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CAT 2023 Slot 3 QA Questions & Answer Key

Quantitative Aptitude questions from CAT 2023 Slot 3 (IIM Lucknow, 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 2023 Slot 3 Quantitative Aptitude (QA) was conducted by IIM Lucknow 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)

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Official Exam Fact Sheet & Direct Answer Snapshot

Verified IIM Convenor Normalization & Question Paper Blueprint

Fact-Checked Archive

Conducting Body

IIM Lucknow

Rotational Conv.

Format & Counts

14 MCQ • 8 TITA

Verified Questions

99%ile Benchmark

28–31 Marks

Out of 66 (~10 net correct)

Marking Scheme

+3 / -1 / 0

Zero TITA Penalty

CAT 2023 Slot 3 QA Questions & Answer Key: CAT 2023 Slot 3 Quantitative Aptitude (QA) was conducted by IIM Lucknow 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.

Cross-verified against convenor response sheets by Team ThinkCATLast Audited: October 2026 • 1:1 TCS iON Simulator

CAT Direct Answer Fact Sheet & Citation Summary

Structured Knowledge Graph • Verified Academic Analysis

Updated for CAT 2026: 1 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 2023 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

Q1A
Q2B
Q3B
Q4A
Q55
Q69
Q7468
Q8A
Q9C
Q10D
Q11A
Q12B
Q13D
Q1436
Q1542
Q16340
Q17C
Q18B
Q1954
Q20C
Q21B
Q223

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Official Exam Questions & Explanations (22 of 22)

Sorted in official convenor sequence

Most-searched questions here

Question 1 of 22

CAT 2023 Slot 3QAModern Math • LogarithmsHard

For a real number

x

, if

\frac{1}{2}, \frac{\log _{3}\left(2^{x} - 9\right)}{\log _{3} 4}

, and

\frac{\log _{5}\left(2^{x}+\frac{17}{2}\right)}{\log _{5} 4}

are in an arithmetic progression, then the common difference is

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Official Convenor Answer Key: A

Question 2 of 22

CAT 2023 Slot 3QAAlgebra • IdentitiesHard

x

is a positive real number such that

x^8 + \frac{1}{x^8} = 47

, then the value of

x^9 + \frac{1}{x^9}

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Official Convenor Answer Key: B

Question 3 of 22

CAT 2023 Slot 3QAAlgebra • Linear EquationModerate

For some real numbers

a

and

b

, the system of equations

x + y = 4

and

(a + 5)x + (b^2 - 15)y = 8b

has infinitely many solutions for

x

and

y

. Then, the maximum possible value of

ab

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Official Convenor Answer Key: B

Question 4 of 22

CAT 2023 Slot 3QAAlgebra • IndicesModerate

Let

n

and

m

be two positive integers such that there are exactly 41 integers greater than

8^m

and less than

8^n

, which can be expressed as powers of

2

. Then, the smallest possible value of

n + m

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Official Convenor Answer Key: A

Question 5 of 22

CAT 2023 Slot 3QAAlgebra • InequalitiesModerate

Let

n

be any natural number such that

5^{n-1} < 3^{n+1}

. Then, the least integer value of m that satisfies

3^{n+1} < 2^{n+m}

for each such

n

, is

TITA Answer:

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Official Convenor Answer Key: 5

Question 6 of 22

CAT 2023 Slot 3QAAlgebra • PolynomialsModerate

A quadratic equation

x^{2}+b x+c=0

has two real roots. It the difference between the reciprocals of the roots is

1 / 3

and the sum of the reciprocals of the squares of the roots is

5 / 9

, then the largest possible value of (b+c) is

TITA Answer:

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Official Convenor Answer Key: 9

Question 7 of 22

CAT 2023 Slot 3QANumber Systems • FactorisationModerate

The sum of the first two natural numbers, each having 15 factors (including 1 and the number itself), is

TITA Answer:

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Official Convenor Answer Key: 468

Question 8 of 22

CAT 2023 Slot 3QAArithmetic • Mixture & AlligationEasy

Anil mixes cocoa with sugar in the ratio

3: 2

to prepare mixture

A

, and coffee with sugar in the ratio

7: 3

to prepare mixture

B

. He combines mixtures

A

and

B

in the ratio

2: 3

to make a new mixture

C

. If he mixes

C

with an equal amount of milk to make a drink, then the percentage of sugar in this drink will

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Official Convenor Answer Key: A

Question 9 of 22

CAT 2023 Slot 3QAArithmetic • Time & WorkHard

Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot

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Official Convenor Answer Key: C

Question 10 of 22

CAT 2023 Slot 3QAArithmetic • PercentagesHard

The population of a town in 2020 was 100000. The population decreased by

y \%

from the year 2020 to 2021, and increased by

\mathrm{x} \%

from the year 2021 to 2022, where x and y are two natural numbers. If population in 2022 was greater than the population in 2020 and the difference between

x

and

y

is 10, then the lowest possible population of the town in 2021 was

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Official Convenor Answer Key: D

Question 11 of 22

CAT 2023 Slot 3QAArithmetic • Profit & LossHard

A merchant purchases a cloth at a rate of Rs. 100 per meter and receives

5 \mathrm{~cm}

length of cloth free for every

100 \mathrm{~cm}

length of cloth purchased by him. He sells the same cloth at a rate of Rs. 110 per meter but cheats his customers by giving

