CAT 2022QASlot 3 · Evening

CAT 2022 Slot 3 QA Question Paper with Solutions

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

Questions

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Q1CAT 2022 Slot 3 QA

If c =

\dfrac{16 x}{y} + \dfrac{49 y}{x}

for some non-zero real numbers x and y, then c cannot take the value

Q2CAT 2022 Slot 3 QA

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A group of N people worked on a project. They finished 35% of the project by working 7 hours a day for 10 days. Thereafter, 10 people left the group and the remaining people finished the rest of the project in 14 days by working 10 hours a day. Then the value of N is

Q3CAT 2022 Slot 3 QA

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Suppose the medians BD and CE of a triangle ABC intersect at a point O. If area of triangle ABC is 108 sq. cm., then, the area of the triangle EOD, in sq. cm., is

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Q4CAT 2022 Slot 3 QA

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A school has less than 5000 students and if the students are divided equally into teams of either 9 or 10 or 12 or 25 each, exactly 4 are always left out. However, if they are divided into teams of 11 each, no one is left out. The maximum number of teams of 12 each that can be formed out of the students in the school is

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Q5CAT 2022 Slot 3 QA

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Two cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take 1.5 hours if they travel towards each other, but 10.5 hours if they travel in the same direction. If the speed of the slower car is 60 km/hr, then the distance traveled, in km, by the slower car when it meets the other car while traveling towards each other, is

Q6CAT 2022 Slot 3 QA

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Let r be a real number and

f(x)=\begin{cases}2x-r, & \text{if } x \geq r\\ r, & \text{if } x < r\end{cases}

. Then, the equation

f(x)=f(f(x))

holds for all real values of x where

Q7CAT 2022 Slot 3 QA

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The lengths of all four sides of a quadrilateral are integer valued. If three of its sides are of length 1 cm, 2 cm and 4 cm, then the total number of possible lengths of the fourth side is

Q8CAT 2022 Slot 3 QA

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3 + 2 \sqrt{2}

is a root of the equation

a x^2 + b x + c = 0

, and

4 + 2 \sqrt{3}

is a root of the equation

a y^2 + m y + n = 0

, where a, b, c, m and n are integers, then the value of

\dfrac{b}{m} + \dfrac{c - 2b}{n}

Q9CAT 2022 Slot 3 QA

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In an examination, the average marks of students in sections A and B are 32 and 60, respectively. The number of students in section A is 10 less than that in section B. If the average marks of all the students across both the sections combined is an integer, then the difference between the maximum and minimum possible number of students in section A is

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Q10CAT 2022 Slot 3 QA

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\left(\sqrt{\dfrac{7}{5}}\right)^{3x-y} = \dfrac{875}{2401}

and

\left(\dfrac{4a}{b}\right)^{6x-y} = \left(\dfrac{2a}{b}\right)^{y-6x}

, for all non-zero real values of a and b, then the value of x + y is

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Q11CAT 2022 Slot 3 QA

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The minimum possible value of

\dfrac{x^2 - 6x + 10}{3 - x}

, for

x < 3

, is

Q12CAT 2022 Slot 3 QA

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A glass contains 500 cc of milk and a cup contains 500 cc of water. From the glass, 150 cc of milk is transferred to the cup and mixed thoroughly. Next, 150 cc of this mixture is transferred from the cup to the glass. Now, the amount of water in the glass and the amount of milk in the cup are in the ratio

Q13CAT 2022 Slot 3 QA

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Consider six distinct natural numbers such that the average of the two smallest numbers is 14, and the average of the two largest numbers is 28. Then, the maximum possible value of the average of these six numbers is

Q14CAT 2022 Slot 3 QA

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Nitu has an initial capital of ₹20,000. Out of this, she invests ₹8,000 at 5.5% in bank A, ₹5,000 at 5.6% in bank B and the remaining amount at x% in bank C, each rate being simple interest per annum. Her combined annual interest income from these investments is equal to 5% of the initial capital. If she had invested her entire initial capital in bank C alone, then her annual interest income, in rupees, would have been

Q15CAT 2022 Slot 3 QA

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The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421, including itself, is

Q16CAT 2022 Slot 3 QA

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Bob can finish a job in 40 days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the first day, Bob and Cole work together on the second day, Cole and Alex work together on the third day, and then, they continue the work by repeating this three-day roster, with Alex and Bob working together on the fourth day, and so on. Then, the total number of days Alex would have worked when the job gets finished, is

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Q17CAT 2022 Slot 3 QA

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A donation box can receive only cheques of ₹100, ₹250, and ₹500. On one good day, the donation box was found to contain exactly 100 cheques amounting to a total sum of ₹15250. Then, the maximum possible number of cheques of ₹500 that the donation box may have contained, is

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Q18CAT 2022 Slot 3 QA

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Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator is

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Q19CAT 2022 Slot 3 QA

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The average of all 3-digit terms in the arithmetic progression 38, 55, 72, ..., is

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Q20CAT 2022 Slot 3 QA

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Two ships are approaching a port along straight routes at constant speeds. Initially, the two ships and the port formed an equilateral triangle with sides of length 24 km. When the slower ship travelled 8 km, the triangle formed by the new positions of the two ships and the port became right-angled. When the faster ship reaches the port, the distance, in km, between the other ship and the port will be

Q21CAT 2022 Slot 3 QA

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In a triangle ABC,

AB = AC = 8

cm. A circle drawn with

BC

as diameter passes through A. Another circle drawn with center at A passes through B and C. Then the area, in sq. cm, of the overlapping region between the two circles is

Q22CAT 2022 Slot 3 QA

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Suppose k is any integer such that the equation

2x^2 + kx + 5 = 0

has no real roots and the equation

x^2 + (k - 5)x + 1 = 0

has two distinct real roots for x. Then, the number of possible values of k is

About CAT 2022 Slot 3 QA

The QA section of CAT 2022 Slot 3 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 3 QA

CAT 2022 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 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 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.