CAT 2022QASlot 1 · Morning

CAT 2022 Slot 1 QA Question Paper with Solutions

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

Questions

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Q1CAT 2022 Slot 1 QA

A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio

1 : 3

, then the ratio of lemon juice and sugar syrup in the new mixture is

Q2CAT 2022 Slot 1 QA

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The average weight of students in a class increases by

600

gm when some new students join the class. If the average weight of the new students is

3

kg more than the average weight of the original students, then the ratio of the number of original students to the number of new students is

Q3CAT 2022 Slot 1 QA

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In a village, the ratio of number of males to females is

5 : 4

. The ratio of number of literate males to literate females is

2 : 3

. The ratio of the number of illiterate males to illiterate females is

4 : 3

. If

3600

males in the village are literate, then the total number of females in the village is

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Q4CAT 2022 Slot 1 QA

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The largest real value of

a

for which the equation

|x + a| + |x - 1| = 2

has an infinite number of solutions for

x

Q5CAT 2022 Slot 1 QA

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For natural numbers

x, y, z

, if

xy + yz = 19

and

yz + xz = 51

, then the minimum possible value of

xyz

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Q6CAT 2022 Slot 1 QA

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Let

0 \leq a \leq x \leq 100

and

f(x) = |x - a| + |x - 100| + |x - a - 50|

. Then the maximum value of

f(x)

becomes

100

when

a

is equal to

Q7CAT 2022 Slot 1 QA

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Let

A

be the largest positive integer that divides all the numbers of the form

3^k + 4^k + 5^k

, and

B

be the largest positive integer that divides all the numbers of the form

4^k + 3(4^k) + 4^{k+2}

, where

k

is any positive integer. Then

(A+B)

equals

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Q8CAT 2022 Slot 1 QA

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For any natural number

n

, suppose the sum of the first

n

terms of an arithmetic progression is

n + 2n^2

. If the

n^{\text{th}}

term of the progression is divisible by

9

, then the smallest possible value of

n

Q9CAT 2022 Slot 1 QA

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Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in

10

minutes while train B takes

9

minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is

Q10CAT 2022 Slot 1 QA

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Let

a

and

b

be natural numbers. If

a^2 + ab + a = 14

and

b^2 + ab + b = 28

, then

(2a + b)

equals

Q11CAT 2022 Slot 1 QA

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A trapezium ABCD has side AD parallel to BC,

\angle BAD = 90^\circ

, BC =

3

cm and AD =

8

cm. If the perimeter of this trapezium is

36

cm, then its area, in sq. cm, is

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Q12CAT 2022 Slot 1 QA

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The average of three integers is

13

. When a natural number

n

is included, the average of these four integers remains an odd integer. The minimum possible value of

n

Q13CAT 2022 Slot 1 QA

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The number of ways of distributing

20

identical balloons among

4

children such that each child gets some balloons but no child gets an odd number of balloons, is

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Q14CAT 2022 Slot 1 QA

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For any real number

x

, let

[x]

be the largest integer less than or equal to

x

. If

\sum_{n=1}^{N} \left[\dfrac{1}{5} + \dfrac{n}{25}\right] = 25

then

N

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Q15CAT 2022 Slot 1 QA

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In a class of

100

students,

73

like coffee,

80

like tea and

52

like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks is

Q16CAT 2022 Slot 1 QA

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Alex invested his savings in two parts. The simple interest earned on the first part at

15\%

per annum for

4

years is the same as the simple interest earned on the second part at

12\%

per annum for

3

years. Then, the percentage of his savings invested in the first part is

Q17CAT 2022 Slot 1 QA

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Amal buys

110

kg of syrup and

120

kg of juice, syrup being

20\%

less costly than juice, per kg. He sells

10

kg of syrup at

10\%

profit and

20

kg of juice at

20\%

profit. Mixing the remaining juice and syrup, Amal sells the mixture at ₹

308.32

per kg and makes an overall profit of

64\%

. Then, Amal’s cost price for syrup, in rupees per kg, is

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Q18CAT 2022 Slot 1 QA

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All the vertices of a rectangle lie on a circle of radius

R

. If the perimeter of the rectangle is

P

, then the area of the rectangle is

Q19CAT 2022 Slot 1 QA

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Let

a, b, c

be non-zero real numbers such that

b^2 < 4ac

, and

f(x) = ax^2 + bx + c

. If the set

S

consists of all integers

m

such that

f(m) < 0

, then the set

S

must necessarily be

Q20CAT 2022 Slot 1 QA

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Ankita buys

4

kg cashews,

14

kg peanuts and

6

kg almonds when the cost of

7

kg cashews is the same as that of

30

kg peanuts or

9

kg almonds. She mixes all the three nuts and marks a price for the mixture in order to make a profit of ₹

1752

. She sells

4

kg of the mixture at this marked price and the remaining at a

20\%

discount on the marked price, thus making a total profit of ₹

744

. Then the amount, in rupees, that she had spent in buying almonds is

Q21CAT 2022 Slot 1 QA

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Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are

(1, 1)

(3, 4)

and

(-2, 8)

, respectively. Then, the coordinates of the vertex D are

Q22CAT 2022 Slot 1 QA

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Pinky is standing in a queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the queue is

3 : 5

. If the total number of persons in the queue is less than

300

, then the maximum possible number of persons standing ahead of Pinky is

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About CAT 2022 Slot 1 QA

The QA section of CAT 2022 Slot 1 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 1 QA

CAT 2022 Slot 1 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 1 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.