95 \mathrm{~cm}

length of cloth for every

100 \mathrm{~cm}

length of cloth purchased by the customers. If the merchant provides a

5 \%

discount, the resulting profit earned by him is

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Official Convenor Answer Key: A

Question 12 of 22

CAT 2023 Slot 3QAArithmetic • Mean, Median & ModeModerate

There are three persons

\mathrm{A}, \mathrm{B}

and

C

in a room. If a person

D

joins the room, the average weight of the persons in the room reduces by

x

kg . Instead of

D

, if person

E

joins the room, the average weight of the persons in the room increases by

2 \mathrm{x} \mathrm{kg}

. If the weight of

E

12 \mathrm{~kg}

more than that of

D

, then the value of

x

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Official Convenor Answer Key: B

Question 13 of 22

CAT 2023 Slot 3QAArithmetic • Time, Speed & DistanceHard

A boat takes 2 hours to travel downstream a river from port A to port B , and 3 hours to return to port A . Another boat takes a total of 6 hours to travel from port

B

to port

A

and return to port

B

. If the speeds of the boats and the river are constant, then the time, in hours, taken by the slower boat to travel from port

A

to port

B

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Official Convenor Answer Key: D

Question 14 of 22

CAT 2023 Slot 3QAArithmetic • Time & WorkModerate

Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only

60 \%

of his usual work on a day, Suhani must do

150 \%

of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is

TITA Answer:

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Official Convenor Answer Key: 36

Question 15 of 22

CAT 2023 Slot 3QAArithmetic • Ratio, Proportion & VariationModerate

The number of coins collected per week by two coin-collectors

A

and

B

are In the ratio

3:4

. If the total number of coins collected by

A

in 5 weeks is a multiple of

7

, and the total number of coins collected by

B

in 3 weeks is a multiple of

24

, then the minimum possible number of coins collected by

A

in one week is

TITA Answer:

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Official Convenor Answer Key: 42

Question 16 of 22

CAT 2023 Slot 3QAAlgebra • Linear EquationHard

A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up

40 \%

of his stock. That day, he sells half of the mangoes, 96 bananas and

40 \%

of the apples. At the end of the day, he ends up selling

50 \%

of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is

TITA Answer:

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Official Convenor Answer Key: 340

Question 17 of 22

CAT 2023 Slot 3QAGeometry • TrianglesHard

Let

\triangle ABC

be an isosceles triangle such that

AB

and

AC

are of equal length.

AD

is the altitude from

A

BC

and

BE

is the altitude from

B

AC

. If

AD

and

BE

intersect at

O

such that

\angle AOB = 105^\circ

, then

AD/BE

equals

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Official Convenor Answer Key: C

Question 18 of 22

CAT 2023 Slot 3QAGeometry • CirclesModerate

A rectangle with the largest possible area is drawn inside a semicircle of radius 2 cm. Then, the ratio of the lengths of the largest to the smallest side of this rectangle is

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Official Convenor Answer Key: B

Question 19 of 22

CAT 2023 Slot 3QAGeometry • PolygonsModerate

In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is

TITA Answer:

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Official Convenor Answer Key: 54

Question 20 of 22

CAT 2023 Slot 3QAAlgebra • Progression & SeriesHard

The value of

1+\left(1+ \frac{1}{3}\right) \frac{1}{4} + \left(1+ \frac{1}{3} + \frac{1}{9}\right) \frac{1}{16} + \left(1+ \frac{1}{3} + \frac{1}{9} + \frac{1}{27}\right) \frac{1}{64} + \ldots \ldots

, is

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Official Convenor Answer Key: C

Question 21 of 22

CAT 2023 Slot 3QAAlgebra • Progression & SeriesModerate

Let

a_n = 46 + 8n

and

b_n = 98 + 4n

be two sequences for natural numbers

n \le 100

. Then, the sum of all terms common to both the sequences is

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Official Convenor Answer Key: B

Question 22 of 22

CAT 2023 Slot 3QAAlgebra • FunctionsModerate

Suppose

f(x, y)

is a real valued function such that

f(3x + 2y, 2x- 5y) = 19x

, for all real numbers

x

and

y

. The value of

x

for which

f(x, 2x) = 27

, is

TITA Answer:

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Official Convenor Answer Key: 3

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Frequently Asked Questions about CAT 2023 Slot 3 QA Questions & Answer Key

How many questions were asked in CAT 2023 Slot 3 QA?

CAT 2023 Slot 3 QA contained 22 questions convened by IIM Lucknow. 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 2023 Slot 3 QA?

Achieving a 99.0th percentile in QA required approximately 28–31 marks (~10 net correct), reflecting the very high difficulty (historic dilr difficulty spike, route networks).

Can I practice other sections of CAT 2023 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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CAT 2023 Slot 3 QA Questions & Answer Key

CAT Direct Answer Fact Sheet & Citation Summary

CAT 2023 Slot 3 QA Answer Key

QA

Attempt under official TCS iON 40-Min countdown timer

Official Exam Questions & Explanations (22 of 22)

Most-searched questions here

Unlock All 24 Full-Length Official Mocks & 6,000+ Questions

Frequently Asked Questions about CAT 2023 Slot 3 QA Questions & Answer Key

How many questions were asked in CAT 2023 Slot 3 QA?

What score was required for a 99th percentile in CAT 2023 Slot 3 QA?

Can I practice other sections of CAT 2023 Slot 3?

Related CAT Papers & Topic Mastery Hubs

CAT 2023 Slot 3 Full Question Paper

CAT 2023 QA All Slots Hub

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