Official CAT 2023 Convenor Archive• Official Answer Keys

CAT 2023 Question Paper (All Slots Archive)

Complete official CAT 2023 exam papers across Slot 1, Slot 2, and Slot 3 with verified IIM answer keys and step-by-step explanations.

198 Total Questions

MCQ: 137 (+3 / -1)

TITA: 61 (0 Negative Penalty)

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Official Exam Questions & Explanations (25 of 198)

Sorted in official convenor sequence

Question 1 of 198

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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Question 2 of 198

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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Question 3 of 198

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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Question 4 of 198

CAT 2023 Slot 1QAAlgebra • IndicesModerate

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

, then

\sqrt{10x + 9}

is equal to

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Question 5 of 198

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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Question 6 of 198

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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Question 7 of 198

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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Question 8 of 198

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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Question 9 of 198

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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Question 10 of 198

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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Question 11 of 198

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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Question 12 of 198

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

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Question 13 of 198

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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Question 14 of 198

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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Question 15 of 198

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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Question 16 of 198

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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Question 17 of 198

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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Question 18 of 198

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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Question 19 of 198

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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Question 20 of 198

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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Question 21 of 198

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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Question 22 of 198

CAT 2023 Slot 1QAAlgebra • Progression & SeriesModerate

A lab experiment measures the number of organisms at

8

am 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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Question 23 of 198

CAT 2023 Slot 1DILRLogical Reasoning • ArrangementsEasy

Caselet / Problem Set Context•~218 words

Faculty members in a management school can belong to one of four departments – Finance and Accounting (F&A), Marketing and Strategy (M&S), Operations and Quants (O&Q) and Behaviour and Human Resources (B&H). The numbers of faculty members in F&A, M&S, O&Q and B&H departments are 9, 7, 5 and 3 respectively.

Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O&Q.

Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below.

There cannot be more than two candidates from a single department.

A candidate cannot vote for himself/herself.

Faculty members cannot vote for a candidate from their own department.

After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi.3a

Which two candidates can belong to the same department?

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Question 24 of 198

CAT 2023 Slot 1DILRLogical Reasoning • ArrangementsEasy

Caselet / Problem Set Context•~218 words

There cannot be more than two candidates from a single department.

A candidate cannot vote for himself/herself.

Faculty members cannot vote for a candidate from their own department.

Which of the following can be the number of votes that Prof. Qureshi received from a single department?

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Question 25 of 198

CAT 2023 Slot 1DILRLogical Reasoning • ArrangementsEasy

Caselet / Problem Set Context•~218 words

There cannot be more than two candidates from a single department.

A candidate cannot vote for himself/herself.

Faculty members cannot vote for a candidate from their own department.

If Prof. Samuel belongs to B&H, which of the following statements is/are true?

Statement A: Prof. Pakrasi belongs to M&S.

Statement B: Prof. Ramaswamy belongs to O&Q.

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Frequently Asked Questions about CAT 2023 Question Paper (All Slots Archive)

How many slots were conducted in CAT 2023?

CAT 2023 was conducted in 3 distinct exam slots by the conducting IIM convenor.

Can I solve slot-wise papers for CAT 2023?

Yes! You can explore individual slot papers (Slot 1, Slot 2, Slot 3) or individual sectional cuts (QA, DILR, VARC) using the links below.

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Official Exam Questions & Explanations (25 of 198)

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Frequently Asked Questions about CAT 2023 Question Paper (All Slots Archive)

How many slots were conducted in CAT 2023?

Can I solve slot-wise papers for CAT 2023?

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