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CAT 2025 Quantitative Aptitude Slot 02 – All Questions with Easy Solutions

Updated: Dec 10, 2025

CAT 2025 Quantitative Aptitude Slot 02

Prepared by Anshu Agarwal, CAT QA 99.97 percentile & XAT QA Topper, known for simplifying Quant for thousands of CAT aspirants across India. With 1100+ videos and real exam-driven teaching, I make even the toughest CAT QA questions feel easy and predictable.

If you are preparing for CAT 2026 or CAT 2027, solving the CAT 2025 QA Slot 02 paper is extremely important to understand:

  • The exact CAT pattern

  • Question types and difficulty

  • Frequently repeated concepts

  • How toppers approach QA

  • Real CAT-style traps and logic

On this page, I will upload:


✔️ All CAT 2025 QA Slot 02 Questions

✔️ Easy and student-friendly written solutions

✔️ Video Solutions for each question



CAT 2025 – Quantitative Aptitude (QA) Slot 02 Solutions



1. The sum of digits of the number (625)⁶⁵ × (128)³⁶ is:


  1. Let 𝑎𝑛 be the nth term of a decreasing infinite geometric progression. If 𝑎₁ + 𝑎₂ + 𝑎₃ = 52 and 𝑎₁𝑎₂ + 𝑎₂𝑎₃ + 𝑎₃𝑎₁ = 624, then the sum of this geometric progression is:


(a) 57

(b) 54

(c) 63

(d) 60


  1. The equations 3𝑥² − 5𝑥 + 𝑝 = 0 and 2𝑥² − 2𝑥 + 𝑞 = 0 have one common root. The sum of the other roots of these two equations is:

(a) 2/3 − 2𝑝 + (2/3)𝑞

(b) 8/3 − 𝑝 + (3/2)𝑞

(c) 2/3 − 𝑝 + (3/2)𝑞

(d) 8/3 + 𝑝 + (1/3)𝑞


4. Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start together on a job, and Bipin leaves the job after 20 days. If the job got completed in 60 days, the number of days needed by Chandan to complete the job alone, is:


5. A mixture of coffee and cocoa, 16% of which is coffee, costs Rs 240 per kg. Another mixture of coffee and cocoa, of which 36% is coffee, costs Rs 320 per kg. If a new mixture of coffee and cocoa costs Rs 376 per kg, then the quantity, in kg, of coffee in 10 kg of this new mixture is

(a) 6

(b) 4

(c) 2.5

(d) 5

“For more such high-level CAT guidance by Anshu Agarwal Sir, explore the CAT 2026 & CAT 2027 Video Courses — India’s most structured preparation.”

Aur links hamesha ye rahenge:


6. A certain amount of money was divided among Pinu, Meena, Rinu and Seema. Pinu received 20% of the total amount and Meena received 40% of the remaining amount. If Seema received 20% less than Pinu, the ratio of the amounts received by Pinu and Rinu is

(a) 2: 1

(b) 1: 2

(c) 8: 5

(d) 5: 8


7. The average number of copies of a book sold per day by a shopkeeper is 60 in the initial seven days and 63 in the initial eight days, after the book launch. On the ninth day, she sells 11 copies less than the eighth day, and the average number of copies sold per day from second day to ninth day becomes 66. The number of copies sold on the first day of the book launch is:


8. If 𝑎, 𝑏, 𝑐 and 𝑑 are integers such that their sum is 46, then the minimum possible value of (𝑎 − 𝑏)² + (𝑎 − 𝑐)² + (𝑎 − 𝑑)² is:


9.

CAT 2025 Quantitative Aptitude

10. Let ABCDEF be a regular hexagon and P and Q be the midpoints of AB and CD, respectively. Then, the ratio of the areas of trapezium PBCQ and hexagon ABCDEF is

(a) 6: 25

(b) 6: 19

(c) 7: 24

(d) 5: 24

“For more such high-level CAT guidance by Anshu Agarwal Sir, explore the CAT 2026 & CAT 2027 Video Courses — India’s most structured preparation.”

