B does 2. Together 5 units a day, so 36/5 = 7.2 days.

Extension: They work together for 4 days, then A leaves. How long does B take for the rest? In 4 days they finish 20 units; 16 remain; B takes 16/2 = 8 more days.

Pipes and cisterns

Same LCM idea, with emptying pipes counted as negative work.

Example: Pipe A fills a tank in 10 hours; pipe B empties it in 15 hours. Both open: LCM = 30 units; A adds 3 per hour, B removes 2, net 1 per hour, so the tank fills in 30 hours.

Time, speed and distance

• To convert km/h to m/s multiply by 5/18; for m/s to km/h multiply by 18/5. So 72 km/h = 20 m/s, 54 km/h = 15 m/s, 36 km/h = 10 m/s.
• Average speed for equal distances at speeds x and y is 2xy/(x + y), not (x + y)/2. Going at 60 km/h and returning at 40 km/h gives 2 × 60 × 40/100 = 48 km/h.
• Relative speed: add speeds when moving towards each other, subtract when moving in the same direction.

Trains: A 200 m train at 72 km/h (20 m/s) passes a pole in 200/20 = 10 s. It crosses a 300 m platform in (200 + 300)/20 = 25 s, because it must cover its own length plus the platform's. Two trains of 150 m and 250 m moving towards each other at 36 and 54 km/h (10 and 15 m/s) cross each other in 400/25 = 16 s.

Boats and streams: downstream speed = u + v, upstream = u - v, where u is the boat's speed in still water and v the stream's. So u = (down + up)/2 and v = (down - up)/2. Downstream 15 km/h and upstream 9 km/h give a still-water speed of 12 km/h and a stream speed of 3 km/h.

Simple and compound interest

SI = P × R × T/100. CI amount = P(1 + R/100)^T. For two years, the difference between CI and SI is P(R/100)², because the only extra in CI is interest earned on the first year's interest.

Example: P = ₹10,000, R = 10%, T = 2 years. CI - SI = 10,000 × 0.01 = ₹100. (Check: SI = 2,000; CI = 12,100 - 10,000 = 2,100.) For three years the difference is P(R/100)²(3 + R/100).

Mixtures and alligation

To mix two items with prices (or concentrations) c and d to get mean m, the ratio of quantities is (d - m) : (m - c), where c is the cheaper price.

Example: Rice at ₹40/kg and ₹60/kg is mixed to sell at a cost of ₹52/kg. Ratio = (60 - 52) : (52 - 40) = 8 : 12 = 2 : 3. Check: (2 × 40 + 3 × 60)/5 = 260/5 = 52.

Number system: unit digits, remainders, divisibility

Unit digit cyclicity: powers of 2 end in 2, 4, 8, 6 (cycle 4); 3 in 3, 9, 7, 1; 7 in 7, 9, 3, 1; 8 in 8, 4, 2, 6; 4 in 4, 6 (cycle 2); 9 in 9, 1; 0, 1, 5, 6 never change. Find the exponent mod the cycle length (use the full cycle length when the remainder is 0).

Example: Unit digit of 7⁹⁵: 95 mod 4 = 3, so it is the 3rd term of (7, 9, 3, 1): 3.

Remainders: find a power that gives remainder 1. Remainder of 2¹⁰⁰ ÷ 7: since 2³ = 8 leaves remainder 1, 2⁹⁹ = (2³)³³ leaves 1, so 2¹⁰⁰ leaves 2 × 1 = 2.

Divisibility rules to know cold: 3 and 9 (digit sum), 4 (last two digits), 8 (last three digits), 11 (alternating digit sum difference divisible by 11), and 7 or 13 rarely. HCF × LCM = product of the two numbers (for two numbers only).

Permutations, combinations and probability

• Arrangements of n distinct objects: n!. With repeated letters, divide by the factorial of each repeat count. "LEVEL" has 5!/(2! × 2!) = 30 arrangements.
• Choosing r from n where order does not matter: nCr = n!/(r!(n - r)!). Handshakes among 10 people: 10C2 = 45.
• Circular arrangements of n people: (n - 1)!. For a necklace that can be flipped: (n - 1)!/2.
• Probability = favourable outcomes / total outcomes. Sum of 8 with two dice: (2,6), (3,5), (4,4), (5,3), (6,2) gives 5/36.
• "At least one" is easiest via the complement: P(at least one head in 3 tosses) = 1 - (1/2)³ = 7/8.

Getting these right also helps in coding assessments, where counting arguments appear regularly; see our maths for coding interviews guide.

Ages and averages

Set up one variable for the present age and translate each sentence. Example: A father is 3 times as old as his son. In 12 years, he will be twice as old. Let the son be x: 3x + 12 = 2(x + 12), so x = 12. Son 12, father 36.

For averages, use deviations from an assumed mean instead of adding big numbers: the average of 67, 72, 75, 70, 66, taken around 70, has deviations -3, +2, +5, 0, -4 summing to 0, so the average is 70.

Clocks and calendars

Clock angle between the hands at H hours and M minutes = |30H - 5.5M| degrees (take 360 minus the value if it exceeds 180 and the question asks for the smaller angle). At 3:40: |90 - 220| = 130°. The hands coincide 11 times in 12 hours, every 65 5/11 minutes.

Calendars use odd days (days beyond complete weeks): an ordinary year has 1 odd day, a leap year 2. A century has 5 odd days, 200 years 3, 300 years 1, and 400 years 0. Century years are leap years only if divisible by 400, so 1900 was not a leap year and 2000 was.

Logical Reasoning: Methods That Work

Reasoning has fewer formulas and more method. The key is a consistent notation so you do not reread the question four times.

