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CAT 2023 Slot 2 Quantitative Aptitude | Easy Solutions + Video Explanations

CAT 2023 Slot 02
CAT 2023 Slot 02

If you’ve been scared of Quantitative Aptitude in CAT, this blog will change that!

Here, you’ll find CAT 2023 Slot 2 QA questions solved in the easiest way possible — not just detailed solutions, but wherever possible, super-short tricks to crack questions in seconds.


And yes, these are not just random methods — they’re taught by Anshu Agarwal Sir (99.97%ile in CAT QA), the mentor behind some of India’s best results. His CAT 2025 and CAT 2026 video courses have helped hundreds of students reach IIMs.

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Every solution here is explained step-by-step so you can understand the logic, but we’ve also added short explanationswherever possible — so you can solve faster in the exam.


This is not just a question bank — it’s your CAT Quant mastery guide, combining clarity with speed. And if you want to learn directly from Anshu Sir, the CAT 2025 & CAT 2026 video courses are the exact system that produced toppers like AIR 5 in IPMAT Indore, 99.93%ile in CAT, and 99.99%ile in XAT QA.


1.

CAT 2023 Slot 02

Short Explanation:


2. For any natural numbers m, n, k, such that k divides both m + 2n and 3m + 4n, k must be a common divisor of:

(a) m and 2n

(b) 2m and n

(c) m and n

(d) 2m and 3n



3. The sum of all possible values of x satisfying the equation

2⁴ˣ² − 2²ˣ²⁺ˣ⁺¹⁶ + 2²ˣ⁺³⁰ = 0, is:

(a) 5/2

(b) 3

(c) 3/2

(d) 1/2



4. Let a, b, m and n be natural numbers such that a > 1 and b > 1.

If aᵐ bⁿ = 144¹⁴⁵, then the largest possible value of n − m is:

(a) 289

(b) 580

(c) 290

(d) 579



5.

CAT 2023 Slot 02


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6. Let k be the largest integer such that the equation (x − 1)² + 2kx + 11 = 0 has no real roots. If y is a positive real number, then the least possible value of k / 4y + 9y is:



7. The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is



8. Anil borrows ₹ 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays ₹ 10320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year. Then, the total interest, in rupees, paid over the three years is nearest to:

(a) 40991

(b) 33130

(c) 51311

(d) 45311

Short Explanation:



9. Minu purchases a pair of sunglasses at ₹ 1000 and sells to Kanu at 20% profit. Then, Kanu sells it back to Minu at 20% loss. Finally, Minu sells the same pair of sunglasses to Tanu. If the total profit made by Minu from all her transactions is ₹ 500, then the percentage of profit made by Minu when she sold the pair of sunglasses to Tanu is

(a) 26%

(b) 31.25%

(c) 35.42%

(d) 52%

Short Explanation:



10. Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by Pipe A to fill the empty tank. When pipes A, B and C are turned on together, the empty tank is filled in two hours. If pipes B and C are turned on together when the tank is empty and Pipe B is turned off after one hour, then Pipe C takes another one hour and 15 minutes to fill the remaining tank. If Pipe A can fill the empty tank in less than five hours, then the time taken, in minutes, by Pipe C to fill the empty tank is:

(a) 60

(b) 75

(c) 120

(d) 90

Short Explanation:



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11. The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is

(a) 16,20,000

(b) 19,44,000

(c) 97,20,000

(d) 12,96,000



12. Ravi is driving at a speed of 40 km/h on a road. Vijay is 54 meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along the same road from the opposite direction at a speed of 50 km/h and is 225 meters away from Ravi. The speed, in km/h, at which Vijay should drive so that all the three cross each other at the same time, is

(a) 64.4

(b) 58.8

(c) 67.2

(d) 61.6

Short Explanation:




13. In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average salary obtained by the manufacturing employees to the average salary obtained by the non- manufacturing employees is:

(a) 4 : 5

(b) 5 : 6

(c) 6 : 5

(d) 5 : 4




14. A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is

Short Explanation:




15. If a certain amount of money is divided equally among n persons, each one receives ₹ 352. However, if two persons receive ₹ 506 each and the remaining amount is divided equally among the other persons, each of them receive less than or equal to ₹ 330. Then, the maximum possible value of n is

Short Explanation:



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16. Jayant bought a certain number of white shirts at the rate of ₹ 1000 per piece and a certain number of blue shirts at the rate of ₹ 1125 per piece. For each shirt, he then set a fixed market price which was 25% higher than the average cost of all the shirts. He sold all the shirts at a discount of 10% and made a total profit of ₹ 51000. If he bought both colors of shirts, then the maximum possible total number of shirts that he could have bought is

Short Explanation:




17. In a rectangle ABCD, AB = 9 cm and BC = 6 cm. P and Q are two points on BC such that the areas of the figures ABP, APQ, and AQCD are in geometric progression. If the area of the figure AQCD is four times the area of triangle ABP, then BP : PQ : QC is:

(a) 1 : 2 : 1

(b) 1 : 1 : 2

(c) 1 : 2 : 4

(d) 2 : 4 : 1



CAT 2023 Slot 02

19. The area of the quadrilateral bounded by the y–axis, the line x = 5 and the lines |x − y| − |x − 5| = 2 is:

Short Explanation:



20. Let both the series a₁, a₂, a₃,… and b₁, b₂, b₃,… be in arithmetic progression such that the common differences of both the series are prime numbers. If a₅ = b₉, a₁₉ = b₁₉ and b₂ = 0, then a₁₁ equals:

(a) 83

(b) 86

(c) 84

(d) 79

Short Explanation:



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21. If p² + q² − 29 = 2pq − 20 = 52 − 2pq, then the difference between maximum and minimum possible value of (p³ − q³) is:

(a) 189

(b) 243

(c) 486

(d) 378

Short Explanation:




22. Let aₙ and bₙ be two sequences such that aₙ = 13 + 6(n − 1) and bₙ = 15 + 7(n − 1) for all natural numbers n. Then, the largest three-digit integer that is common to both these sequences is:

Short Explanation:



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The CAT 2023 Slot 2 Quantitative Aptitude section reminded us of a simple truth — the exam doesn’t reward who studies the most, it rewards who prepares the smartest.

Every question you just saw was solved in the easiest possible way, and wherever possible, we even gave short tricks so you can save precious seconds in the exam hall.


If you can understand and apply these methods, you’re already ahead of thousands of aspirants.

And if you want this clarity, speed, and accuracy for every single topic of CAT QA, then my CAT 2025 and CAT 2026 video courses will give you exactly that — with complete video lessons, printed material, test series, and doubt support, designed from scratch for future toppers.


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Your next step? Don’t just read solutions — master the approach. Because in CAT, it’s not about solving all questions, it’s about solving the right ones in the right way.

Now go practice, and I’ll see you in the list of top scorers.



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