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CAT 2022 Slot 1 QA Questions & Answer Key

Quantitative Aptitude questions from CAT 2022 Slot 1 (IIM Bangalore, Morning Session (8:30 AM – 10:30 AM IST); 22 in the exam) with the answer key and step-by-step solutions

Executive Answer & Section Summary

CAT 2022 Slot 1 Quantitative Aptitude (QA) was conducted by IIM Bangalore during the Morning Session (8:30 AM – 10:30 AM 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: 13 (+3 / -1)
TITA: 9 (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
22 Qs
13 MCQ + 9 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 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

  1. Q182
  2. Q234
  3. Q3D
  4. Q48
  5. Q5C
  6. Q6D
  7. Q7B
  8. Q8160
  9. Q943200
  10. Q10C
  11. Q11D
  12. Q12C
  13. Q1384
  14. Q14B
  15. Q1566
  16. Q16A
  17. Q17B
  18. Q1844
  19. Q19B
  20. Q20C
  21. Q21111
  22. Q22D
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Official Exam Questions & Explanations (22 of 22)

Sorted in official convenor sequence
Question 1 of 22
CAT 2022 Slot 1QANumber Systems • HCF/LCMModerate
Let A be the largest positive integer that divides all the numbers of the form 3k+4k+5k3^k + 4^k + 5^k , and B be the largest positive integer that divides all the numbers of the form 4k+3(4k)+4k+24^k + 3(4^k) + 4^{k + 2} , where k is any positive integer. Then (A + B) equals
TITA Answer:
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Question 2 of 22
CAT 2022 Slot 1QAAlgebra • Minima & MaximaModerate
For natural numbers x,y,andx , y , andz , if xy+yz=19xy + yz = 19 and yz+xz=51,thentheminimumpossiblevalueofyz + xz = 51 , then the minimum possible value ofxyz$ is
TITA Answer:
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Question 3 of 22
CAT 2022 Slot 1QAArithmetic • Simple & Compound InterestEasy
Alex invested his savings in two parts. The simple interest earned on the first part at 15%15 \% per annum for 4 years is the same as the simple interest earned on the second part at 12%12 \% per annum for 3 years. Then, the percentage of his savings invested in the first part is
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Question 4 of 22
CAT 2022 Slot 1QAAlgebra • Linear EquationModerate
Let a and b be natural number. If a2+ab+a=14a^2 + ab + a = 14 and b2+ab+b=28b^2 + ab + b = 28 , then (2a+b)(2a + b) equals
TITA Answer:
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Question 5 of 22
CAT 2022 Slot 1QAModern Math • Set TheoryHard
In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks is
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Question 6 of 22
CAT 2022 Slot 1QAArithmetic • Mixture & AlligationEasy
A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1:31: 3 , then the ratio of lemon juice and sugar syrup in the new mixture is
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Question 7 of 22
CAT 2022 Slot 1QAAlgebra • PolynomialsModerate
Let a,b,ca, b, c be non-zero real numbers such that b2<4acb^2 < 4ac , and f(x)=ax2+bx+cf(x) = ax^2 + bx + c. If the set S consists of all integers m such that f(m)<0f(m) < 0 , then the set S must necessarily
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Question 8 of 22
CAT 2022 Slot 1QAArithmetic • Profit & LossHard
Amal buys 110 kg110 \mathrm{~kg} of syrup and 120 kg120 \mathrm{~kg} of juice, syrup being 20% less costly than juice, per kg. He sells 10 kg10 \mathrm{~kg} of syrup at 10% profit and 20 kg20 \mathrm{~kg} of juice at 20%20 \% profit. Mixing the remaining juice and syrup, Amal sells the mixture at Rs. 308.32308.32 per kg and makes an overall profit of 64%64 \%. Then, Amal's cost price for syrup, in rupees per kg, is
TITA Answer:
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Question 9 of 22
CAT 2022 Slot 1QAArithmetic • Ratio, Proportion & VariationHard
In a village, the ratio of number of males to females is 5:45: 4. The ratio of number of literate males to literate females is 2:32 : 3. The ratio of the number of illiterate males to illiterate females is 4:34: 3. If 3600 males in the village are literate, then the total number of females in the village is
TITA Answer:
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Question 10 of 22
CAT 2022 Slot 1QAGeometry • CirclesModerate
All the vertices of a rectangle lie on a circle of radius RR. If the perimeter of the rectangle is PP , then the area of the rectangle is
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Question 11 of 22
CAT 2022 Slot 1QAGeometry • QuadrilateralsEasy
