CAT 2020QASlot 3 · Evening

CAT 2020 Slot 3 QA Question Paper with Solutions

40 Minutes26 QuestionsNov 29, 20203 marks correct · −1 wrong

Questions

0 / 26 answered0 correct0 wrong

Q1CAT 2020 Slot 3 QA

Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and going in the clockwise direction. If they run at speeds of 15 km/hr, 10 km/hr, and 8 km/hr, respectively, how much distance in km will Ravi have run when Anil and Sunil meet again for the first time at the starting point?

Q2CAT 2020 Slot 3 QA

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Let

m

and

n

be natural numbers such that

n

is even and

0.2 < \dfrac{m}{20}, \dfrac{n}{m}, \dfrac{n}{11} < 0.5

. Then

m - 2n

equals

Q3CAT 2020 Slot 3 QA

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A contractor agreed to construct a 6 km road in 200 days. He employed 140 persons for the work. After 60 days, he realized that only 1.5 km road has been completed. How many additional people would he need to employ in order to finish the work exactly on time?

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Q4CAT 2020 Slot 3 QA

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Let

k

be a constant. The equations

kx + y = 3

and

4x + ky = 4

have a unique solution if and only if

Q5CAT 2020 Slot 3 QA

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In a trapezium ABCD, AB is parallel to DC, BC is perpendicular to DC and

\angle BAD = 45^\circ

. If DC = 5 cm, BC = 4 cm, the area of the trapezium in sq cm is

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Q6CAT 2020 Slot 3 QA

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\dfrac{2 \times 4 \times 8 \times 16}{(\log_2 4)^2(\log_4 8)^3(\log_8 16)^4}

equals

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Q7CAT 2020 Slot 3 QA

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How many pairs

(a, b)

of positive integers are there such that

a \leq b

and

ab = 4^{2017}

Q8CAT 2020 Slot 3 QA

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The points

(2,1)

and

(-3,-4)

are opposite vertices of a parallelogram. If the other two vertices lie on the line

x + 9y + c = 0

, then

c

Q9CAT 2020 Slot 3 QA

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How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

Q10CAT 2020 Slot 3 QA

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Vimla starts for office every day at 9 am and reaches exactly on time if she drives at her usual speed of 40 km/hr. She is late by 6 minutes if she drives at 35 km/hr. One day, she covers two-thirds of her distance to office in one-thirds of her usual time to reach office, and then stops for 8 minutes. The speed, in km/hr, at which she should drive the remaining distance to reach office exactly on time is

Q11CAT 2020 Slot 3 QA

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Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick's age is 1 year less than the average age of all three, then Harry's age, in years, is

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Q12CAT 2020 Slot 3 QA

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\log_a 30 = A

\log_a \dfrac{5}{3} = -B

and

\log_2 a = \dfrac{1}{3}

, then

\log_3 a

equals

Q13CAT 2020 Slot 3 QA

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The vertices of a triangle are

(0,0)

(4,0)

and

(3,9)

. The area of the circle passing through these three points is

Q14CAT 2020 Slot 3 QA

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Let

N

x

and

y

be positive integers such that

N = x + y

2 < x < 10

and

14 < y < 23

. If

N > 25

, then how many distinct values are possible for

N

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Q15CAT 2020 Slot 3 QA

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f(x + y) = f(x)f(y)

and

f(5) = 4

, then

f(10) - f(-10)

is equal to

Q16CAT 2020 Slot 3 QA

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A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs 18522. The amount, in rupees, that the person had invested is

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Q17CAT 2020 Slot 3 QA

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Let

m

and

n

be positive integers. If

x^2 + mx + 2n = 0

and

x^2 + 2nx + m = 0

have real roots, then the smallest possible value of

m+n

Q18CAT 2020 Slot 3 QA

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In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and that by Asha is 34 more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored 84%, is

Q19CAT 2020 Slot 3 QA

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A man buys 35 kg of sugar and sets a marked price in order to make a 20% profit. He sells 5 kg at this price, and 15 kg at a 10% discount. Accidentally, 3 kg of sugar is wasted. He sells the remaining sugar by raising the marked price by

p

percent so as to make an overall profit of 15%. Then

p

is nearest to

Q20CAT 2020 Slot 3 QA

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Two alcohol solutions, A and B, are mixed in the proportion 1:3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72% alcohol. If solution A has 60% alcohol, then the percentage of alcohol in solution B is

Q21CAT 2020 Slot 3 QA

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How many integers in the set

\{100, 101, 102, \ldots, 999\}

have at least one digit repeated?

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Q22CAT 2020 Slot 3 QA

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The area, in sq. units, enclosed by the lines

x = 2

y = |x - 2| + 4

, the X-axis and the Y-axis is equal to

Q23CAT 2020 Slot 3 QA

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x_1 = -1

and

x_m = x_{m+1} + (m+1)

for every positive integer

m

, then

x_{100}

equals

Q24CAT 2020 Slot 3 QA

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A and B are two railway stations 90 km apart. A train leaves A at 9:00 am, heading towards B at a speed of 40 km/hr. Another train leaves B at 10:30 am, heading towards A at a speed of 20 km/hr. The trains meet each other at

Q25CAT 2020 Slot 3 QA

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a

b

c

are non-zero and

14^a = 36^b = 84^c

, then

6b\left(\dfrac{1}{c} - \dfrac{1}{a}\right)

is equal to

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Q26CAT 2020 Slot 3 QA

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A batsman played

n + 2

innings and got out on all occasions. His average score in these

n + 2

innings was 29 runs and he scored 38 and 15 runs in the last two innings. The batsman scored less than 38 runs in each of the first

n

innings. In these

n

innings, his average score was 30 runs and lowest score was

x

runs. The smallest possible value of

x

About CAT 2020 Slot 3 QA

The QA section of CAT 2020 Slot 3 was conducted on November 30, 2020, 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 2020 Slot 3 QA

CAT 2020 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 2020 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 2020 Slot 3 paper with a live timer and percentile benchmarking.

Tips for CAT QA Preparation

Reading Comprehension accounts for roughly two-thirds of the QAsection. 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.