October 10, 2026
Practise CAT Quantitative Aptitude questions from Arithmetic, Algebra, Geometry, Number System and Modern Math with answers and step-by-step solutions. These questions are useful for CAT 2026 preparation, revision of important formulas and timed practice before attempting a full-length mock test.
Before practising, go through the CAT Syllabus and understand the CAT exam pattern. This will help you identify the topics you need to cover and plan your practice sessions.

The Quantitative Aptitude (QA) section tests your understanding of mathematical concepts, calculations and problem-solving. The questions are based mainly on topics covered in school-level mathematics, but some require more than one step to solve. You can also check CAT PYQs to understand the exam pattern, question types, and level of questions asked in CAT.
| Particulars | Details |
|---|---|
| Section | Quantitative Aptitude |
| Major topics | Arithmetic, Algebra, Geometry, Number System and Modern Math |
| Question format | MCQs and Type In The Answer (TITA) |
| Practice Plan | Learn the concepts, solve topic-wise questions and then try mixed sets |
| Helpful Resources | CAT Quant practice questions, past papers and mock tests |
| Number System CAT Questions PDF | |
| Arithmetic CAT Questions PDF | |
| Number Theory CAT Questions PDF | |
| Quadratic Equation CAT Questions PDF | |
| CAT Inequalities Questions PDF | |
| Logarithms, Surds & Indices Questions PDF | |
| Time, Speed & Distance Questions PDF | |
| Linear Equations Questions PDF | |
| Ratio, Proportion & Variations Questions PDF | |
| Simple Interest - Compound Interest Questions PDF | |
| Profit & Loss CAT Questions PDF |
The following CAT quantitative aptitude questions are modelled on the actual CAT Exam Pattern and calibrated to CAT difficulty. Work through each topic block systematically and review answers immediately to build genuine reasoning clarity.
ARITHMETIC — 20 Questions
Q1. A trader marks goods 40% above cost price and offers a 20% discount. What is the profit percentage?
Answer: C) 12%
Q2. Two pipes A and B fill a tank in 12 and 18 hours. Pipe C empties it in 36 hours. If all three are open, how long to fill the tank?
Answer: A) 9 hrs
Q3. If 20% of A = 30% of B, then A : B is:
Answer: B) 3:2
Q4. Train A of length 200 m passes a platform of 300 m in 25 seconds. What is its speed in km/h?
Answer: A) 72 km/h
Q5. A sum doubles in 8 years at simple interest. In how many years will it triple?
Answer: B) 16 years
Q6. A mixture of 60 litres contains milk and water in ratio 7:3. How many litres of water must be added to make it 3:7?
Answer: C) 80 litres
Q7. If the selling price of 20 articles equals the cost price of 25 articles, the profit percentage is:
Answer: B) 25%
Q8. A boat goes 30 km upstream in 3 hours and 30 km downstream in 2 hours. The speed of the current is:
Answer: B) 2.5 km/h
Q9. A, B, C complete work in 10, 15, 20 days. They start together but A leaves after 2 days. How many more days do B and C take?
Answer: A) 4.5 days
Q10. A shopkeeper gives 2 articles free on purchase of 10. The effective discount percentage is:
Answer: B) 16.67%
Q11. Population increases 10% in year 1 and decreases 10% in year 2. Net percentage change is:
Answer: B) −1%
Q12. Two cars cover the same distance in 5 and 6 hours. If the faster car's speed is 12 km/h more, find the distance.
Answer: C) 360 km
Q13. Compound interest on ₹10,000 at 10% p.a. for 2 years exceeds simple interest by:
Answer: B) ₹100
Q14. In what ratio must rice at ₹45/kg be mixed with rice at ₹60/kg so the mixture costs ₹50/kg?
Answer: B) 2:1
Q15. A man spends 75% of his income and saves ₹3,000. His monthly income is:
Answer: C) ₹12,000
Q16. A is twice as efficient as B. Together they finish work in 10 days. How long for A alone?
