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CAT 2023 Slot 1 QA Questions & Answer Key

Quantitative Aptitude questions from CAT 2023 Slot 1 (IIM Lucknow, 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 2023 Slot 1 Quantitative Aptitude (QA) was conducted by IIM Lucknow 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: 14 (+3 / -1)

TITA: 8 (0 Negative Penalty)

Attempt QA Section in Timed 40-Min Mode Solve Questions on this Page

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 1 QA Questions & Answer Key: CAT 2023 Slot 1 Quantitative Aptitude (QA) was conducted by IIM Lucknow 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.

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: 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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Citation Format: ThinkCAT Academic Archive (thinkcat.in)

CAT 2023 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

Q1D
Q2C
Q3C
Q4B
Q53
Q66
Q72
Q8A
Q9A
Q10B
Q11D
Q12C
Q13A
Q14972
Q1520808
Q1627
Q17B
Q18D
Q192
Q20A
Q21A
Q2219

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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 1QAModern Math • LogarithmsModerate

x

and

y

are positive real numbers such that

\log_{x}\left(x^{2} + 12\right)=4

and

3 \log _{y} x=1

, then

x+y

equals

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⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution

Official Convenor Answer Key: D

Question 2 of 22

CAT 2023 Slot 1QANumber Systems • FactorisationModerate

Let

n

be the least positive integer such that 168 is a factor of

1134^n

. If m is the least positive integer such that

1134^{n}

. is a factor of

168^m

, then

m + n

equals

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Official Convenor Answer Key: C

Question 3 of 22

CAT 2023 Slot 1QAAlgebra • IdentitiesModerate

x

and

y

are real numbers such that

x^2 + (x - 2y − 1)^2 = - 4y(x + y)

, then the value

x - 2y

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Official Convenor Answer Key: C

Question 4 of 22

CAT 2023 Slot 1QAAlgebra • IndicesModerate

\sqrt{5x+9}+ \sqrt{5x-9} = 3(2+ \sqrt{2})

, then

\sqrt{10x + 9}

is equal to

Practice More Questions

⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution

Official Convenor Answer Key: B

Question 5 of 22

CAT 2023 Slot 1QAAlgebra • ModulusModerate

The number of integer solutions of equation

2|x|\left(x^{2} + 1\right)=5 x^{2}

TITA Answer:

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Official Convenor Answer Key: 3

Question 6 of 22

CAT 2023 Slot 1QAAlgebra • PolynomialsModerate

Let

\alpha

and

\beta

be the two distinct roots of the equation

2x^2 - 6x + k = 0

, such that

(\alpha + \beta)

and

\alpha \beta

are the distinct roots of the equation

x^2 + px + p = 0

. Then, the value of

8 (k - p)

TITA Answer:

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Official Convenor Answer Key: 6

Question 7 of 22

CAT 2023 Slot 1QAAlgebra • PolynomialsModerate

The equation

x^3 + (2r + 1)x^2 + (4r - 1)x + 2 = 0

has

- 2

as one of the roots. If the other two roots are real, then the minimum possible non-negative integer value of

r

TITA Answer:

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Official Convenor Answer Key: 2

Question 8 of 22

CAT 2023 Slot 1QAArithmetic • Time, Speed & DistanceModerate

The minor angle between the hours hand and minutes hand of a clock was observed at 8:48 am. The minimum duration, in minutes, after

8.48

am when this angle increases by

50 \%

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Official Convenor Answer Key: A

Question 9 of 22

CAT 2023 Slot 1QAArithmetic • Mixture & AlligationEasy

A mixture P is formed by removing a certain amount of coffee from a coffee jar and replacing the same amount with cocoa powder. The same amount is again removed from mixture

P

and replaced with same amount of cocoa powder to form a new mixture

Q

. If the ratio of coffee and cocoa in the mixture

Q

16: 9

, then the ratio of cocoa in mixture

P

to that in mixture

Q

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Official Convenor Answer Key: A

Question 10 of 22

CAT 2023 Slot 1QAArithmetic • Mean, Median & ModeHard

In an examination, the average marks of 4 girls and 6 boys is

24

. Each of the girls has the same marks while each of the boys has the same marks. If the marks of any girl is at most double the marks of any boy, but not less than the marks of any boy, then the number of possible distinct integer values of the total marks of 2 girls and 6 boys is

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Official Convenor Answer Key: B

Question 11 of 22

CAT 2023 Slot 1QANumber Systems • MiscellaneousModerate

Brishti went on an 8-hour trip in a car. Before the trip, the car had travelled a total of x km till then, where x is a whole number and is palindromic, i.e.,

x

remains unchanged when its digits are reversed. At the end of the trip, the car had traveled a total of

26862 \mathrm{~km}

till then, this number again being palindromic. If Brishti never drove at more than

110 \mathrm{~km} / \mathrm{hr}

, then the greatest possible average speed at which she drove during the trip, in km/hr, was

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⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution

Official Convenor Answer Key: D

Question 12 of 22

CAT 2023 Slot 1QAArithmetic • Profit & LossModerate

Gita sells two objects

A

and

B

at the same price such that she makes a profit of

20 \%

on object

A

and

a

loss of

10 \%

on object

B

. If she increases the selling price such that objects

A

and

B

are still sold at an equal price and a profit of

10 \%

is made on object

B

, then the profit made on object A will be nearest to

Practice More Questions

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Official Convenor Answer Key: C

Question 13 of 22

CAT 2023 Slot 1QAArithmetic • Ratio, Proportion & VariationEasy

The salaries of three friends Sita, Gita and Mita are initially in the ratio

5 : 6 : 7

, respectively. In the first year, they get salary hikes of

20\% , 25\%

and

20\%

, respectively. In the second year, Sita and Mita get salary hikes of

40\%

and

25\%

, respectively, and the salary of Gita becomes equal to the mean salary of the three friends. The salary hike of Gita in the second year is

