CAT 2023QASlot 2 · Afternoon

CAT 2023 Slot 2 QA Question Paper with Solutions

40 Minutes22 QuestionsNov 26, 20233 marks correct · −1 wrong

Questions

0 / 22 answered0 correct0 wrong

Q1CAT 2023 Slot 2 QA

For any natural numbers

m

n

and

k

, such that

k

divides both

m + 2n

and

3m + 4n

k

must be a common divisor of

Q2CAT 2023 Slot 2 QA

View Standalone Page

The sum of all possible values of

x

satisfying the equation

2^{4x^{2}} - 2^{2x^{2} + x + 16} + 2^{2x + 30} = 0

, is

Q3CAT 2023 Slot 2 QA

View Standalone Page

Any non-zero real numbers

x

y

such that

y \neq 3

and

\dfrac{x}{y} < \dfrac{x + 3}{y - 3}

, will satisfy the condition

Q4CAT 2023 Slot 2 QA

View Standalone Page

Let

a

b

m

and

n

be natural numbers such that

a > 1

and

b > 1

. If

a^{m}b^{n} = 144^{145}

, then the largest possible value of

n - m

Q5CAT 2023 Slot 2 QA

View Standalone Page

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

Type your answer

Q6CAT 2023 Slot 2 QA

View Standalone Page

For some positive real number

x

, if

\log_{\sqrt{3}}(x) + \dfrac{\log_{x}(25)}{\log_{x}(0.008)} = \dfrac{16}{3}

, then the value of

\log_{3}(3x^{2})

Type your answer

Q7CAT 2023 Slot 2 QA

View Standalone Page

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

\dfrac{k}{4y} + 9y

Type your answer

Q8CAT 2023 Slot 2 QA

View Standalone Page

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

Q9CAT 2023 Slot 2 QA

View Standalone Page

Minu purchases a pair of sunglasses at Rs.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 Rs.500, then the percentage of profit made by Minu when she sold the pair of sunglasses to Tanu is

Q10CAT 2023 Slot 2 QA

View Standalone Page

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

Q11CAT 2023 Slot 2 QA

View Standalone Page

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

Q12CAT 2023 Slot 2 QA

View Standalone Page

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

Q13CAT 2023 Slot 2 QA

View Standalone Page

Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 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

Q14CAT 2023 Slot 2 QA

View Standalone Page

Jayant bought a certain number of white shirts at the rate of Rs 1000 per piece and a certain number of blue shirts at the rate of Rs 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 Rs 51000. If he bought both colors of shirts, then the maximum possible total number of shirts that he could have bought is

Type your answer

Q15CAT 2023 Slot 2 QA

View Standalone Page

If a certain amount of money is divided equally among

n

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

n

Type your answer

Q16CAT 2023 Slot 2 QA

View Standalone Page

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

Type your answer

Q17CAT 2023 Slot 2 QA

View Standalone Page

n 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

Q18CAT 2023 Slot 2 QA

View Standalone Page

A triangle is drawn with its vertices on the circle

C

such that one of its sides is a diameter of

C

and the other two sides have their lengths in the ratio of

a : b

. If the radius of the circle is

r

, then the area of the triangle is

Q19CAT 2023 Slot 2 QA

View Standalone Page

The area of the quadrilateral bounded by the Y-axis, the line

x = 5

, and the lines

\left|x - y\right| - \left|x - 5\right| = 2

, is

Type your answer

Q20CAT 2023 Slot 2 QA

View Standalone Page

Let both the series

a_1, a_2, a_3, \ldots

and

b_1, b_2, b_3, \ldots

be in arithmetic progression such that the common differences of both the series are prime numbers. If

a_5 = b_9

a_{19} = b_{19}

and

b_2 = 0

, then

a_{11}

equals

Q21CAT 2023 Slot 2 QA

View Standalone Page

p^{2} + q^{2} - 29 = 2pq - 20 = 52 - 2pq

, then the difference between the maximum and minimum possible value of

p^{3} - q^{3}

Q22CAT 2023 Slot 2 QA

View Standalone Page

Let

a_n

and

b_n

be two sequences such that

a_n = 13 + 6(n - 1)

and

b_n = 15 + 7(n - 1)

for all natural numbers

n

. Then, the largest three digit integer that is common to both these sequences, is

Type your answer

About CAT 2023 Slot 2 QA

The QA section of CAT 2023 Slot 2 was conducted on November 30, 2023, the last Sunday of November — consistent with IIM's scheduling across all recent years. The section contains 24 questions to be answered in 40 minutes, carrying 72 marks in total. There is no sectional time limit within the overall exam, but students choosing to switch sections mid-paper lose the ability to return — making pacing within QA critical.

Passage Topics in CAT 2023 Slot 2 QA

CAT 2023 Slot 2 QA featured four reading comprehension passages and a standalone Verbal Ability block. The RC passages spanned complexity theory and global systems, the aesthetics of electronic music, the economics of income inequality, and the legal history of criminal responsibility — a typical CAT spread across the sciences, humanities, and social sciences. The VA section included Para Jumbles, Para Summary, and Odd Sentence Out questions, consistent with the pattern since CAT 2019.

CAT 2023 QA Marking Scheme

Correct answer (MCQ): +3 marks
Wrong answer (MCQ): −1 mark
Unattempted (MCQ): 0 marks
TITA questions (if any): +3 correct, no negative marking

How to Use This Question Paper

Click any answer option to immediately check your answer. The correct option is highlighted in green; if you selected the wrong option, it is shown in red and the correct answer is revealed. A detailed explanation appears below each question after you answer it, along with statistics showing what percentage of students answered correctly in the actual exam.

The question navigator at the top of the page updates in real time — green bubbles indicate correct answers and red indicate wrong. Use this to spot weak areas at a glance. To practice under timed conditions, use the Take Full Mock button to attempt the complete CAT 2023 Slot 2 paper with a live timer and percentile benchmarking.

Tips for CAT QA Preparation

Reading Comprehension accounts for roughly two-thirds of the QA section. The passages in CAT are dense and argumentative — they reward close reading of the author's position rather than skimming for facts. Practising on past papers is the most reliable way to calibrate your reading speed, improve inference accuracy, and recognise the types of questions IIM setters favour. Use the answer statistics on this page to benchmark yourself; questions where more than 50% of test-takers answered correctly are ones you should aim to get right every time.