CAT 2024QASlot 3 · Evening

CAT 2024 Slot 3 QA Question Paper with Solutions

40 Minutes22 QuestionsNov 24, 20243 marks correct · −1 wrong

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Q1CAT 2024 Slot 3 QA

For any non-zero real number

x

, let

f(x) + 2f(\dfrac{1}{x}) = 3x

. Then, the sum of all possible values of

x

for which

f(x) = 3

, is

Q2CAT 2024 Slot 3 QA

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A regular octagon ABCDEFGH has sides of length

6

cm each. Then the area, in sq. cm, of the square ACEG is

Q3CAT 2024 Slot 3 QA

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(a + b\sqrt{3})^{2} = 52 + 30\sqrt{3}

, where

a

and

b

are natural numbers, then

a + b

equals

Q4CAT 2024 Slot 3 QA

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The number of all positive integers up to

500

with non-repeating digits is

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Q5CAT 2024 Slot 3 QA

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Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayna in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayna on the second day, Mohit and Ayna on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is

Q6CAT 2024 Slot 3 QA

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Gopi marks a price on a product in order to make

20\%

profit. Ravi gets

10\%

discount on this marked price, and thus saves Rs

15

. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is

Q7CAT 2024 Slot 3 QA

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In a group of

250

students, the percentage of girls was at least

44\%

and at most

60\%

. The rest of the students were boys. Each student opted for either swimming or running or both. If

50\%

of the boys and

80\%

of the girls opted for swimming while

70\%

of the boys and

60\%

of the girls opted for running, then the minimum and maximum possible number of students who opted for both swimming and running, are

Q8CAT 2024 Slot 3 QA

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A certain amount of water was poured into a

300

litre container and the remaining portion of the container was filled with milk. Then an amount of this solution was taken out from the container which was twice the volume of water that was earlier poured into it, and water was poured to refill the container again. If the resulting solution contains

72\%

milk, then the amount of water, in litres, that was initially poured into the container was

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Q9CAT 2024 Slot 3 QA

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Aman invests Rs

4000

in a bank at a certain rate of interest, compounded annually. If the ratio of the value of the investment after

3

years to the value of the investment after

5

years is

25:36

, then the minimum number of years required for the value of the investment to exceed Rs

20000

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Q10CAT 2024 Slot 3 QA

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The sum of all distinct real values of

x

that satisfy the equation

10^x + \dfrac{4}{10^x} = \dfrac{81}{2}

Q11CAT 2024 Slot 3 QA

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For some constant real numbers

p

k

and

a

, consider the following system of linear equations in

x

and

y

px - 4y = 2

3x + ky = a

A necessary condition for the system to have no solution for

(x,y)

, is

Q12CAT 2024 Slot 3 QA

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10^{68}

is divided by

13

, the remainder is

Q13CAT 2024 Slot 3 QA

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A circular plot of land is divided into two regions by a chord of length

10\sqrt{3}

meters such that the chord subtends an angle of

120^\circ

at the center. Then, the area, in square meters, of the smaller region is

Q14CAT 2024 Slot 3 QA

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Rajesh and Vimal own

20

hectares and

30

hectares of agricultural land, respectively, which are entirely covered by wheat and mustard crops. The cultivation area of wheat and mustard in the land owned by Vimal are in the ratio of

5:3

. If the total cultivation area of wheat and mustard are in the ratio

11:9

, then the ratio of cultivation area of wheat and mustard in the land owned by Rajesh is

Q15CAT 2024 Slot 3 QA

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The number of distinct real values of

x

, satisfying the equation

\max\{x,2\} - \min\{x,2\} = |x + 2| - |x - 2|

, is

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Q16CAT 2024 Slot 3 QA

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The midpoints of sides AB, BC, and AC in

\triangle ABC

are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of

\triangle ABC

1440

sq cm, then the area, in sq cm, of

\triangle XYZ

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Q17CAT 2024 Slot 3 QA

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3^{a} = 4,\;4^{b} = 5,\;5^{c} = 6,\;6^{d} = 7,\;7^{e} = 8

and

8^{f} = 9

, then the value of the product

abcdef

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Q18CAT 2024 Slot 3 QA

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Consider the sequence

t_1 = 1,\;t_2 = -1

and

t_n = \left(\dfrac{n - 3}{n - 1}\right)t_{n - 2}

for

n\geq 3

. Then, the value of the sum

\dfrac{1}{t_2} + \dfrac{1}{t_4} + \dfrac{1}{t_6} + \cdots + \dfrac{1}{t_{2022}} + \dfrac{1}{t_{2024}}

, is

Q19CAT 2024 Slot 3 QA

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The average of three distinct real numbers is

28

. If the smallest number is increased by

7

and the largest number is reduced by

10

, the order of the numbers remains unchanged, and the new arithmetic mean becomes

2

more than the middle number, while the difference between the largest and the smallest numbers becomes

64

. Then, the largest number in the original set of three numbers is

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Q20CAT 2024 Slot 3 QA

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After two successive increments, Gopal’s salary became

187.5\%

of his initial salary. If the percentage of salary increase in the second increment was twice of that in the first increment, then the percentage of salary increase in the first increment was

Q21CAT 2024 Slot 3 QA

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The number of distinct integer solutions

(x,y)

of the equation

|x + y| + |x - y| = 2

, is

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Q22CAT 2024 Slot 3 QA

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A train travelled a certain distance at a uniform speed. Had the speed been

6

km per hour more, it would have needed

4

hours less. Had the speed been

6

km per hour less, it would have needed

6

hours more. The distance, in km, travelled by the train is

About CAT 2024 Slot 3 QA

The QA section of CAT 2024 Slot 3 was conducted on November 30, 2024, 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 2024 Slot 3 QA

CAT 2024 Slot 3 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 2024 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 2024 Slot 3 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.