Seating arrangements and puzzles

1. Draw the frame first. A line of seats or a circle with positions marked. For circular arrangements facing the centre, remember that left and right are reversed compared with a line facing you.
2. Place definite clues first. "A sits at an end", "B is third from the left". Skip conditional clues initially.
3. Branch on the next most restrictive clue. Draw two or three candidate arrangements side by side and eliminate with the remaining clues.
4. Answer only what is asked. Often you need just one position, not the full arrangement.

Blood relations

Draw a family tree with symbols: a square or "+" for male, a circle or "-" for female, horizontal lines for siblings and spouses, vertical lines for generations. Example: "Pointing to a man, Riya says, 'His mother is the only daughter of my mother.'" The only daughter of Riya's mother is Riya herself, so Riya is the man's mother. Most blood-relation questions collapse like this once you identify who "the only daughter" or "my father's only son" is.

Syllogisms

Use Venn diagrams and look for any diagram consistent with the statements in which the conclusion fails. Example: Statements: All pens are books. Some books are tables. Conclusion: Some pens are tables. Draw pens inside books, and tables overlapping books but outside the pens circle: that is consistent with the statements and the conclusion fails, so it does not follow. Rules that save time: "All A are B" does not imply "All B are A", but it does imply "Some B are A". Two "some" statements never give a definite conclusion. Watch for "either-or" pairs, such as "some A are B" and "no A are B", where one of the two must be true.

Coding-decoding

Write the alphabet positions once at the top of your rough sheet (A = 1 to Z = 26) and the reverse pairs (A-Z, B-Y, C-X, sums to 27). Example: If CAT is coded as DBU, each letter shifts by +1, so DOG becomes EPH. If CAT is coded as XZG, each letter maps to its reverse (C↔X, A↔Z, T↔G), so DOG becomes WLT.

Series

Check differences, then differences of differences, then ratios, then alternating patterns, then squares and cubes. 2, 6, 12, 20, 30, ? has differences 4, 6, 8, 10, so the next is 42 (also n(n+1)). 3, 5, 9, 17, 33, ? doubles the difference each time (2, 4, 8, 16), so the next is 65.

Direction sense and data sufficiency

For directions, always draw with north up and track each turn; the final distance is usually a Pythagorean calculation (walking 3 km east and 4 km north leaves you 5 km from the start). For data sufficiency, evaluate each statement alone first, then together, and do not actually compute the answer once you know it can be computed.

Verbal Ability: Where Engineers Lose Easy Marks

Engineers often prepare verbal last and lose easy marks to a sectional cut-off. Verbal improves slowly, so start it from day one alongside quant.

• Reading comprehension: read the questions first, then the passage. Answer from the passage only, not from general knowledge. Eliminate options that are too extreme ("always", "never") unless the passage is equally absolute.
• Sentence correction and error spotting: check subject-verb agreement, tense consistency, pronoun reference, prepositions and parallel structure, in that order. "Each of the students have" should be "has". "Neither the manager nor the employees was" should be "were", because the verb agrees with the nearer subject.
• Para jumbles: find the opening sentence (it introduces a subject without pronouns like "this" or "he"), then find mandatory pairs (a sentence with "however" or "this" must follow the sentence it refers to).
• Vocabulary: do not memorize word lists in bulk. Read one editorial a day from a national newspaper and note five unfamiliar words with their sentences.
• Written communication tests (an email or essay in some drives) reward clear structure: greeting, purpose in the first line, two or three short paragraphs, a polite close, and no spelling errors.

A 30-Day Aptitude Preparation Plan

This plan assumes 90 to 120 minutes a day alongside your coding preparation. If you are also preparing for coding rounds, our 30-day coding plan runs well in parallel.

Exam-Day Strategy

1. Two-pass approach. In the first pass, answer everything you can do in under a minute. Mark the rest. In the second pass, return to marked questions with the remaining time.
2. Set a hard cap per question. If you have spent 90 seconds without a clear path, guess (if there is no negative marking), mark it and move on. One stubborn question can cost you three easy ones.
3. Use the options. Back-substitute options in ages, numbers and equation problems. Eliminate options with the wrong unit digit or parity before calculating.
4. Approximate. If options are far apart, round numbers: 49.7% of 801 is roughly 400.
5. Know the platform rules. Some tests do not let you return to a previous question or section. Read the instructions screen fully; it is part of the strategy.
6. Technical setup for remote tests. Proctored online tests need a stable connection, a working webcam, and a quiet room. Close other applications; switching tabs can be flagged.

Recommended Resources

• R.S. Aggarwal, Quantitative Aptitude for Competitive Examinations: concept explanations and plenty of easy-to-medium problems; enough for mass-recruiter quant.
• R.S. Aggarwal, A Modern Approach to Verbal and Non-Verbal Reasoning: covers every reasoning type that appears in placement tests.
• Arun Sharma's quantitative aptitude book: written for CAT; use selectively if you target higher-tier tracks and want harder problems.
• Free practice websites with topic-wise question banks (IndiaBix is widely used) for daily practice sets.
• Company-specific mock platforms for full-length mocks in each recruiter's pattern. Treat any "previous year questions" as indicative; actual drives draw from large question pools.
• Official recruiter pages: each company's careers or test registration page publishes the current syllabus and pattern. Always check it once before your drive.

Aptitude gets you into the room; coding and interviews get you the offer. Once you are consistently scoring well in mocks, shift time towards the coding section (see our online assessment tips) and towards the interview stage, including the HR interview questions for freshers. For the wider strategy across drives, read our off-campus placement strategy.

Frequently Asked Questions

Pranjal Jain

Ex-Microsoft SDE · IIT Kanpur · Founder of Prepflix. Helps engineers crack startup and product company interviews across India.