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Official Convenor Answer Key: A

Question 14 of 22

CAT 2023 Slot 1QAArithmetic • Time, Speed & DistanceModerate

Arvind travels from town

A

to town

B

, and Surbhi from town B to town

A

, both starting at the same time along the same route. After meeting each other, Arvind takes 6 hours to reach town

B

while Surbhi takes 24 hours to reach town

A

. If Arvind travelled at a speed of

54 \mathrm{~km} / \mathrm{h}

, then the distance, in km, between town

A

and town

B

TITA Answer:

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Official Convenor Answer Key: 972

Question 15 of 22

CAT 2023 Slot 1QAArithmetic • Simple & Compound InterestModerate

Anil invests Rs. 22000 for 6 years in a certain scheme with

4 \%

interest per annum, compounded half-yearly. Sunil invests in the same scheme for 5 years, and then reinvests the entire amount received at the end of 5 years for one year at

10 \%

simple interest. If the amounts received by both at the end of 6 years are same, then the initial investment made by Sunil, in rupees, is

TITA Answer:

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Official Convenor Answer Key: 20808

Question 16 of 22

CAT 2023 Slot 1QAArithmetic • Time & WorkHard

The amount of job that Amal, Sunil and Kamal can individually do in a day, are in harmonic progression. Kamal takes twice as much time as Amal to do the same amount of job. If Amal and Sunil work for 4 days and 9 days, respectively, Kamal needs to work for 16 days to finish the remaining job. Then the number of days Sunil will take to finish the job working alone, is

TITA Answer:

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Official Convenor Answer Key: 27

Question 17 of 22

CAT 2023 Slot 1QAGeometry • QuadrilateralsHard

A quadrilateral

A B C D

is inscribed in a circle such that

A B: C D=2: 1

and

B C: A D=5: 4

. If

A C

and

B D

intersect at the point

E

, then

A E

C E

equals

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Official Convenor Answer Key: B

Question 18 of 22

CAT 2023 Slot 1QAGeometry • CirclesModerate

Let

C

be the circle

x^2 + y^2 + 4x - 6y - 3 = 0

and

L

be the locus of the point of intersection of a pair of tangents to

C

with the angle between the two tangents equal to

60°

. Then, the point at which

L

touches the line

x = 6

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Official Convenor Answer Key: D

Question 19 of 22

CAT 2023 Slot 1QAGeometry • TrianglesModerate

In a right-angled triangle

\triangle

A B C , the altitude

A B

5 \mathrm{~cm}

, and the base

B C

12 \mathrm{~cm}

P

and

Q

are two points on

B C

such that the areas of

\triangle \mathrm{ABP}, \triangle \mathrm{ABQ}

and

\triangle \mathrm{ABC}

are in arithmetic progression. If the area of

\triangle \mathrm{ABC}

1.5

times the area of

\triangle \mathrm{ABP}

, the length of PQ in cm , is

TITA Answer:

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Official Convenor Answer Key: 2

Question 20 of 22

CAT 2023 Slot 1QAAlgebra • Progression & SeriesModerate

For some positive and distinct real numbers

x, y

and

z

, if

\frac{1}{\sqrt{y} + \sqrt{z}}

is the arithmetic mean of

\frac{1}{\sqrt{x} + \sqrt{z}}

and

\frac{1}{\sqrt{x} + \sqrt{y}}

, then the relationship which will always hold true, is

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Official Convenor Answer Key: A

Question 21 of 22

CAT 2023 Slot 1QAModern Math • Permutation & CombinationModerate

The number of all natural numbers up to 1000 with non-repeating digits is

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Official Convenor Answer Key: A

Question 22 of 22

CAT 2023 Slot 1QAAlgebra • Progression & SeriesModerate

A lab experiment measures the number of organisms at 8am every day. Starting with 2 organisms on the first day, the number of organisms on any day is equal to 3 more than twice the number on the previous day. If the number of organisms on nth day exceeds one million, then the lowest possible value of

n

TITA Answer:

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Official Convenor Answer Key: 19

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Frequently Asked Questions about CAT 2023 Slot 1 QA Questions & Answer Key

How many questions were asked in CAT 2023 Slot 1 QA?

CAT 2023 Slot 1 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 1 QA?

Achieving a 99.0th percentile in QA required approximately 28–31 marks (~10 net correct), reflecting the high difficulty (iim lucknow signature rigor, dense quant).

Can I practice other sections of CAT 2023 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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CAT Arithmetic PYQs 8 Qs CAT Algebra PYQs 7 Qs CAT Geometry PYQs 3 Qs CAT Modern Math PYQs 2 Qs CAT Polynomials & Roots of Equations Questions 2 Qs CAT Time, Speed & Distance (TSD) Questions 2 Qs

CAT 2023 Slot 1 QA Questions & Answer Key

CAT Direct Answer Fact Sheet & Citation Summary

CAT 2023 Slot 1 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 1 QA Questions & Answer Key

How many questions were asked in CAT 2023 Slot 1 QA?

What score was required for a 99th percentile in CAT 2023 Slot 1 QA?

Can I practice other sections of CAT 2023 Slot 1?

Related CAT Papers & Topic Mastery Hubs

CAT 2023 Slot 1 Full Question Paper

CAT 2023 QA All Slots Hub

CAT 2023 Slot 1 VARC

CAT 2023 Slot 1 DILR

CAT 2023 Slot 2 QA

CAT 2023 Slot 3 QA

Topics in this paper