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CAT 2020 Slot 2 QA Questions & Answer Key

Quantitative Aptitude questions from CAT 2020 Slot 2 (IIM Indore, Afternoon Session (12:30 PM – 2:30 PM IST); 26 in the exam) with the answer key and step-by-step solutions

Executive Answer & Section Summary

CAT 2020 Slot 2 Quantitative Aptitude (QA) was conducted by IIM Indore during the Afternoon Session (12:30 PM – 2:30 PM 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)
Attempt QA Section in Timed 40-Min ModeSolve Questions on this Page

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.
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Editorial & Academic Authority: Verified by ThinkCAT Academic & Editorial Council.
Citation Format: ThinkCAT Academic Archive (thinkcat.in)

CAT 2020 Slot 2 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

  1. Q1800
  2. Q217
  3. Q3C
  4. Q490000
  5. Q5B
  6. Q6A
  7. Q7315
  8. Q82704
  9. Q9C
  10. Q10A
  11. Q11A
  12. Q1210
  13. Q13D
  14. Q14C
  15. Q15C
  16. Q16A
  17. Q17B
  18. Q18D
  19. Q19D
  20. Q20C
  21. Q21D
  22. Q22A
  23. Q234
  24. Q24B
  25. Q2523
  26. Q26A
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Official Exam Questions & Explanations (25 of 26)