Answer: B) 15 days
Q17. The average of 5 numbers is 40. If one is excluded, the average drops to 35. The excluded number is:
Answer: B) 60
Q18. A train crosses a pole in 9 seconds and a 240 m bridge in 21 seconds. The length of the train is:
Answer: C) 180 m
Q19. A dealer buys at 20% discount on MRP and sells at 10% discount. His profit percentage is:
Answer: C) 12.5%
Q20. The difference between a two-digit number and the number formed by reversing its digits is 36. How many such numbers are possible?
Answer: C) 6
ALGEBRA — 20 Questions
Q21. If x + 1/x = 3, find x² + 1/x².
Answer: A) 7
Q22. The sum of roots of 2x² − 5x + 3 = 0 is:
Answer: B) 5/2
Q23. If f(x) = x² − 3x + 2, find f(f(0)).
Answer: B) 2
Q24. The 10th term of an AP is 52 and the 3rd term is 10. The common difference is:
Answer: C) 6
Q25. Find the sum of the first 20 terms of the AP: 5, 8, 11, …
Answer: C) 680
Q26. For what value of k does kx² + 4x + 4 = 0 have equal roots?
Answer: B) 1
Q27. A GP has first term 3 and common ratio 2. The 6th term is:
Answer: B) 96
Q28. Solve: |2x − 5| ≤ 9. The solution set is:
Answer: A) −2 ≤ x ≤ 7
Q29. If log 2 = 0.301 and log 3 = 0.477, the value of log 12 is:
Answer: A) 1.079
Q30. How many integers x satisfy x² − 5x − 6 < 0?
Answer: C) 5
Q31. The product of two consecutive even integers is 288. The larger integer is:
Answer: B) 18
Q32. If a + b = 10 and ab = 16, then a² + b² is:
Answer: A) 68
Q33. Find x if 3^(2x−1) = 27.
Answer: B) 2
Q34. If the AM of two numbers is 10 and their GM is 8, the numbers are:
Answer: A) 4 & 16
Q35. The sum of an infinite GP is 12 and its first term is 4. The common ratio is:
Answer: C) 2/3
Q36. The number of real roots of x⁴ − 5x² + 4 = 0 is:
Answer: B) 4
Q37. If f(x) = (x+2)/(x−3), then f⁻¹(x) is:
Answer: A) (3x+2)/(x−1)
Q38. The expression (x² − 9)/(x − 3) equals x + 3 for:
Answer: A) All integers except x = 3
Q39. The sum of all values of x satisfying x² − |x| − 6 = 0 is:
Answer: A) 0
Q40. If α and β are roots of x² − px + q = 0, then α² + β² equals:
Answer: A) p² − 2q
NUMBER SYSTEM — 20 Questions
Q41. The remainder when 2^100 is divided by 3 is:
Answer: B) 1
Q42. HCF of 72, 108, and 180 is:
Answer: C) 36
Q43. The number of factors of 360 is:
Answer: C) 24
Q44. The units digit of 7^95 is:
Answer: C) 7
Q45. LCM of two numbers is 120 and HCF is 10. If one number is 40, the other is:
Answer: C) 30
Q46. Two-digit numbers divisible by both 3 and 5:
Answer: B) 6
Q47. The remainder when 17 × 19 × 23 is divided by 7 is:
Answer: C) 3
Q48. A number when divided by 5, 6, and 8 leaves remainder 4. The smallest such number is:
Answer: C) 124
Q49. Prime numbers between 50 and 80:
Answer: C) 7
Q50. N = 2^a × 3^b × 5^c has 18 factors with a > b > c. The minimum value of N is:
Answer: A) 180
Q51. Which pair is a perfect square? (441, 512, 676, 800)
Answer: C) Both 441 & 676
Q52. Trailing zeros in 7! (5040) are:
Answer: B) 1
Q53. 1000 can be expressed as a product of two co-prime numbers in how many ways?
Answer: C) 4
Q54. If p is a prime > 5, then p mod 6 is:
Answer: C) Either 1 or 5
Q55. Sum of all 3-digit numbers divisible by 7 is:
Answer: A) 70,329
Q56. Smallest number to be subtracted from 4000 to make it a perfect square is:
Answer: A) 39
Q57. Find the remainder when 14^15 + 15^14 is divided by 5.
