The role of Quantitative Ability in CAT
Quantitative Ability (QA) is the third section of CAT, with 22 questions in 40 minutes in CAT 2025. Its mathematics is mostly at the level of school mathematics, extended with a few topics such as permutation-combination and logarithms; what makes it hard is the combination of speed, uneven difficulty and the presence of type-in questions with no options to guide you. Candidates from engineering backgrounds often have an advantage in comfort with the topics, but not necessarily in selection, which is the main driver of the score.
Topic map
The IIMs do not publish a syllabus. The map below reflects the areas from which recent papers have drawn questions; the relative weight of each varies by year.
| Area | Topics | Typical difficulty |
|---|---|---|
| Arithmetic | Percentages, profit and loss, ratio and proportion, interest, averages, mixtures, time and work, time-speed-distance | Easy to moderate; high yield |
| Algebra | Linear and quadratic equations, inequalities, functions, logarithms, progressions, surds and indices | Moderate to hard |
| Number system | Divisibility, remainders, factors, HCF and LCM, base systems | Moderate |
| Geometry and mensuration | Triangles, circles, polygons, coordinate geometry, areas and volumes | Moderate to hard |
| Modern maths | Permutation and combination, probability, set theory | Moderate |
Arithmetic and algebra supply the largest share of questions in most recent papers, which is why most preparation plans start there. For arithmetic drills, see percentage, profit and loss, time and work and time, speed and distance.
Difficulty is uneven: the central fact of QA
A typical CAT QA section has a handful of questions that most prepared candidates can solve in a minute or less, a larger group that need two to four minutes and a few that are designed to be hard. A candidate who works through the section in order, solving each question to the end, will usually run out of time before reaching the easy questions near the end. That is why triage is the first QA skill. The second is accuracy: with a −1 penalty on MCQs and no options on type-in questions, a calculation slip costs more than in an exam where options help.
A two-pass method
- First pass (about 20 minutes): go through all 22 questions. For each, spend up to 20 seconds deciding if you can see the method. Solve if yes; flag if no.
- Second pass (about 16 minutes): return to the flagged questions that look solvable with some thought. Attempt in order of how close you felt.
- Final minutes (about 4 minutes): make sure every type-in question has an entry, and re-check any answer where you had doubts about arithmetic.
The numbers are indicative. The principle is to harvest the easy marks before the hard ones, and to never be in a situation where a question you could have solved goes unseen because you sank time earlier.
Question types and how they differ
MCQ questions
Options allow back-solving (testing each option in the question), elimination by range or parity and estimation. They also contain traps, such as options that correspond to common errors. Look for these in review: if your wrong answer is among the options, it is likely a common mistake that you can learn to avoid.
Type-in (non-MCQ) questions
You must produce the exact answer. No option means no back-solving. Because there is no negative marking, you should attempt every type-in question for which you have even a partial result, but accuracy depends on clean arithmetic. For these, write steps on the scratch pad and sanity-check the final value for size and sign before entering it.
A worked triage: six questions, three decisions
To see what the first-pass decision looks like in practice, here are six questions of the kind that appear in QA sections, sorted the way a prepared candidate might sort them on a first read.
| Question | Decision | Why and how |
|---|---|---|
| 1. What is 18% of 250? | Solve now | 10% is 25, 8% is 20, so 18% is 45 |
| 2. A shopkeeper marks up goods by 40% and then gives a 25% discount. What is the profit percentage? | Solve now | Selling price = 1.4 × 0.75 = 1.05 of cost, so a 5% profit |
| 3. If x + 1/x = 5, find x² + 1/x². | Solve now | Square both sides: x² + 2 + 1/x² = 25, so the answer is 23 |
| 4. How many three-digit numbers are divisible by 7? | Second pass | The first is 105 = 7 × 15 and the last is 994 = 7 × 142, so there are 142 − 15 + 1 = 128 |
| 5. In how many ways can the letters of LEVEL be arranged? | Second pass | Five letters with L twice and E twice: 5! ÷ (2! × 2!) = 30 |
| 6. What is the remainder when 7100 is divided by 5? | Second pass | 7 leaves remainder 2; powers of 2 mod 5 cycle 2, 4, 3, 1; 100 is a multiple of 4, so the remainder is 1 |
The first three are quick: the method is visible at once, and each takes under a minute. The last three are medium: each is a standard idea (counting an arithmetic progression, repeated letters, remainder cycles) that takes a minute or two if you know it and is a good candidate for the second pass if you have to think. A real section also has questions you cannot see a way into within twenty seconds. Those are the ones to flag and leave.