Sorted in official convenor sequence
Question 1 of 26
CAT 2020 Slot 2QAArithmetic • Ratio, Proportion & VariationEasy
A sum of money is split among Amal, Sunil and Mita so that the ratio of the shares of Amal and Sunil is 3:23: 2 , while the ratio of the shares of Sunil and Mita is 4:54: 5. If the difference between the largest and the smallest of these three shares is Rs 400400 , then Sunil's share, in rupees, is
TITA Answer:
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Question 2 of 26
CAT 2020 Slot 2QANumber Systems • Integral SolutionsModerate
The number of pairs of integers (x, y) satisfy x≥y≥−20x \geq y \geq-20 and 2x+5y=992 x+5 y=99 is
TITA Answer:
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Question 3 of 26
CAT 2020 Slot 2QAAlgebra • IndicesModerate
The number of integers that satisfy the equality (x2−5x+7)x+1=1(x^2 - 5x + 7)^{x + 1} = 1 is
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Question 4 of 26
CAT 2020 Slot 2QAArithmetic • Simple & Compound InterestModerate
For the same principal amount, the compound interest for two years at 5%5\% per annum exceeds the simple interest for three years at 3%3\% per annum by Rs. 11251125. Then the principal amount in rupees is
TITA Answer:
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Question 5 of 26
CAT 2020 Slot 2QAAlgebra • Linear EquationHard
Aron bought some pencils and sharpeners. Spending the same amount of money as Aron, Aditya bought twice as many pencils and 10 less sharpeners. If the cost of one sharpener is Rs. 2 more than the cost of a pencil, then the minimum possible number of pencils bought by Aron and Aditya together is
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Question 6 of 26
CAT 2020 Slot 2QAArithmetic • PercentagesModerate
In May, John bought the same amount of rice and the same amount of wheat as he had bought in April, but spent Rs. 150 more due to price increase of rice and wheat by 20%20 \% and 12%12 \% , respectively. If John had spent Rs. 450 on rice in April, then how much did he spend on wheat in May?
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Question 7 of 26
CAT 2020 Slot 2QAModern Math • Permutation & CombinationHard
How many 44 - digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3?
TITA Answer:
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Question 8 of 26
CAT 2020 Slot 2QAAlgebra • Minima & MaximaModerate
If xx and yarepositiverealnumberssatisfyingx+y=102,thentheminimumpossiblevalueof2601(1+1x)(1+1yyare positive real numbers satisfyingx + y = 102 , then the minimum possible value of2601(1+ \frac{1}{x})(1+ \frac{1}{y})$ is
TITA Answer:
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Question 9 of 26
CAT 2020 Slot 2QAAlgebra • ModulusModerate
In how many ways can a pair of integers (x,a)(x, a) be chosen such that x2−2∣x∣+∣a−2∣=0x^2 - 2 | x | + | a - 2 | = 0?
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Question 10 of 26
CAT 2020 Slot 2QAArithmetic • Time, Speed & DistanceHard
Two runners, Alice and Bob, are racing on two different circular tracks, T1T1 and T2T2 , with radii 60 m60 \mathrm{\ m} and 40 m40 \mathrm{\ m} respectively. They both start from point PP at the same moment. Alice runs on track T1T1 at a constant speed of 12 km/hr12 \mathrm{\ km} / \mathrm{hr} and Bob runs on track T2T2 at a constant speed of 8 km/hr8 \mathrm{\ km} / \mathrm{hr}. After how many full rounds of Alice does she meet Bob again for the first time since the race started?
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Question 11 of 26
CAT 2020 Slot 2QAAlgebra • PolynomialsModerate
Let f(x)=x2+ax+bf(x)= x^{2} + a x+b and g(x)=f(x+1)−f(x−1)g(x)=f(x+1)-f(x-1). If f(x)≥0f(x) \geq 0 for all real xx , and g(20)=72g(20)=72 , then the smallest possible value of bb is
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Question 12 of 26
CAT 2020 Slot 2QAGeometry • CirclesModerate
Let C1C1 and C2C2 be concentric circles such that the diameter of C1C1 is 2 cm2 \mathrm{~cm} longer than that of C2C2. If a chord of C1C1 has length 6 cm6 \mathrm{~cm} and is a tangent of C2C2 , then the diameter, in cm, of C1C1 is
TITA Answer:
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Question 13 of 26
CAT 2020 Slot 2QAGeometry • TrianglesHard
The sum of the perimeters of an equlateral triangle and a rectangle is 90 cm90 \mathrm{~cm} the area, TT , of the triangle and the area, RR , of the rectangle, both in sq cm, satisfy the relationship R=T2R=T^{2}. If the sides of the rectangle are in the ratio 1:31: 3 , then the length, in cm , of the longer side of the rectangle, is
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Question 14 of 26
CAT 2020 Slot 2QAArithmetic • Time, Speed & DistanceModerate
The distance from BB to CC is thrice that from AA to BB. Two trains travel from AA to CC via BB. The speed of train 2 is double that of train 1 while traveling from AA to BB and their speeds are interchanged while traveling from BB to CC. The ratio of the time taken by train 1 to that taken by train 2 in travelling from AA to CC is
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Question 15 of 26
CAT 2020 Slot 2QAArithmetic • Mean, Median & ModeHard
In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 4747. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by
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Question 16 of 26
CAT 2020 Slot 2QAAlgebra • Progression & SeriesHard
Let the mthm^{th} and nthn^{th} terms of a geometric progression be 3/43 / 4 and 1212 , respectively, where m<nm<n. If the common ratio of the progression is an integer rr , then the smallest possible value of r+n−mr+n-m is
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Question 17 of 26
CAT 2020 Slot 2QAArithmetic • Time, Speed & DistanceEasy
AA and BB are two points on a straight line. Ram runs from AA to BB while Rahim runs from BB to AA. After crossing each other, Ram and Rahim reach their destinations in one minute and four minutes, respectively. If they start at the same time, then the ratio of Ram's speed to Rahim's speed is
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Question 18 of 26
CAT 2020 Slot 2QAArithmetic • Time, Speed & DistanceModerate
In a car race, car AA beats car BB by 45 km45 \mathrm{~km} , car BB beats car CC by 50 km, and car AA beats CC by 90 km90 \mathrm{~km}. the distance (in km) over which the race has been conducted is
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Question 19 of 26
CAT 2020 Slot 2QAGeometry • TrianglesModerate
From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is ss. Then the area of triangle is
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Question 20 of 26
CAT 2020 Slot 2QAModern Math • Set TheoryModerate
Students in a college have to choose at least two subjects from Chemistry, Mathematics and Physics. The number of students choosing all three subjects is 1818 , choosing Mathematics as one of their subjects is 23 and choosing Physics as one of their subjects is 2525. The smallest possible number of students who could choose Chemistry as one of their subjects is
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Question 21 of 26
CAT 2020 Slot 2QAArithmetic • Profit & LossModerate
Anil buys 12 toys and labels each with the same selling price. He sells 8 toys initially at 20%20 \% discount on the labeled price. Then he sells the remaining 4 toys at an additional 25%25 \% discount on the discounted price. Thus, he gets a total of Rs 2112,2112, and makes a 10%10\% profit. With no discounts, his percentage of profit would have been
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Question 22 of 26
CAT 2020 Slot 2QAAlgebra • Minima & MaximaModerate
For real x,x, the maximum possible value of x1+x4\frac{x}{\sqrt{1+x^4}} is
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Question 23 of 26
CAT 2020 Slot 2QAArithmetic • Time & WorkModerate
John takes twice as much time as Jack to finish a job. Jack and Jim together take one-thirds of the time to finish the job than John takes working alone. Moreover, in order to finish the job, John takes three days more than that taken by three of them working together. In how many days will Jim finish the job working alone?
TITA Answer:
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Question 24 of 26
CAT 2020 Slot 2QAModern Math • LogarithmsModerate
The value of log⁡a(ab)+log⁡b(ba)\log_a \left(\frac{a}{b}\right) + \log_b \left(\frac{b}{a}\right) , for 1<a≤b1 < a \leq b cannot be equal to
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Question 25 of 26
CAT 2020 Slot 2QAAlgebra • InequalitiesModerate
If xx and yy are non-negative integers such that x+9=z,y+1=zx+9=z, y+1=z and x+y<z+5x+y<z+5 , then the maximum possible value of 2x+y2 x+y ?
TITA Answer:
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Frequently Asked Questions about CAT 2020 Slot 2 QA Questions & Answer Key

How many questions were asked in CAT 2020 Slot 2 QA?

CAT 2020 Slot 2 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 2 QA?

Achieving a 99.0th percentile in QA required approximately 28–31 marks (~10 net correct), reflecting the high speed test (dense venn diagrams, rapid arithmetic).

Can I practice other sections of CAT 2020 Slot 2?

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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Topics in this paper

CAT Arithmetic PYQs 10 QsCAT Algebra PYQs 8 QsCAT Geometry PYQs 4 QsCAT Modern Math PYQs 3 QsCAT Time, Speed & Distance (TSD) Questions 4 QsCAT Circles Geometry & Tangents Questions 2 Qs