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CAT 2019 Slot 2 QA Questions & Answer Key

Quantitative Aptitude questions from CAT 2019 Slot 2 (IIM Kozhikode, Afternoon Session (12:30 PM – 2:30 PM IST); 34 in the exam) with the answer key and step-by-step solutions

Executive Answer & Section Summary

CAT 2019 Slot 2 Quantitative Aptitude (QA) was conducted by IIM Kozhikode during the Afternoon Session (12:30 PM – 2:30 PM IST). The section comprised 34 questions administered under a strict 60-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.

34 Total Questions
MCQ: 23 (+3 / -1)
TITA: 11 (0 Negative Penalty)
Attempt QA Section in Timed 60-Min ModeSolve Questions on this Page

CAT Direct Answer Fact Sheet & Citation Summary

Structured Knowledge Graph • Verified Academic Analysis
Updated for CAT 2026: 2 November 2026
Verified Questions
34 Qs
23 MCQ + 11 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 2019 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. Q1C
  2. Q2B
  3. Q3C
  4. Q4B
  5. Q5C
  6. Q6C
  7. Q7A
  8. Q8C
  9. Q912
  10. Q10B
  11. Q11A
  12. Q12C
  13. Q13A
  14. Q14B
  15. Q154
  16. Q16C
  17. Q17D
  18. Q1812
  19. Q19B
  20. Q2013
  21. Q21B
  22. Q2280
  23. Q2344
  24. Q2448
  25. Q25A
  26. Q26B
  27. Q27A
  28. Q287
  29. Q29B
  30. Q304851
  31. Q31150
  32. Q32C
  33. Q3320920
  34. Q34B
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Official Exam Questions & Explanations (25 of 34)

