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CAT 2022 Slot 2 QA Questions & Answer Key

Quantitative Aptitude questions from CAT 2022 Slot 2 (IIM Bangalore, Afternoon Session (12:30 PM – 2:30 PM IST); 22 in the exam) with the answer key and step-by-step solutions

Executive Answer & Section Summary

CAT 2022 Slot 2 Quantitative Aptitude (QA) was conducted by IIM Bangalore during the Afternoon Session (12:30 PM – 2:30 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 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. Q24
  3. Q3D
  4. Q46
  5. Q5B
  6. Q624
  7. Q710
  8. Q8C
  9. Q9B
  10. Q10A
  11. Q11C
  12. Q12B
  13. Q13A
  14. Q14B
  15. Q15D
  16. Q1620
  17. Q17B
  18. Q1814
  19. Q19C
  20. Q2012
  21. Q2147
  22. Q22B
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Official Exam Questions & Explanations (22 of 22)

Sorted in official convenor sequence
Question 1 of 22
CAT 2022 Slot 2QAAlgebra • PolynomialsModerate
Let f(x)f(x) be quadratic polynomial in xx such that f(x)≥0f(x) \geq 0 for all real numbers xx. if f(2)=0f(2)=0 and f(4)=6f(4)=6 , then f(−2)f(-2) is equal to
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Question 2 of 22
CAT 2022 Slot 2QAAlgebra • IndicesHard
The number of integer solutions of the equation (x2−10)(x2−3x−10)=1\left(x^{2}-10\right)^{\left(x^{2}-3 x-10\right)}=1 is
TITA Answer:
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Question 3 of 22
CAT 2022 Slot 2QAArithmetic • Mean, Median & ModeEasy
Manu earns Rs. 4000 per month and wants to save an average of Rs. 550 per month in a year. In the first nine months, his monthly expense was Rs. 35003500 , and he foresees that, tenth month onward, his monthly expense will increase to Rs. 37003700. In order to meet his yearly savings target, his monthly earnings, in rupees, from the tenth month onward should
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Question 4 of 22
CAT 2022 Slot 2QAArithmetic • Time & WorkModerate
Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5:8:105: 8: 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is
TITA Answer:
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Question 5 of 22
CAT 2022 Slot 2QAArithmetic • Mean, Median & ModeModerate
Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit is
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Question 6 of 22
CAT 2022 Slot 2QAAlgebra • Linear EquationModerate
In an examination, there were 75 questions. 3 marks were awarded for each correct answer, 1 mark was deducted for each wrong answer and 1 mark was awarded for each unattempted question. Rayan scored a total of 97 marks in the examination. If the number of unattempted questions was higher than the number of attempted questions, then the maximum number of correct answers that Rayan could have given in the examination is
TITA Answer:
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Question 7 of 22
CAT 2022 Slot 2QAGeometry • PolygonsEasy
Regular polygons AA and BB have number of sides in the ratio 1:21: 2 and interior angles in the ratio 3:43: 4. Then the number of sides of BB equals
TITA Answer:
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Question 8 of 22
CAT 2022 Slot 2QAArithmetic • Mixture & AlligationHard
There are two containers of the same volume, first container half-filled with sugar syrup and the second container half-filled with milk. Half the content of the first container is transferred to the second container, and then the half of this mixture is transferred back to the first container. Next, half the content of the first container is transferred back to the second container. Then the ratio of sugar syrup and milk in the second container is
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Question 9 of 22
CAT 2022 Slot 2QAArithmetic • Time, Speed & DistanceModerate
Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are 60 km60 \mathrm{~km} apart. If the speed of one of the ships is 6 km6 \mathrm{~km} per hour more than the other one, then the speed, in km per hour, of the slower ship is
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Question 10 of 22
CAT 2022 Slot 2QAGeometry • TrianglesModerate
The length of each side of an equilateral triangle ABC is 3 cm3 \mathrm{~cm}. Let D be a point on BC such that the area of triangle ADC is half the area of triangle ABDA B D. Then the length of AA D , in cm , is
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Question 11 of 22