Let ABCDABCD be a parallelogram such that the coordinates of its three vertices A,B,CA, B, C are (1,1),(3,4)(1, 1), (3, 4) and (−2,8)(-2, 8) , respectively. Then, the coordinates of the vertex DD are
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Question 12 of 22
CAT 2022 Slot 1QAAlgebra • ModulusModerate
The largest real value of a for which the equation ∣x+a∣+∣x−1∣=2|x + a| + |x - 1| = 2 has an infinite number of solutions for xx is
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Question 13 of 22
CAT 2022 Slot 1QAModern Math • Permutation & CombinationModerate
The number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is
TITA Answer:
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Question 14 of 22
CAT 2022 Slot 1QAAlgebra • Progression & SeriesModerate
For any natural number n, suppose the sum of the first n terms of an arithmetic progression is (n+2n2)(n + 2n^2). If the nthn^{th} term of the progression is divisible by 99 , then the smallest possible value of nn is
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Question 15 of 22
CAT 2022 Slot 1QAGeometry • QuadrilateralsModerate
A trapezium ABCDABCD has side ADAD parallel to BC,∠BC , \angleBAD = 90° , BC=3BC = 3cm and AD=8AD = 8cm. If the perimeter of this trapezium is 36 cm, then its area, in sq. cm, is
TITA Answer:
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Question 16 of 22
CAT 2022 Slot 1QAAlgebra • ModulusModerate
Let 0≤a≤x≤1000 \leq a \leq x \leq 100 and f(x)=∣x−a∣+∣x−100∣+∣x−a−50∣f(x)=|x-a|+|x-100|+|x-a-50|. Then the maximum value of f(x)f(x) becomes 100 when aa is equal to
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Question 17 of 22
CAT 2022 Slot 1QAArithmetic • Mean, Median & ModeModerate
The average of three integers is 1313. When a natural number nn is included, the average of these four integers remains an odd integer. The minimum possible value of nn is
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Question 18 of 22
CAT 2022 Slot 1QAAlgebra • FunctionsModerate
For any real number x, let [x] be the largest integer less than or equal to x. If ∑n=1N\sum_{n=1}^{N} [15+n25\frac{1}{5} + \frac{n}{25}] = 2525 then N is
TITA Answer:
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Question 19 of 22
CAT 2022 Slot 1QAArithmetic • Profit & LossHard
Ankita buys 4 kg4 \mathrm{~kg} cashews, 14 kg14 \mathrm{~kg} peanuts and 6 kg6 \mathrm{~kg} almonds when the cost of 7 kg7 \mathrm{~kg} cashews is the same as that of 30 kg30 \mathrm{~kg} peanuts or 9 kg9 \mathrm{~kg} almonds. She mixes all the three nuts and marks a price for the mixture in order to make a profit of Rs.1752. She sells 4 kg of the mixture at this marked price and the remaining at a 20%20 \% discount on the marked price, thus making a total profit of Rs.
744
Then the amount, in rupees, that she had spent in buying almonds is
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Question 20 of 22
CAT 2022 Slot 1QAArithmetic • Mean, Median & ModeEasy
The average weight of students in a class increases by 600gm when some new students join the class. If the average weight of the new students is 3 kg more than the average weight of the original students, then the ratio of the number of original students to the number of new students is
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Question 21 of 22
CAT 2022 Slot 1QAArithmetic • Ratio, Proportion & VariationEasy
Pinky is standing in a queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the queue is 3:53: 5. If the total number of persons in the queue is less than 300300 , then the maximum possible number of persons standing ahead of Pinky is
TITA Answer:
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Question 22 of 22
CAT 2022 Slot 1QAArithmetic • Time, Speed & DistanceHard
Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train BB to travel from station YY to station XX is
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Frequently Asked Questions about CAT 2022 Slot 1 QA Questions & Answer Key

How many questions were asked in CAT 2022 Slot 1 QA?

CAT 2022 Slot 1 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 1 QA?

Achieving a 99.0th percentile in QA required approximately 28–31 marks (~10 net correct), reflecting the moderate difficulty (iim bangalore modern blueprint).

Can I practice other sections of CAT 2022 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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Topics in this paper

CAT Arithmetic PYQs 9 QsCAT Algebra PYQs 7 QsCAT Geometry PYQs 3 QsCAT Modern Math PYQs 2 QsCAT Profit, Loss & Discount Questions 2 QsCAT Circles Geometry & Tangents Questions 1 Q