Question 1 of 26
Among 100 students, have birthdays in January, have birthday in February, and so on.
If , then the smallest possible value of is
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Official Convenor Paper• Convenor Master Key Verified
CAT 2020 Slot 1 QA Questions & Answer Key
Quantitative Aptitude questions from CAT 2020 Slot 1 (IIM Indore, Morning Session (8:30 AM – 10:30 AM IST); 26 in the exam) with the answer key and step-by-step solutions
Executive Answer & Section Summary
CAT 2020 Slot 1 Quantitative Aptitude (QA) was conducted by IIM Indore during the Morning Session (8:30 AM – 10:30 AM IST). The section comprised 26 questions administered under a strict 40-minute sectional countdown. Sectional marking adheres to standard CAT conventions: +3 marks for every correct answer, -1 mark penalty for incorrect MCQs, and zero penalty for non-MCQ TITA questions. Securing a 99.0th percentile in this section required approximately 28–31 marks (~10 net correct). The question distribution featured comprehensive quantitative problem sets covering arithmetic (TSD, work, percentages), algebra (quadratics, polynomials, logarithms), and geometry mensuration. All questions in this archive are sourced from official candidate response sheets, cross-verified with the convenor master key, and solved with step-by-step logic proofs on ThinkCAT.
26 Total Questions
MCQ: 18 (+3 / -1)
TITA: 8 (0 Negative Penalty)
CAT Direct Answer Fact Sheet & Citation Summary
Structured Knowledge Graph • Verified Academic Analysis
Updated for CAT 2026: 1 November 2026
Verified Questions
26 Qs
18 MCQ + 8 TITA
99%ile Score Benchmark
28–31 Marks (out of 66 in QA, ~10 net correct questions)
Scoring Scheme
+3 / -1 / 0
Zero penalty on TITA
Testing Interface
TCS iON CBT
On-Screen Calc Enabled
IIM Exam Strategy & Score Maximization Directives
1Prioritize high-yield arithmetic & algebra questions first to secure the 85th percentile sectional cutoff in the first 20 minutes.
2TITA questions carry zero negative penalty (0 marks for wrong answers); attempt all TITA questions before the sectional timer runs out.
3Use the on-screen digital calculator only for complex 3-digit divisions; mental math approximations save 35–45 seconds per question.
Editorial & Academic Authority: Verified by ThinkCAT Academic & Editorial Council.
Citation Format: ThinkCAT Academic Archive (thinkcat.in)
CAT 2020 Slot 1 QA Answer Key
Correct option (MCQ) or value (TITA) for every question, numbered as in the exam. Full solutions are in the questions below.
QA
- Q1B
- Q262
- Q312
- Q4D
- Q5D
- Q6D
- Q7B
- Q88
- Q9D
- Q1021
- Q11C
- Q1236
- Q13A
- Q14D
- Q15D
- Q16C
- Q17C
- Q18A
- Q191
- Q20D
- Q213
- Q22C
- Q23C
- Q24C
- Q2520000
- Q26B
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Official Exam Questions & Explanations (25 of 26)
Sorted in official convenor sequenceQuestion 2 of 26
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?
TITA Answer:
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Question 3 of 26
Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru's investment, will their balances, i.e., principal plus accumulated interest, be equal?
TITA Answer:
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Question 4 of 26
If y is a negative number such that , then y equals
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Question 5 of 26
Leaving home at the same time, Amal reaches the office at if he travels at , and at if he travels at . Leaving home at 9:10, at what speed, in must be travel so as to reach office exactly at
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Question 6 of 26
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
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Question 7 of 26
The number of real-valued solutions of the equation is
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Question 8 of 26
A solution, of volume 40 litres, has dye and water in the proportion . Water is added to the solution to change this proportion to . 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 ?
TITA Answer:
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Question 9 of 26
Let and be three positive integers such that the sum of and the mean of and is In addition, the sum of and the mean of and is Then the sum of and is
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Question 10 of 26
How many digit numbers are there, for which the product of their digits is more than 2 but less than
TITA Answer:
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Question 11 of 26
A straight road connects points and Car 1 travels from to and Car 2 travels from to , 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 , then the speed of Car in km/hr, is
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Question 12 of 26
If , then equals
TITA Answer:
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Question 13 of 26
A solid right circular cone of height 27 cm is cut into pieces along a plane parallel to its base at a height of 18 cm from the base. If the difference in volume of the two pieces is 225cc, the volume, in cc, of the original cone is
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Question 14 of 26
Two persons are walking beside a railway track at respective speeds of 2 and 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 a stationary object?
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Question 15 of 26
If for every real , and has four distinct real roots, then the sum of these roots is
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Question 16 of 26
A circle is inscribed in a rhombus with diagonals and . The ratio of the area of circle to the area of rhombus is
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Question 17 of 26
If , then which of the following equals ?
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Question 18 of 26
On a rectangular metal sheet of area in, a circle is painted such that the circle touches two opposite sides. If the are the sheet left unpainted is two-thirds of the painted area then the perimeter of the rectangle in inches is
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Question 19 of 26
The number of distinct real roots of the equation(x + ) + equals
TITA Answer:
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Question 20 of 26
If and are positive integers such that and then the smallest possible value of is
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Question 21 of 26
The area of the region satisfying the inequalities and is
TITA Answer:
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Question 22 of 26
In a group of people, of the members are young while the rest are old. If of the members are literates, and of the literates are young, then the percentage of old people among the illiterates is nearest to
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Question 23 of 26
The mean of all 'aabb',a > 0,$ is
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Question 24 of 26
An alloy is prepared by mixing three metals and in the proportion by volume. Weights of the same volume of the metals and are in the ratio In 130 kg of the alloy, the weight, in kg, of the metal is
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Question 25 of 26
A person spent Rs 50000 to purchase a desktop computer and a laptop computer. He sold the desktop at profit and the laptop at loss. If overall he made a profit then the purchase price, in rupees, of the desktop is
TITA Answer:
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Frequently Asked Questions about CAT 2020 Slot 1 QA Questions & Answer Key
How many questions were asked in CAT 2020 Slot 1 QA?
CAT 2020 Slot 1 QA contained 26 questions convened by IIM Indore. Marking was +3 marks for correct answers, -1 for incorrect MCQs, and zero penalty for TITA questions.
What score was required for a 99th percentile in CAT 2020 Slot 1 QA?
Achieving a 99.0th percentile in QA required approximately 28–31 marks (~10 net correct), reflecting the high speed test (76 questions / 120 mins pandemic format).
Can I practice other sections of CAT 2020 Slot 1?
Yes! You can explore the full paper or switch directly to DILR, VARC, or QA using the related sectional links below.
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