Answer: A) 0
Q58. The greatest 4-digit number divisible by 15 is:
Answer: C) 9990
Q59. If 5^n ends in 0, then n is:
Answer: C) Impossible (5^n always ends in 5)
Q60. The LCM of first 10 natural numbers is:
Answer: B) 2520
GEOMETRY & MENSURATION — 20 Questions
Q61. Area of an equilateral triangle with side 6 cm is:
Answer: A) 9√3 cm²
Q62. In a right-angled triangle, hypotenuse is 13 cm and one leg is 5 cm. The other leg is:
Answer: C) 12 cm
Q63. A circle has a chord of 8 cm at 3 cm from the centre. The radius is:
Answer: B) 5 cm
Q64. Volume of a cone with radius 7 cm and height 12 cm (π = 22/7) is:
Answer: A) 616 cm³
Q65. Two similar triangles have sides in ratio 3:5. The ratio of their areas is:
Answer: C) 9:25
Q66. Diagonals of a rhombus are 24 and 10. Its perimeter is:
Answer: A) 52 cm
Q67. The angle subtended by a diameter at the circumference is:
Answer: C) 90°
Q68. Total surface area of a hemisphere of radius 7 cm (π = 22/7) is:
Answer: A) 462 cm²
Q69. In triangle ABC, angle A = 60°, angle B = 70°. The exterior angle at C is:
Answer: C) 130°
Q70. Distance between (3, −4) and (−3, 4) on a coordinate plane is:
Answer: C) 10
Q71. In a circle with radius 10, a chord subtends a central angle of 60°. The chord length is:
Answer: B) 10 cm
Q72. If the circumradius of an equilateral triangle is 6, the side is:
Answer: B) 6√3 cm
Q73. A trapezium has parallel sides 10 and 14 cm with height 6 cm. Area is:
Answer: B) 72 cm²
Q74. The slope of a line perpendicular to 2x − 3y + 5 = 0 is:
Answer: B) −3/2
Q75. A sector of radius 14 cm subtends 90°. Its area (π = 22/7) is:
Answer: A) 154 cm²
Q76. In triangle PQR, PQ = QR = 5 and PR = 6. The median from Q has length:
Answer: A) 4 cm
Q77. The locus of a point equidistant from two fixed points is:
Answer: C) Perpendicular bisector
Q78. If sides of a triangle are 7, 24, 25, it is:
Answer: C) Right-angled
Q79. A cube of side 4 cm is melted into a sphere. The radius of the sphere is approximately:
Answer: A) ~2.48 cm
Q80. The area of a circle inscribed in an equilateral triangle of side 6 cm (π = 22/7) is:
Answer: C) ~9.57 cm²
MODERN MATH (P&C, Probability, Set Theory) — 10 Questions
Q81. In how many ways can 5 books be arranged on a shelf?
Answer: C) 120
Q82. Probability of drawing a king from a standard deck of 52 cards:
Answer: D) Both A & C
Q83. From 6 men and 4 women, a committee of 4 with at least 2 women can be formed in:
Answer: D) 111 ways
Q84. In a group of 70 people, 37 like coffee and 52 like tea. Each likes at least one. How many like both?
Answer: B) 19
Q85. Two dice are rolled. Probability that the sum is at least 10:
Answer: A) 1/6
Q86. Number of ways to select 3 vowels from EQUATION:
Answer: C) 20 (⁶C₃)
Q87. A bag has 3 red and 5 blue balls. Two drawn without replacement. P(both red) =
Answer: A) 3/28
Q88. 4-digit numbers using digits 1–7 without repetition:
Answer: B) 840
Q89. In a class of 40, 20 play cricket and 25 play football. 10 play both. How many play neither?
Answer: C) 5
Q90. If ⁿC₂ = 21, then n =
Answer: C) 7
TIME, SPEED & WORK — 10 Questions
Q91. A covers 1 km in 5 min, B in 6 min. By how much distance does A beat B in a 1 km race?
