CAT 2020QASlot 1 · Morning

CAT 2020 Slot 1 QA Question Paper with Solutions

40 Minutes24 QuestionsNov 29, 20203 marks correct · −1 wrong

Questions

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Q1CAT 2020 Slot 1 QA

On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two-thirds of the painted area then the perimeter of the rectangle in inches is

Q2CAT 2020 Slot 1 QA

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a

b

and

c

are positive integers such that

ab = 432

bc = 96

and

c < 9

, then the smallest possible value of

a + b + c

Q3CAT 2020 Slot 1 QA

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A solution, of volume 40 litres, has dye and water in the proportion 2 : 3. Water is added to the solution to change this proportion to 2 : 5. If one-fourths of this diluted solution is taken out, how many litres of dye must be added to the remaining solution to bring the proportion back to 2 : 3?

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Q4CAT 2020 Slot 1 QA

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How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?

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Q5CAT 2020 Slot 1 QA

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Two persons are walking beside a railway track at respective speeds of 2 and 4 km per hour in the same direction. A train came from behind them and crossed them in 90 and 100 seconds, respectively. The time, in seconds, taken by the train to cross an electric post is nearest to

Q6CAT 2020 Slot 1 QA

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The number of distinct real roots of the equation

(x + \dfrac{1}{x})^2 - 3(x + \dfrac{1}{x}) + 2 = 0

equals

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Q7CAT 2020 Slot 1 QA

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An alloy is prepared by mixing three metals A, B and C in the proportion 3 : 4 : 7 by volume. Weights of the same volume of the metals A, B and C are in the ratio 5 : 2 : 6. In 130 kg of the alloy, the weight, in kg, of the metal C is

Q8CAT 2020 Slot 1 QA

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\log_{4} 5 = (\log_{4} y)(\log_{6} \sqrt{5})

, then

y

equals

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Q9CAT 2020 Slot 1 QA

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y

is a negative number such that

2^{y^2 \log_{3} 5} = 5^{\log_{2} 3}

, then

y

equals

Q10CAT 2020 Slot 1 QA

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The mean of all 4-digit even natural numbers of the form 'aabb', where

a > 0

, is

Q11CAT 2020 Slot 1 QA

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Among 100 students,

x_1

have birthdays in January,

x_2

have birthdays in February, and so on. If

x_0 = \max(x_1, x_2, \ldots, x_{12})

, then the smallest possible value of

x_0

Q12CAT 2020 Slot 1 QA

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The area of the region satisfying the inequalities

|x| - y \leq 1

y \geq 0

and

y \leq 1

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Q13CAT 2020 Slot 1 QA

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A train travelled at one-thirds of its usual speed, and hence reached the destination 30 minutes after the scheduled time. On its return journey, the train initially travelled at its usual speed for 5 minutes but then stopped for 4 minutes for an emergency. The percentage by which the train must now increase its usual speed so as to reach the destination at the scheduled time, is nearest to

Q14CAT 2020 Slot 1 QA

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A circle is inscribed in a rhombus with diagonals 12 cm and 16 cm. The ratio of the area of the circle to the area of the rhombus is

Q15CAT 2020 Slot 1 QA

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A person spent Rs 50000 to purchase a desktop computer and a laptop computer. He sold the desktop at 20% profit and the laptop at 10% loss. If overall he made a 2% profit then the purchase price, in rupees, of the desktop is

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Q16CAT 2020 Slot 1 QA

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A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stock exhausts after he takes care of 5 children. How many toffees were there in his stock initially?

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Q17CAT 2020 Slot 1 QA

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In a group of people, 28% of the members are young while the rest are old. If 65% of the members are literates, and 25% of the literates are young, then the percentage of old people among the illiterates is nearest to

Q18CAT 2020 Slot 1 QA

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x = (4096)^{7 + 4 \sqrt{3}}

, then which of the following equals 64?

Q19CAT 2020 Slot 1 QA

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A straight road connects points A and B. Car 1 travels from A to B and Car 2 travels from B to A, both leaving at the same time. After meeting each other, they take 45 minutes and 20 minutes, respectively, to complete their journeys. If Car 1 travels at the speed of 60 km/hr, then the speed of Car 2, in km/hr, is

Q20CAT 2020 Slot 1 QA

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f(5 + x) = f(5 - x)

for every real

x

, and

f(x) = 0

has four distinct real roots, then the sum of these roots is

Q21CAT 2020 Slot 1 QA

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A solid right circular cone of height 27 cm is cut into 2 pieces along a plane parallel to its base at a height of 18 cm from the base. If the difference in the volume of the two pieces is 225 cc, the volume, in cc, of the original cone is

Q22CAT 2020 Slot 1 QA

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Leaving home at the same time, Amal reaches office at 10:15 am if he travels at 8 km/hr, and at 9:40 am if he travels at 15 km/hr. Leaving home at 9:10 am, at what speed, in km/hr, must he travel so as to reach office exactly at 10:00 am?

Q23CAT 2020 Slot 1 QA

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Let

A

B

and

C

be three positive integers such that the sum of

A

and the mean of

B

and

C

is 5. In addition, the sum of

B

and the mean of

A

and

C

is 7. Then the sum of

A

and

B

Q24CAT 2020 Slot 1 QA

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The number of real-valued solutions of the equation

2^x + 2^{-x} = 2 - (x - 2)^2

About CAT 2020 Slot 1 QA

The QA section of CAT 2020 Slot 1 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 1 QA

CAT 2020 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 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 1 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.