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CAT 2022 Slot 3 QA Questions & Answer Key

Quantitative Aptitude questions from CAT 2022 Slot 3 (IIM Bangalore, Evening Session (4:30 PM – 6:30 PM IST); 22 in the exam) with the answer key and step-by-step solutions

Executive Answer & Section Summary

CAT 2022 Slot 3 Quantitative Aptitude (QA) was conducted by IIM Bangalore during the Evening Session (4:30 PM – 6:30 PM IST). The section comprised 22 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.

22 Total Questions
MCQ: 14 (+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: 3 November 2026
Verified Questions
22 Qs
14 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 2022 Slot 3 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. Q1A
  2. Q212
  3. Q3D
  4. Q460
  5. Q5B
  6. Q6B
  7. Q79
  8. Q811
  9. Q9A
  10. Q10A
  11. Q11B
  12. Q1214
  13. Q1363
  14. Q14B
  15. Q15A
  16. Q16150
  17. Q17A
  18. Q18A
  19. Q19C
  20. Q20548
  21. Q21D
  22. Q22A
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Official Exam Questions & Explanations (22 of 22)

Sorted in official convenor sequence
Question 1 of 22
CAT 2022 Slot 3QAArithmetic • Time & WorkEasy
A group of NN people worked on a project. They finished 35%35 \% of the project by working 7 hours a day for 10 days. Thereafter, 10 people left the group and the remaining people finished the rest of the project in 14 days by working 10 hours a day. Then the value of NN is
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Question 2 of 22
CAT 2022 Slot 3QAAlgebra • Linear EquationModerate
A donation box can receive only cheques of Rs. 100,Rs.100 , Rs.250 , and Rs. 500500. On one good day, the donation box was found to contain exactly 100 cheques amounting to a total sum of Rs. 1525015250. Then, the maximum possible number of cheques of Rs. 500 that the donation box may have contained, is
TITA Answer:
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Question 3 of 22
CAT 2022 Slot 3QAModern Math • Permutation & CombinationModerate
The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 14211421 , including itself, is
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Question 4 of 22
CAT 2022 Slot 3QAArithmetic • Time, Speed & DistanceModerate
Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator is
TITA Answer:
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Question 5 of 22
CAT 2022 Slot 3QAGeometry • QuadrilateralsModerate
The lengths of all four sides of a quadrilateral are integer valued. If three of its sides are of length 1 cm, 2 cm and 4 cm, then the total number of possible lengths of the fourth side is
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Question 6 of 22
CAT 2022 Slot 3QAAlgebra • Minima & MaximaModerate
The minimum possible value of x2−6x+103−x\frac{x^2-6x+10}{3-x} , for x<3x < 3 , is
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Question 7 of 22
CAT 2022 Slot 3QAGeometry • TrianglesModerate
Suppose the medians BDBD and CECE of a triangle ABCABC intersect at a point OO. If area of triangle ABCABC is 108sq. cm., then, the area of the triangle EODEOD , in sq. cm., is
TITA Answer:
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Question 8 of 22
CAT 2022 Slot 3QAArithmetic • Time & WorkHard
Bob can finish a job in 40 days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the first day, Bob and Cole work together on the second day, Cole and Alex work together on the third day, and then, they continue the work by repeating this three- day roster, with Alex and Bob working together on the fourth day, and so on. Then, the total number of days Alex would have worked when the job gets finished, is
TITA Answer:
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Question 9 of 22
CAT 2022 Slot 3QAAlgebra • FunctionsHard
Let r be a real number and f(x)={2x−rif x≥rrif x<rf(x) = \begin{cases} 2x-r & \text{if } x \ge r \\ r & \text{if } x < r \end{cases}. Then, the equation f(x)=f(f(x))f(x) = f(f(x)) holds for all real values of x where.
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Question 10 of 22
CAT 2022 Slot 3QAGeometry • CirclesHard
In a triangle ABC,AB=AC=8ABC, AB = AC = 8cm. AA circle drawn with BCBC as diameter passes through AA. Another circle drawn with center at AA passes through BB and CC. Then the area, in sq. cm, of the overlapping region between the two circles is
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Question 11 of 22
CAT 2022 Slot 3QAArithmetic • Mixture & AlligationEasy
A glass contains 500cc500 \mathrm{cc} of milk and a cup contains 500cc500 \mathrm{cc} of water. From the glass, 150cc150 \mathrm{cc} of milk is transferred to the cup and mixed thoroughly. Next, 150cc150 \mathrm{cc} of this mixture is transferred from the cup to the glass. Now, the amount of water in the glass and the amount of milk in the cup are in the ratio
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Question 12 of 22
CAT 2022 Slot 3QAAlgebra • IndicesHard