Answer: C) 166.7 m
Q92. 6 workers complete work in 12 days. Workers needed to finish in 8 days:
Answer: C) 9
Q93. A car averages 40 km/h for 100 km and 60 km/h for next 100 km. Average speed is:
Answer: A) 48 km/h
Q94. Trains of 100 m and 80 m in opposite directions at 72 and 54 km/h. Time to cross each other:
Answer: C) 6 sec
Q95. A and B alternate (starting A) completing work in 10 and 20 days. Total days to finish:
Answer: C) 13.5 days
Q96. Man walks at 4 km/h, cycles at 12 km/h. Covers 48 km in 6 hours. Distance walked:
Answer: D) 12 km
Q97. Pipe A fills in 4 hrs, B in 6 hrs. Time to fill 2/3 of tank together:
Answer: B) 1.6 hrs
Q98. A is 3× as fast as B and finishes 40 days ahead. Days to finish together:
Answer: C) 15 days
Q99. A to B at 60 km/h, return at 40 km/h. Average speed for round trip:
Answer: A) 48 km/h
Q100. 12 men complete work in 20 days. After 5 days, 4 more join. Remaining days needed:
Answer: C) ~12 days
Solving more questions helps, but the way you practise matters too. Follow these steps to improve your accuracy and speed.
Looking at previous CAT papers can help you decide which Quant topics to practise first. Arithmetic and Algebra have remained important over the years, while Geometry, Number System and Modern Math have also appeared in the exam. However, the number of questions from each topic changes across years and slots.
The table below gives an approximate topic-wise distribution of CAT Quantitative Aptitude questions. The 2019 paper had 34 Quant questions, the 2020 paper had 26, and the section has had 22 questions in each slot in recent years. The figures for older papers and topic classifications may vary across analyses.
| CAT Year | Arithmetic | Algebra | Geometry & Mensuration | Number System | Modern Math |
|---|---|---|---|---|---|
| 2019 | 13–14 | 8–9 | 5–6 | 3–4 | 2–3 |
| 2020 | 8–10 | 5–8 | 2–4 | 1–5 | 0–2 |
| 2021 | 8–11 | 5–8 | 3–4 | 1–2 | 1–3 |
| 2022 | 8–9 | 7–8 | 3–4 | 2–4 | 1–2 |
| 2023 | 8–9 | 7–8 | 2–4 | 1–3 | 1–2 |
| 2024 | 8 | 8 | 3 | 2 | 1 |
| 2025 | 8–10 | 6–8 | 3–4 | 1–3 | 1–2 |
Arithmetic and Algebra should be a priority because they account for a large share of recent CAT Quant questions. Still, avoid skipping an entire topic based only on its past weightage. The distribution can change in the next paper.
The difficulty of CAT Quantitative Aptitude questions depends on the concepts involved, the number of steps required and the time needed to solve them. A question may use a familiar formula but still be challenging if it requires several calculations or combines two topics.
CAT 2025 analysis reports generally placed Quant in the moderate to difficult range, although individual slot assessments differed. This is why practising questions at different difficulty levels is useful.
Difficulty Level of CAT Quant Questions
| Difficulty Level | What to Expect | How to Practise |
|---|---|---|
| Easy | Questions based on basic formulas and simple calculations | Practise regularly and focus on getting the answers right |
| Moderate | Questions that need a few steps or more than one concept | Solve topic-wise questions and work on your calculation speed |
| Difficult | Questions with lengthy calculations or concepts that are harder to apply | Learn the basics first, then practise these questions and understand the solutions |
The difficulty of a topic depends on your preparation, but the following order can help beginners organise their practice.
1. Easy to start with
These topics help you build confidence and revise concepts used in other questions.
2. Topics that need regular practice
These questions may require you to choose the right formula or combine more than one concept.
3. Topics That Need More Practice
These topics may take more time to solve, so practise them regularly. Once you understand the basic concepts, many questions become easier to handle.
Regular practice is the best way to become more comfortable with CAT Quantitative Aptitude questions. Start with the topics you find difficult, revise formulas and gradually increase the difficulty of your practice sets. Use CAT Previous Year Papers and CAT Mock Tests to check your progress and identify areas that need more attention.
Frequently Asked Questions
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