CAT 2022 Slot 2QAModern Math • Permutation & CombinationModerate
The number of integers greater than 2000 that can be formed with the digits 0,1,2,3,4,50, 1, 2, 3, 4, 5 , using each digit at most once, is
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Question 12 of 22
CAT 2022 Slot 2QAAlgebra • PolynomialsModerate
Let rr and cc be real numbers, if rr and −r- r are roots of 5x3+c5x^{3} + c x2−10x+9=0x^{2} - 10 x+9=0 , then cc equals
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Question 13 of 22
CAT 2022 Slot 2QAAlgebra • Progression & SeriesModerate
On day one, there are 100 particles in laboratory experiment. On day nn , where n≥n \geq 2 , one out of every nn particles produces another particle. If the total number of particles in the laboratory experiment increases to 1000 on day mm , then mm equals.
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Question 14 of 22
CAT 2022 Slot 2QAArithmetic • Ratio, Proportion & VariationEasy
In an election, there were four candidates and 80%80\% of the registered voters casted their votes. One of the candidates received 30%30 \% of the casted votes while the other three candidates received the remaining casted votes in the proportion 1:2:31: 2: 3. If the winner of the election received 2512 votes more than the candidate with the second highest votes, then the number of registered voters was
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Question 15 of 22
CAT 2022 Slot 2QAGeometry • TrianglesModerate
In triangle ABC, altitudes AD and BE are drawn to the corresponding bases. If ∠BAC=45∘\angle BAC = 45^\circ and ∠ABC=θ\angle ABC = \theta , then ADBE\frac{AD}{BE} equals
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Question 16 of 22
CAT 2022 Slot 2QAArithmetic • Simple & Compound InterestEasy
Mr. Pinto invests one-fifth of his capital at 6%6\% , one-third at 10%10\% and the remaining at 1%1\% , each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is
TITA Answer:
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Question 17 of 22
CAT 2022 Slot 2QANumber Systems • MiscellaneousModerate
For some natural number nn , assume that (15000)!(15000)! is divisible by (n!)!(n!)!. The largest possible value of nn is
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Question 18 of 22
CAT 2022 Slot 2QAAlgebra • Progression & SeriesHard
The average of a non-decreasing sequence of NN numbers a1,a2,…,aNa_{1}, a_{2}, \ldots, a_{N} is 300300. If a1a_{1} is replaced by 6a16 a_{1} , the new average becomes 400400. Then, the number of possible values of a1a_{1} is
TITA Answer:
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Question 19 of 22
CAT 2022 Slot 2QAAlgebra • Progression & SeriesModerate
Consider the arithmetic progression 3, 7, 11, ..... and let Aₙ denote the sum of the first n terms of this progression. Then the value of 125∑n=125An\frac{1}{25} \sum_{n=1}^{25} A_n is
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Question 20 of 22
CAT 2022 Slot 2QAAlgebra • FunctionsModerate
Suppose for all integers x, there are two function f and g such that f(x)+f(x−1)−1=0f(x) + f(x-1) - 1 = 0 and g(x)=x2g(x) = x^2. If f(x2−x)=5f(x^2 - x) = 5 , then the value of the sum f(g(5))+g(f(5))f(g(5)) + g(f(5)) is
TITA Answer:
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Question 21 of 22
CAT 2022 Slot 2QAModern Math • LogarithmsModerate
The number of distinct integer values of n satisfying 4−log⁡2n3−log⁡4n<0\frac{4-\log_2 n}{3-\log_4 n} < 0 , is
TITA Answer:
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Question 22 of 22
CAT 2022 Slot 2QAAlgebra • Minima & MaximaEasy
If aa and bb are non-negative real numbers such that a+2b=6a + 2b = 6 , then the average of the maximum and minimum possible values of (a+b)(a + b) is
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Frequently Asked Questions about CAT 2022 Slot 2 QA Questions & Answer Key

How many questions were asked in CAT 2022 Slot 2 QA?

CAT 2022 Slot 2 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 2 QA?

Achieving a 99.0th percentile in QA required approximately 28–31 marks (~10 net correct), reflecting the moderate to high difficulty (dense philosophical rc, graph di).

Can I practice other sections of CAT 2022 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 Algebra PYQs 9 QsCAT Arithmetic PYQs 7 QsCAT Geometry PYQs 3 QsCAT Modern Math PYQs 2 QsCAT Polynomials & Roots of Equations Questions 2 QsCAT Triangles Geometry Questions 2 Qs