Aur links hamesha ye rahenge:


11. Rita and Sneha can row a boat at 5 km/h and 6 km/h in still water, respectively. In a river flowing with a constant velocity, Sneha takes 48 minutes more to row 14 km upstream than to row the same distance downstream. If Rita starts from a certain location in the river, and returns downstream to the same location, taking a total of 100 minutes, then the total distance, in km, Rita will cover is:


12. An item with a cost price of Rs. 1650 is sold at a certain discount on a fixed marked price to earn a profit of 20% on the cost price. If the discount doubled, the profit would have been Rs. 110. The rate of discount, in percentage, at which the profit percentage would be equal to the rate of discount, nearest to

(a) 14

(b) 12

(c) 18

(d) 16


13. If 𝑚 and 𝑛 are integers such that (𝑚 + 2𝑛)(2𝑚 + 𝑛) = 27, then the maximum possible value of (2m – 3n) is:


14. The set of all real values of 𝑥 for which (𝑥² − |𝑥 + 9| + 𝑥) > 0, is:

(a) (−∞, −3) ∪ (3, ∞)

(b) (−∞, −9) ∪ (9, ∞)

(c) (−∞, −9) ∪ (3, ∞)

(d) (−9, −3) ∪ (3, ∞)


15. The number of divisors of (2⁶ × 3⁵ × 5³ × 7²), which are of the form (3r + 1), where r is a non-negative integer is:

(a) 56

(b) 36

(c) 24

(d) 42

“For more such high-level CAT guidance by Anshu Agarwal Sir, explore the CAT 2026 & CAT 2027 Video Courses — India’s most structured preparation.”

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16. Let 𝑓(𝑥) = 𝑥 / (2𝑥 − 1) and 𝑔(𝑥) = 𝑥 / (𝑥 − 1).

Then, the domain of the function ℎ(𝑥) = 𝑓(𝑔(𝑥)) + 𝑔(𝑓(𝑥)) is all real numbers except:

(a) −1/2, 1/2 and 1

(b) 1/2 and 1

(c) 1/2, 1 and 3/2

(d) −1, 1/2 and 1


17. In a ∆ABC, points D and E are on the sides BC and AC, respectively. BE and AD intersect at point T such that AD: AT = 4: 3, and BE: BT = 5: 4. Point F lies on AC such that DF is parallel to BE. Then, BD: CD is:

(a) 15: 4

(b) 9: 4

(c) 11: 4

(d) 7: 4


18. A loan of Rs 1000 is fully repaid by two installments of Rs 530 and Rs 594, paid at the end of first and second year, respectively. If the interest is compounded annually, then the rate of interest, in percentage, is

(a) 8

(b) 11

(c) 9

(d) 10


19. The ratio of expenditures of Lakshmi and Meenakshi is 2 : 3, and the ratio of income of Lakshmi to expenditure of Meenakshi is 6 : 7. If excess of income over expenditure is saved by Lakshmi and Meenakshi, and the ratio of their savings is 4 : 9, then the ratio of their incomes is

(a) 7: 8

(b) 3: 5

(c) 2: 1

(d) 5: 6


20. Two tangents drawn from a point P touch a circle with centre O at points Q & R. Points A and B lie on PQ and PR respectively, such that AB is also a tangent to the same circle. If ∠AOB = 50°, then ∠APB in degrees equals:

“For more such high-level CAT guidance by Anshu Agarwal Sir, explore the CAT 2026 & CAT 2027 Video Courses — India’s most structured preparation.”

Aur links hamesha ye rahenge:


21.

CAT 2025 Quantitative Aptitude

22. Suppose 𝑎, 𝑏, 𝑐 are three distinct natural numbers, such that 3𝑎𝑐 = 8(𝑎 + 𝑏). Then, the smallest possible value of 3𝑎 + 2𝑏 + 𝑐 is:


Why CAT 2026 & CAT 2027 Aspirants Must Solve CAT 2025 Slot 02

  • Understand CAT’s real difficulty level

  • Identify common QA patterns

  • Learn the logic behind CAT’s trickiest questions

  • Improve speed, accuracy, and exam temperament

  • Strengthen conceptual clarity with actual PYQs

  • Make overall CAT prep more structured & predictable


All solutions will be kept simple and easy to follow.

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