Notice that questions 1 to 3 are each solved by restructuring the problem (build 18% from 10% and 1%; multiply the factors; square the identity) rather than by brute force. This is what the preparation for CAT quant mostly consists of: a library of such restructurings, each recognised from the wording.
Five families of questions that keep reappearing
- Percent-and-ratio chains: successive changes, mixtures and profit and loss, solved by multiplying factors.
- Remainders and divisibility: cycles of powers, factor counting, last digits.
- Counting: arrangements with repetition, selections with conditions, and complementary counting.
- Algebraic identities: expressions in x + 1/x, sums of squares, symmetric functions of roots.
- Geometry with a single trick: similar triangles, an angle in a semicircle, areas through ratios.
When you review a mock, tag each question with its family. After a month, the tag counts will show which families cost you most, and that is where to direct your topic tests.
Calculation skills that save minutes
- Squares to 30, cubes to 15 and common fractions to percentages by heart; see squares, cubes and roots practice.
- Estimation to decide between options that are far apart.
- Factorisation tricks for HCF, LCM and divisibility questions; see HCF and LCM practice.
- Choosing special values (for example x = 1) to test algebraic identities.
- Working with ratios and parts instead of absolute numbers in arithmetic.
Our guide to mental maths techniques collects methods you can practise in ten minutes a day.
Time management
| Type of question | Time budget | If you exceed it |
|---|---|---|
| Quick (method visible at once) | Up to 1 minute | Check for a missing insight; move on after one more minute |
| Medium (needs several steps) | 2 to 3 minutes | Flag and return in the second pass |
| Hard (no clear approach) | 0 on the first pass | Attempt only with leftover time |
Track in every mock how many minutes each question really took. You will find that a few questions consume a disproportionate share of the section; learn to recognise them early.
Negative marking in QA
MCQs: +3 for correct, −1 for wrong. If you can eliminate even one option, the expected value of a guess is positive; if you cannot, leave it. Type-in questions: attempt anything for which you have a result. Work out your own marginal accuracy using accuracy versus attempts. Check the CAT marking scheme for the detail.
How to practise: topic tests, sectionals and mocks
- Topic tests (daily in the early phase). Study one topic, then take a 10 to 15 question test on it. Review all errors before moving on.
- Mixed sets (weekly). A 15 to 20 question set mixing topics, timed, to practise recognising the topic from the question.
- QA sectional mocks (once or twice a week in the middle phase). A full 22-question, 40-minute section with the two-pass method.
- Full-length mocks. To see how fatigue after VARC and DILR affects your QA accuracy.
When a topic keeps costing you marks, return to topic tests before taking more sectionals, because taking more mocks does not repair a gap.
Analysing your QA result
| Pattern | Probable cause | Action |
|---|---|---|
| Wrong answers cluster in one topic | Concept gap | Revisit the topic; 15 questions within a week |
| Right approach, wrong number | Calculation errors | Daily calculation drills; write steps |
| Easy questions left unattempted at the end | Triage failure: time sunk early | Strict first pass; time ceilings |
| Many guessed MCQs wrong | Guessing without elimination | Define a rule; guess only after eliminating an option |
| Accuracy falls late in the section | Fatigue or pressure | Practise full mocks; keep a two-minute buffer |
A four-week QA improvement cycle
| Week | Focus | How |
|---|---|---|
| 1 | Arithmetic fluency | Daily 15-question mixed sets from percentage, ratio, profit and loss; 10 minutes of calculation drills |
| 2 | Algebra and number system | Topic tests on equations, inequalities, remainders; build a one-page formula and trick sheet |
| 3 | Geometry and counting | Topic tests; for each question write the one idea it used |
| 4 | Sectional practice | Two timed 40-minute sectionals using the two-pass method; review by family and cause of error |
After the fourth week, compare the sectional accuracy with the first sectional of the cycle. If accuracy has risen but attempts have not, the next cycle should push speed. If attempts have risen but accuracy has dropped, tighten selection.
Common mistakes in QA preparation
- Studying advanced topics before securing arithmetic and algebra, which yield more marks per hour.
- Solving questions without a clock for too long, and so never learning triage.
- Learning shortcuts without understanding why they work, which leads to misapplication.
- Skipping the review of questions answered correctly but slowly; the slow ones are tomorrow's wrong answers.
- Ignoring type-in practice and then being unsettled by questions with no options.
Related pages
Return to the CAT hub, the CAT mock test strategy and the other sections: VARC and DILR. For an example of how the numbers from a mock can change your plan, read how to use mock tests for CAT preparation. The QA-related tests available on TestMint are listed below when institutes have published them.
Note: the structure above reflects CAT 2025; confirm the current pattern in the official notification.
