CAT 2022QASlot 2 · Afternoon

CAT 2022 Slot 2 QA Question Paper with Solutions

40 Minutes22 QuestionsNov 27, 20223 marks correct · −1 wrong

Questions

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Q1CAT 2022 Slot 2 QA

For some natural number

n

, assume that

(15,000)!

is divisible by

(n!)!

. The largest possible value of

n

Q2CAT 2022 Slot 2 QA

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Consider the arithmetic progression

3, 7, 11, \ldots

and let

A_n

denote the sum of the first

n

terms of this progression. Then the value of

\dfrac{1}{25}\sum_{n=1}^{25} A_n

Q3CAT 2022 Slot 2 QA

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Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is

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Q4CAT 2022 Slot 2 QA

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Regular polygons A and B have number of sides in the ratio 1 : 2 and interior angles in the ratio 3 : 4. Then the number of sides of B equals

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Q5CAT 2022 Slot 2 QA

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The length of each side of an equilateral triangle ABC is 3 cm. Let D be a point on BC such that the area of triangle ADC is half the area of triangle ABD. Then the length of AD, in cm, is

Q6CAT 2022 Slot 2 QA

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Manu earns ₹4000 per month and wants to save an average of ₹550 per month in a year. In the first nine months, his monthly expense was ₹3500, and he foresees that, tenth month onward, his monthly expense will increase to ₹3700. In order to meet his yearly savings target, his monthly earnings, in rupees, from the tenth month onward should be

Q7CAT 2022 Slot 2 QA

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In an examination, there were 75 questions. 3 marks were awarded for each correct answer, 1 mark was deducted for each wrong answer and 1 mark was awarded for each unattempted question. Rayan scored a total of 97 marks in the examination. If the number of unattempted questions was higher than the number of attempted questions, then the maximum number of correct answers that Rayan could have given in the examination is

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Q8CAT 2022 Slot 2 QA

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The number of distinct integer values of

n

satisfying

\dfrac{4 - \log_2 n}{3 - \log_4 n} < 0

, is

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Q9CAT 2022 Slot 2 QA

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On day one, there are 100 particles in a laboratory experiment. On day

n

, where

n \geq 2

, one out of every

n

particles produces another particle. If the total number of particles in the laboratory experiment increases to 1000 on day

m

, then

m

equals

Q10CAT 2022 Slot 2 QA

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Suppose for all integers

x

, there are two functions

f

and

g

such that

f(x)+f(x-1)-1=0

and

g(x)=x^2

. If

f(x^2-x)=5

, then the value of the sum

f(g(5))+g(f(5))

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Q11CAT 2022 Slot 2 QA

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Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is

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Q12CAT 2022 Slot 2 QA

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In an election, there were four candidates and 80% of the registered voters casted their votes. One of the candidates received 30% of the casted votes while the other three candidates received the remaining casted votes in the proportion 1 : 2 : 3. If the winner of the election received 2512 votes more than the candidate with the second highest votes, then the number of registered voters was

Q13CAT 2022 Slot 2 QA

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The average of a non-decreasing sequence of

N

numbers

a_1, a_2, \ldots, a_N

is 300. If

a_1

is replaced by

6a_1

, the new average becomes 400. Then, the number of possible values of

a_1

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Q14CAT 2022 Slot 2 QA

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There are two containers of the same volume, first container half-filled with sugar syrup and the second container half-filled with milk. Half the content of the first container is transferred to the second container, and then the half of this mixture is transferred back to the first container. Next, half the content of the first container is transferred back to the second container. Then the ratio of sugar syrup and milk in the second container is

Q15CAT 2022 Slot 2 QA

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Let

f(x)

be a quadratic polynomial in

x

such that

f(x) \geq 0

for all real numbers

x

. If

f(2)=0

and

f(4)=6

, then

f(-2)

is equal to

Q16CAT 2022 Slot 2 QA

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Let

r

and

c

be real numbers. If

r

and

-r

are roots of

5x^3 + cx^2 - 10x + 9 = 0

, then

c

equals

Q17CAT 2022 Slot 2 QA

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Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit is

Q18CAT 2022 Slot 2 QA

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The number of integer solutions of the equation

(x^2 - 10)^{x^2 - 3x - 10} = 1

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Q19CAT 2022 Slot 2 QA

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The number of integers greater than 2000 that can be formed with the digits 0, 1, 2, 3, 4, 5, using each digit at most once, is

Q20CAT 2022 Slot 2 QA

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a

and

b

are non-negative real numbers such that

a + 2b = 6

, then the average of the maximum and minimum possible values of

a+b

Q21CAT 2022 Slot 2 QA

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Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are 60 km apart. If the speed of one of the ships is 6 km per hour more than the other one, then the speed, in km per hour, of the slower ship is

Q22CAT 2022 Slot 2 QA

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In triangle ABC, altitudes AD and BE are drawn to the corresponding bases. If

\angle BAC = 45^\circ

and

\angle ABC = \theta

, then

\dfrac{AD}{BE}

equals

About CAT 2022 Slot 2 QA

The QA section of CAT 2022 Slot 2 was conducted on November 30, 2022, 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 2022 Slot 2 QA

CAT 2022 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 2022 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 2022 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.