If (75)3x−y=8752401\left(\sqrt{\frac{7}{5}}\right)^{3 x-y}=\frac{875}{2401} and (4ab)6x−y=(2ab)y−6x\left(\frac{4 a}{b}\right)^{6 x-y}=\left(\frac{2 a}{b}\right)^{y-6 x}
for all non-zero real values of aa and bb , then the value of x+yx + y is
TITA Answer:
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Question 13 of 22
CAT 2022 Slot 3QAArithmetic • Mean, Median & ModeModerate
In an examination, the average marks of students in sections AA and BB are 32 and 6060 , respectively. The number of students in section AA is 10 less than that in section BB . If the average marks of all the students across both the sections combined is an integer, then the difference between the maximum and minimum possible number of students in section AA is
TITA Answer:
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Question 14 of 22
CAT 2022 Slot 3QAAlgebra • PolynomialsModerate
Suppose kk is any integer such that the equation 2x2+kx+5=02x^{2} + k x+5=0 has no real roots and the equation x2+(k−5)x+1=0x^{2}+(k-5) x+1=0 has two distinct real roots for xx. Then, the number of possible values of kk is
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Question 15 of 22
CAT 2022 Slot 3QAGeometry • TrianglesHard
Two ships are approaching a port along straight routes at constant speeds. Initially, the two ships and the port formed an equilateral triangle with sides of length 24 km. When the slower ship travelled 8 km, the triangle formed by the new positions of the two ships and the port became right-angled. When the faster ship reaches the port, the distance, in km, between the other ship and the port will
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Question 16 of 22
CAT 2022 Slot 3QANumber Systems • HCF/LCMModerate
A school has less than 5000 students and if the students are divided equally into teams of either 9 or 10 or 12 or 25 each, exactly 4 are always left out. However, if they are divided into teams of 11 each, no one is left out. The maximum number of teams of 12 each that can be formed out of the students in the school is
TITA Answer:
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Question 17 of 22
CAT 2022 Slot 3QAArithmetic • Time, Speed & DistanceModerate
Two cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take 1.51.5 hours if they travel towards each other, but 10.510.5 hours if they travel in the same direction. If the speed of the slower car is 60 km/hr, then the distance traveled, in km, by the slower car when it meets the other car while traveling towards each other, is
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Question 18 of 22
CAT 2022 Slot 3QAArithmetic • Mean, Median & ModeModerate
Consider six distinct natural numbers such that the average of the two smallest numbers is 1414 , and the average of the two largest numbers is 2828. Then, the maximum possible value of the average of these six numbers is
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Question 19 of 22
CAT 2022 Slot 3QAAlgebra • InequalitiesModerate
If C=16xy+49yxC = \frac{16x}{y} + \frac{49y}{x} for some non-zero real numbers xx and yy , then cc cannot take the value
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Question 20 of 22
CAT 2022 Slot 3QAAlgebra • Progression & SeriesModerate
The average of all 3-digit terms in the arithmetic progression 38,55,72,…38, 55, 72, \dots , is
TITA Answer:
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Question 21 of 22
CAT 2022 Slot 3QAAlgebra • PolynomialsModerate
If (3+22)(3+2\sqrt{2}) is a root of the equation ax2+bx+c=0ax^2 + bx + c = 0 , and (4+23)(4+2\sqrt{3}) is a root of the equation ay2+my+n=0ay^2 + my + n = 0 , where a,b,c,ma, b, c, m and nn are integers, then the value of (bm+c−2bn)(\frac{b}{m} + \frac{c-2b}{n}) is
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Question 22 of 22
CAT 2022 Slot 3QAArithmetic • Simple & Compound InterestEasy
Nitu has an initial capital of Rs. 20,00020,000. Out of this, she invests Rs. 8,0008,000 at 5.5%5.5\% in bank AA , Rs. 5,0005,000 at 5.6%5.6\% in bank BB and the remaining amount at x%x \% in bank CC , each rate being simple interest per annum. Her combined annual interest income from these investments is equal to 5%5 \% of the initial capital. If she had invested her entire initial capital in back CC alone, then her annual interest income, in rupees, would have been
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Frequently Asked Questions about CAT 2022 Slot 3 QA Questions & Answer Key

How many questions were asked in CAT 2022 Slot 3 QA?

CAT 2022 Slot 3 QA contained 22 questions convened by IIM Bangalore. 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 2022 Slot 3 QA?

Achieving a 99.0th percentile in QA required approximately 28–31 marks (~10 net correct), reflecting the moderate to high difficulty (arrangement depth, arithmetic sprints).

Can I practice other sections of CAT 2022 Slot 3?

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 Algebra PYQs 8 QsCAT Arithmetic PYQs 8 QsCAT Geometry PYQs 4 QsCAT Modern Math PYQs 1 QCAT Polynomials & Roots of Equations Questions 2 QsCAT Time and Work & Pipes-Cisterns Questions 2 Qs