Aptitude for placements: questions by topic, with answers
The aptitude section of a placement test is a speed test. Nobody fails it for not knowing what a percentage is; people fail it by solving a three-line problem in twelve lines. The skill is recognising the shape of a question — a base that changes, a rate that adds, a total dressed up as an average, a ratio hiding a common multiple — and reaching for the one method that finishes it before the clock does.
Quantitative aptitude is a small set of families that recur in every company's paper: percentages and the profit-and-loss, simple- and compound-interest problems built on them, ratio and proportion with its offshoots in mixtures and in ages, time and work, time, speed and distance, averages, permutations and combinations with the probability built on them, and number systems with their divisibility rules. Logical reasoning adds pattern families — number series, coding-decoding, blood relations — where the whole question is finding the rule.
Each page below takes one family: the shapes that recur, the method for each, worked numbers, and one question exactly as the diagnostic asks it. The diagnostic samples across every aptitude topic in the bank and shows you which families cost you time.
Aptitude topics, one page each
- Time, speed and distance questionsAverage speed, relative speed, trains crossing poles and platforms, boats and streams, late-and-early problems — placement questions, worked out.
- Percentage aptitude questionsSuccessive percentage changes, the increase-then-decrease asymmetry, x% more vs x% less, expenditure, growth and pass-mark questions — worked out.
- Time and work questionsWork rates and the LCM method, working together, leaving midway, men-days, efficiency ratios, pipes and cisterns, wage splits — worked out.
- Profit and loss questionsProfit percent on cost, cost price from selling price, marked price and discount, equal profit and loss, false weights, successive discounts — worked.
- Ratio and proportion questionsDividing in a ratio, combining A:B and B:C, ratios that change, direct and inverse proportion, partnership shares, mean proportional, coins — worked.
- Simple interest questionsThe SI formula and its rearrangements, rate or time from interest, amount vs interest, doubling and tripling, two rates on one sum, SI vs CI — worked.
- Averages questionsTotal from average, a member joining or leaving, a wrongly entered value, consecutive numbers, weighted averages, combined groups, cricket averages.
- Probability questionsFavourable over total, dice and coins, the complement rule, addition with overlap, cards, without replacement, independent events, odds — worked.
- Number system and divisibility questionsDivisibility rules for 3, 4, 8, 9 and 11, units digits of powers, remainders of powers, HCF and LCM, common-remainder problems, factors, trailing zeros.
- Number series questionsHow to crack a number series fast: differences and second differences, ratios, squares and cubes, alternating series, double-and-add, the wrong term.
- Coding-decoding questionsLetter-shift codes, reversal codes, letter-to-number codes, symbol substitution, word-substitution puzzles, position-dependent codes, classifying each.
- Problems on agesAges problems with one unknown and a table of times: ratios now and later, the fixed age gap, totals, 'when I was your age', averages — worked.
- Blood relations questionsBlood relations by a drawn family tree: chains read from the speaker, the 'only son' trap, coded relations, unknown genders, photo puzzles — worked.
- Compound interest questionsThe CI formula and the year-by-year method, half-yearly compounding, CI minus SI, principal, rate and time, doubling, depreciation — worked.
- Permutations and combinations questionsOrder or no order, the counting rules, repeated letters, items kept together, 'at least' committees, round tables, digit problems, probability — worked.
- Mixtures and alligation questionsThe alligation rule as a weighted average run backwards: prices, strengths, adding water, repeated replacement, mixing mixtures, profit — worked.
One question, exactly as the diagnostic asks it
From the Aptitude bank — 110 questions across 17 topics. The answer is marked because this one is public; in a sitting you choose first, then see why each option is right or wrong.
In a class of 80 students, 65% passed the mathematics exam. How many students passed?
- 155
- 252correct
- 360
- 448
65% of 80 = (65/100) x 80 = 52, so 52 students passed. A quick check: 10% of 80 is 8, so 65% is 6.5 x 8 = 52. The other options are other shares of 80: 48 is 60%, 60 is 75% and 55 is 68.75%, none of them 65%.
Measure it
Reading the answers tells you what’s true. A diagnostic tells you what you get wrong.
10 Aptitude questions across its topics, easy to hard, about fifteen minutes. You get a readiness figure with the arithmetic shown, the topics you missed named, and a practice set sized for today. Free: a diagnostic in every subject, a retake a month and 15 problems a day. No card.