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CAT 2025 Quantitative Aptitude Slot 01 – All Questions with Easy Solutions

Updated: 22 hours ago

CAT 2025 Quantitative Aptitude Slot 01

Prepared by Anshu Agarwal, CAT QA 99.97 percentiler & XAT QA Topper, known for making Quant the easiest section for thousands of students across India. With 1100+ videos and years of real exam experience, I simplify even the toughest CAT questions into the easiest possible methods.


If you are preparing for CAT 2026 or CAT 2027, then solving the CAT 2025 QA Slot 01 paper is one of the smartest ways to understand:


  • The exact CAT pattern

  • Types of questions asked

  • Difficulty level

  • Repeating concepts

  • How toppers think in the QA section

On this page, I will upload:

✔️ All CAT 2025 QA Slot 01 Questions

✔️ Easy and student-friendly written solutions

✔️ Video Solutions for each question


CAT 2025 – Quantitative Aptitude (QA) Slot 01 Solutions



1. If the length of a side of a rhombus is 36 cm and the area of the rhombus is 396 sq. cm, then the absolute value of the difference between the lengths, in cm, of the diagonals of the rhombus is:


2. If a − 6b + 6c = 4 and 6a + 3b − 3c = 50

, where a, b and c are real numbers, the value of 2a + 3b − 3c is:

(a) 20

(b) 15

(c) 14

(d) 18


3. At a certain simple rate of interest, a given sum amounts to Rs 13920 in 3 years, and to Rs 18960 in 6 years and 6 months. If the same given sum had been invested for 2 years at the same rate as before but with interest compounded every 6 months, then the total interest earned, in rupees, would have been nearest to:

(a) 3096

(b) 3180

(c) 3221

(d) 3150


4. Arun, Varun and Tarun, if working alone, can complete a task in 24, 21, and 15 days, respectively. They charge Rs 2160, Rs 2400, and Rs 2160 per day, respectively, even if they are employed for a partial day. On any given day, any of the workers may or may not be employed to work. If the task needs to be completed in 10 days or less, then the minimum possible amount, in rupees, required to be paid for the entire task is:

(a) 34400

(b) 38400

(c) 38880

(d) 47040


5. Shruti travels a distance of 224 km in four parts for a total travel time of 3 hours. Her speeds in these four parts follow an arithmetic progression, and the corresponding time taken to cover these four parts follow another arithmetic progression. If she travels at a speed of 960 meters per minute for 30 minutes to cover the first part, then the distance, in meters, she travels in the fourth part is

(a) 86400

(b) 112000

(c) 76800

(d) 96000

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6. In a class, there were more than 10 boys and a certain number of girls. After 40% of the girls and 60% of the boys left the class, the remaining number of girls was 8 more than the remaining number of boys. Then, the minimum possible number of students initially in the class was:


7. The (x, y) coordinates of vertices P, Q and R of a parallelogram PQRS are (-3, -2), (1, -5) and (9, 1) respectively. If the diagonal SQ intersects the x- axis at (a, 0), then the value of a is:

(a) 29/9

(b) 27/7

(c) 13/4

(d) 10/3


8. A cafeteria offers 5 types of sandwiches. For each type, a customer can choose one of 4 breads and choose small/large. Optionally, they may add up to 2 out of 6 sauces. The number of ways to order is:

(a) 880

(b) 600

(c) 840

(d) 800


9. A value of c for which the minimum value of f(x) = x² − 4cx + 8c is greater than the maximum value of g(x) = −x² + 3cx − 2c, is:

(a) –1/2

(b) 2

(c) 1/2

(d) –2


10. In the set of odd numbers {1, 3, 5, …, 57}, there is a number k such that sum of all numbers less than k equals sum of all numbers greater than k. Then k equals:

(a) 41

(b) 43

(c) 37

(d) 39

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11. Number of pairs (x, y) of integers satisfying x > y ≥ 3 and x + y < 14, is:


12. Stocks A, B and C are priced at Rs 120, 90, 150. A trader holds 10 shares of A and 20 shares of B and C combined. If total value is Rs 3300, number of B shares is:


13. Ratio of morning:afternoon students is 13:9. After 21 shift, ratio is 19:14. More join in ratio 3:8 and final ratio becomes 5:4. Number of new students is:

(a) 88

(b) 99

(c) 121

(d) 110


  1. For any natural number k, let

aₖ = 3ᵏ. Smallest natural number m for which

( (a₁)¹ × (a₂)² × … × (a₂₀)²⁰ ) < ( a₂₁ × a₂₂ × … × a₂₀₊ₘ ) is:

(a) 56

(b) 59

(c) 58

(d) 57


15. Let 3 ≤ x ≤ 6 and [x²] = [x]²

, where [x] is the greatest integer ≤ x. A possible subset of S is:


(a) [3, √10] ∪ [4, √17] ∪ {6}

(b) (3, √10) ∪ [5, √26) ∪ {6}

(c) [3, √10] ∪ [5, √26]

(d) (4, √18) ∪ [5, √27) ∪ {6}

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  1. Number of integers n for which

(a) 1

(b) 0

(c) infinite

(d) 2

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  1. Kamala divided her investment of Rs 100000 between stocks, bonds, and gold. Her investment in bonds was 25% of her investment in gold. With annual returns of 10%, 6%, 8% on stocks, bonds, and gold, respectively, she gained a total amount of Rs 8200 in one year. The amount, in rupees, that she gained from the bonds, was


  1. A 3-digit number N has all non-zero, distinct digits. None is a perfect square, and exactly one is a prime. Number of factors of minimum such N is:


19. In a circle with centre C and radius 6√2 centimetre PQ and SR are two parallel chords separated by one of the diameters. If ∠PQC = 45° and the ratio of the perpendicular distance of PQ and SR from C is 3: 2. Then the area in sq. cm. of the quadrilateral PQRS is.

(a) 4(3 + √14)

(b) 20(3 + √14)

(c) 20(3√2 + √7)

(d) 4(3√2 + √7)


20. A container holds 200 litres of a solution of acid and water, having 30% acid by volume. Atul replaces 20% of this solution with water, then replaces 10% of the resulting solution with acid, and finally replaces 15% of the solution thus obtained, with water. The percentage of acid by volume in the final solution obtained after these three replacements, is nearest to

(a) 23

(b) 25

(c) 27

(d) 29

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21. A shopkeeper offers a discount of 22% on the marked price of each chair, and gives 13 chairs to a customer for the discounted price of 12 chairs to earn a profit of 26% on the transaction. If the cost price of each chair is Rs 100, then the marked price, in rupees, of each chair is:


22. Number of non-negative integers K for which x² − 5x + K = 0 has only integer roots is:

If you are preparing for CAT/IPMAT, make sure you learn from one of the most trusted and structured courses by Anshu Agarwal Sir — covering Complete Quant, DI LR, Full-Length Test Series, Topic-wise Tests, and Printed Material.

The course is designed to give you conceptual clarity, exam-focused practice, and consistent guidance throughout your preparation.


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Why Every CAT 2026 & CAT 2027 Aspirant Should Solve CAT 2025 QA

  • Gives exposure to real CAT-level difficulty

  • Shows the concepts that repeat every year

  • Improves exam-level speed & accuracy

  • Helps identify strengths & weaknesses

  • Builds confidence with actual PYQs

  • Makes preparation more predictable and structured


All solutions will be kept simple and easy to follow.


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