Sorted in official convenor sequence
Question 1 of 34
CAT 2019 Slot 2QAArithmetic • Mixture & AlligationModerate
The strength of a salt solution is p%\mathrm{p} \% if 100ml100 \mathrm{ml} of the solution contains pp grams of salt. Each of three vessels A,B,C\mathrm{A}, \mathrm{B}, \mathrm{C} contains 500ml500 \mathrm{ml} of salt solution of strengths 10%,22%10 \%, 22 \% , and 32%32 \% , respectively. Now, 100ml100 \mathrm{ml} of the solution in vessel A is transferred to vessel B. Then, 100ml100 \mathrm{ml} of the solution in vessel BB is transferred to vessel CC. Finally, 100ml100 \mathrm{ml} of the solution in vessel CC is transferred to vessel AA. The strength, in percentage, of the resulting solution in vessel AA is
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Question 2 of 34
CAT 2019 Slot 2QAAlgebra • PolynomialsEasy
The quadratic equation x2+bx+c=0x² + bx + c = 0 has two roots 4a4a and 3a,3a, where a is an integer. Which of the following is a possible value of b2+cb² + c?
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Question 3 of 34
CAT 2019 Slot 2QAArithmetic • Time, Speed & DistanceModerate
Two ants AA and BB start from a point PP on a circle at the same time, with AA moving clock-wise and BB moving anti-clockwise. They meet for the first time at 10:0010:00 am when AA has covered 60%60\% of the track. If AA returns to PP at 10:1210:12 am, then BB returns to PP at
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Question 4 of 34
CAT 2019 Slot 2QAGeometry • SolidsModerate
The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle, length of each side being 20 cm. The vertical height of the pyramid, in cm, is
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Question 5 of 34
CAT 2019 Slot 2QAAlgebra • Minima & MaximaModerate
What is the largest positive integer such that n2+7n+12n2−n−12\frac{n^2 + 7n + 12}{n^2 - n - 12} is also a positive integer?
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Question 6 of 34
CAT 2019 Slot 2QAAlgebra • PolynomialsModerate
Let AA be a real number. Then the roots of the equation x2−4x−log⁡2A=0x^2 - 4x - \log_2A = 0 are real and distinct if and only if
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Question 7 of 34
CAT 2019 Slot 2QAArithmetic • Profit & LossEasy
Mukesh purchased 10 bicycles in 20172017 , all at the same price. He sold six of these at a profit of 25%25 \% and the remaining four at a loss of 25%25 \%. If he made a total profit of Rs. 2000,2000, then his purchase price of a bicycle, in Rupees, was
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Question 8 of 34
CAT 2019 Slot 2QAArithmetic • Mean, Median & ModeModerate
The average of 30 integers is 55. Among these 30 integers, there are exactly 20 which do not exceed 55. What is the highest possible value of the average of these 20 integers?
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Question 9 of 34
CAT 2019 Slot 2QAAlgebra • FunctionsModerate
Let ff be a function such that f(mn)=f(m)f(n)f(mn) = f(m)f(n) for every positive integers m and n. If f(1),f(2)f(1) , f(2) and f(3)f(3) are positive integers, f(1)<f(2)f(1) < f(2) , and f(24)=54f(24) = 54 , then f(18)f(18) equals
TITA Answer:
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Question 10 of 34
CAT 2019 Slot 2QAAlgebra • Progression & SeriesModerate
Let a1,a2,...a_1, a_2, ... be integers such that a1−a2+a3−a4+...+(−1)n−1an=na_1 - a_2 + a_3 - a_4 + ... + (-1)^{n - 1} a_n = n , for all n≥1n \ge 1. Then a51+a52+...+a1023a_{51} + a_{52} + ... + a_{1023} equals
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Question 11 of 34
CAT 2019 Slot 2QAArithmetic • Ratio, Proportion & VariationModerate
In an examination, Rama's score was one-twelfth of the sum of the scores of Mohan and Anjali. After a review, the score of each of them increased by 66. The revised scores of Anjali, Mohan, and Rama were in the ratio 11:10:311:10:3. Then Anjali's score exceeded Rama's score by
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Question 12 of 34
CAT 2019 Slot 2QAArithmetic • Time, Speed & DistanceModerate
A cyclist leaves AA at 10am and reaches BB at 11am. Starting from 10:0110:01 am, every minute a motor cycle leaves AA and moves towards BB. Forty-five such motor cycles reach BB by 11am. All motor cycles have the same speed. If the cyclist had doubled his speed, how many motor cycles would have reached BB by the time the cyclist reached BB?
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Question 13 of 34
CAT 2019 Slot 2QAGeometry • TrianglesModerate
Let ABCABC be a right-angled triangle with hypotenuse BCBC of length 20 cm. If APAP is perpendicular on BCBC , then the maximum possible length of APAP , in cm, is
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Question 14 of 34
CAT 2019 Slot 2QAGeometry • TrianglesModerate
In a triangle ABCABC , medians ADAD and BEBE are perpendicular to each other, and have lengths 12 cm12 \mathrm{~cm} and 9 cm9 \mathrm{~cm} , respectively. Then, the area of triangle ABCABC , in sq cm, is
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Question 15 of 34
CAT 2019 Slot 2QANumber Systems • Integral SolutionsModerate
How many pairs (m,n)(m, n) of positive integers satisfy the equation m2+105=n2m^2 + 105 = n^2?
TITA Answer:
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Question 16 of 34
CAT 2019 Slot 2QAModern Math • LogarithmsModerate
The real root of the equation 26x+23x+2−21=02^{6x} + 2^{3x+2} - 21 = 0 is
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Question 17 of 34
CAT 2019 Slot 2QAModern Math • LogarithmsHard
If xx is a real number, then log⁡e4x−x23\sqrt{\log_e \frac{4x-x^2}{3}} is a real number if and only if
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Question 18 of 34
CAT 2019 Slot 2QAAlgebra • Linear EquationModerate
John gets Rs 57 per hour of regular work and Rs 114 per hour of overtime work. He works altogether 172 hours and his income from overtime hours is 15%15\% of his income from regular hours. Then, for how many hours did he work overtime?
TITA Answer:
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Question 19 of 34
CAT 2019 Slot 2QAGeometry • CirclesHard
Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, is
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Question 20 of 34
CAT 2019 Slot 2QAAlgebra • IndicesModerate
If 5x−3y=134385^{x}- 3^{y} = 13438 and 5x−1+3y+1=96865^{x-1}+ 3^{y+1} = 9686 , then x+yx+y equals
TITA Answer:
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Question 21 of 34
CAT 2019 Slot 2QAGeometry • SolidsHard
A man makes complete use of 405cc405 \mathrm{cc} of iron, 783cc783 \mathrm{cc} of aluminium, and 351cc351 \mathrm{cc} of copper to make a number of solid right circular cylinders of each type of metal. These cylinders have the same volume and each of these has radius 3 cm3 \mathrm{~cm}. If the total number of cylinders is to be kept at a minimum, then the total surface area of all these cylinders, in sq cm, is
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Question 22 of 34
CAT 2019 Slot 2QAArithmetic • PercentagesEasy
In an examination, the score of AA was 10%10\% less than that of BB , the score of BB was 25%25\% more than that of CC , and the score of CC was 20%20\% less than that of DD. If A scored 7272 , then the score of DD was
TITA Answer:
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Question 23 of 34
CAT 2019 Slot 2QANumber Systems • FactorisationEasy
How many factors of 24×35×1042^4 \times 3^5 \times 10^4 are perfect squares which are greater than 1?1?
TITA Answer:
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Question 24 of 34
CAT 2019 Slot 2QAArithmetic • Time, Speed & DistanceModerate
John jogs on track AA at 6 kmph and Mary jogs on track BB at 7.57.5 kmph. The total length of tracks AA and BB is 325 metres. While John makes 9 rounds of track AA , Mary makes 5 rounds of track BB. In how many seconds will Mary make one round of track AA?
TITA Answer:
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Question 25 of 34
CAT 2019 Slot 2QAAlgebra • InequalitiesHard
Let a,b,x,ya, b, x, y be real number such a2+b2=25,x2+y2=169a² + b² = 25, x² + y² = 169 , and axax + by = 65.65. If k=ay−bx,k = ay - bx, then
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Frequently Asked Questions about CAT 2019 Slot 2 QA Questions & Answer Key

How many questions were asked in CAT 2019 Slot 2 QA?

CAT 2019 Slot 2 QA contained 34 questions convened by IIM Kozhikode. 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 2019 Slot 2 QA?

Achieving a 99.0th percentile in QA required approximately 28–31 marks (~10 net correct), reflecting the standard cat difficulty profile.

Can I practice other sections of CAT 2019 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 13 QsCAT Algebra PYQs 10 QsCAT Geometry PYQs 6 QsCAT Number Systems PYQs 3 QsCAT Time, Speed & Distance (TSD) Questions 3 QsCAT Logarithms & Exponential Equations Questions 2 Qs