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CAT 2018 Slot 2 QA Questions & Answer Key

Quantitative Aptitude questions from CAT 2018 Slot 2 (IIM Calcutta, Afternoon Session (12:30 PM – 2:30 PM IST); 34 in the exam) with the answer key and step-by-step solutions

Executive Answer & Section Summary

CAT 2018 Slot 2 Quantitative Aptitude (QA) was conducted by IIM Calcutta during the Afternoon Session (12:30 PM – 2:30 PM IST). The section comprised 34 questions administered under a strict 60-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.

34 Total Questions

MCQ: 22 (+3 / -1)

TITA: 12 (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 Calcutta

Rotational Conv.

Format & Counts

22 MCQ • 12 TITA

Verified Questions

99%ile Benchmark

28–31 Marks

Out of 66 (~10 net correct)

Marking Scheme

+3 / -1 / 0

Zero TITA Penalty

CAT 2018 Slot 2 QA Questions & Answer Key: CAT 2018 Slot 2 Quantitative Aptitude (QA) was conducted by IIM Calcutta during the Afternoon Session (12:30 PM – 2:30 PM IST). The section comprised 34 questions administered under a strict 60-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: 2 November 2026

Verified Questions

34 Qs

22 MCQ + 12 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 2018 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

Q1C
Q248
Q3C
Q4B
Q5A
Q6A
Q736
Q8C
Q9B
Q101098
Q11A
Q12B
Q134000
Q14A
Q15C
Q16A
Q17D
Q18A
Q19D
Q20105
Q21C
Q225
Q2320
Q24D
Q2524
Q26D
Q2724
Q288
Q29B
Q30D
Q3110
Q32A
Q3350
Q34D

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Official Exam Questions & Explanations (25 of 34)

Sorted in official convenor sequence

Question 1 of 34

CAT 2018 Slot 2QAArithmetic • Time, Speed & DistanceModerate

Points

A, P, Q

and

B

lie on the same line such that

P, Q

and

B

are, respectively,

100 \mathrm{~km}, 200 \mathrm{~km}

and

300 \mathrm{~km}

away from

A

. Cars 1 and 2 leave

A

at the same time and move towards

B.

Simultaneously, car 3 leaves

B

and moves towards

A

. Car 3 meets car 1 at

Q

, and car 2 at

P

. If each car is moving in uniform speed then the ratio of the speed of car 2 to that of car 1 is

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Official Convenor Answer Key: C

Question 2 of 34

CAT 2018 Slot 2QAArithmetic • Time & WorkModerate

A water tank has inlets of two types

A

and

B

. All inlets of type

A

when open, bring in water at the same rate. All inlets of type

B

, when open, bring in water at the same rate. The empty tank is completely filled in 30 minutes if 10 inlets of type

A

and 45 inlets of type

B

are open, and in 1 hour if 8 inlets of type

A

and 18 inlets of type

B

are open. In how many minutes will the empty tank get completely filled if 7 inlets of type

A

and 27 inlets of type

B

are open?

TITA Answer:

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Official Convenor Answer Key: 48

Question 3 of 34

CAT 2018 Slot 2QAAlgebra • InequalitiesModerate

How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits?

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Official Convenor Answer Key: C

Question 4 of 34

CAT 2018 Slot 2QAArithmetic • Time & WorkHard

A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump

A

or pump

B

or both start working until the tank is full. On Monday,

A

alone completed filling the tank at

8 \mathrm{pm}

. On Tuesday, B alone completed filling the tank at

6 \mathrm{pm}

. On Wednesday,

A

alone worked till

5 \mathrm{pm}

, and then B worked alone from

5 \mathrm{pm}

7 \mathrm{pm}

, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along?

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Official Convenor Answer Key: B

Question 5 of 34

CAT 2018 Slot 2QAGeometry • QuadrilateralsModerate

The area of a rectangle and the square of its perimeter are in the ratio

1:25

. Then the lengths of the shorter and longer sides of the rectangle are in the ratio

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Official Convenor Answer Key: A

Question 6 of 34

CAT 2018 Slot 2QAAlgebra • InequalitiesEasy

If the sum of squares of two numbers is

97

, then which one of the following cannot be their product?

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Official Convenor Answer Key: A

Question 7 of 34

CAT 2018 Slot 2QAAlgebra • InequalitiesModerate

a

and

b

are integers such that

2x^2 - ax + 2 > 0

and

x^2 −bx + 8 \geq 0

for all real numbers

x,

then the largest possible value of

2a-6b

TITA Answer:

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Official Convenor Answer Key: 36

Question 8 of 34

CAT 2018 Slot 2QAAlgebra • Progression & SeriesHard

The value of the sum

7 \times 11 + 11 \times 15 + 15 \times 19 + \dots + 95 \times 99

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Official Convenor Answer Key: C

Question 9 of 34

CAT 2018 Slot 2QAModern Math • Set TheoryModerate

A=\left\{6^{2 n}-35 n-1: n=1,2,3, \ldots\right\}

and

B=\{35(n-1): n=1,2,3, \ldots\}

then which of the following is true?

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Official Convenor Answer Key: B

Question 10 of 34

CAT 2018 Slot 2QAModern Math • Permutation & CombinationModerate

In a tournament, there are 43 junior level and 51 senior level participants. Each pair of juniors play one match. Each pair of seniors play one match. There is no junior versus senior match. The number of girl versus girl matches in junior level is

153

, while the number of boy versus boy matches in senior level is

276

. The number of matches a boy plays against a girl is

TITA Answer:

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Official Convenor Answer Key: 1098

Question 11 of 34

CAT 2018 Slot 2QAGeometry • CirclesModerate

A chord of length

5 \mathrm{~cm}

subtends an angle of

60^{\circ}

at the centre of a circle. The length, in cm , of a chord that subtends an angle of

120^{\circ}

at the centre of the same circle is

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Official Convenor Answer Key: A

Question 12 of 34

CAT 2018 Slot 2QAGeometry • CirclesModerate

From a rectangle

ABCD

of area

768 \text{ sq cm}

, a semicircular part with diameter

AB

and area

72\pi \text{ sq cm}

is removed. The perimeter of the leftover portion, in cm, is

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Official Convenor Answer Key: B

Question 13 of 34

CAT 2018 Slot 2QAArithmetic • Simple & Compound InterestModerate

Gopal borrows Rs.

X

from Ankit at

8 \%

annual interest. He then adds Rs.

Y

of his own money and lends Rs.

X+Y

to Ishan at

10 \%

annual interest. At the end of the year, after returning Ankit's dues, the net interest retained by Gopal is the same as that accrued to Ankit. On the other hand, had Gopal lent Rs.

X+2Y

to Ishan at

10 \%

, then the net interest retained by him would have increased by Rs.

150

. If all interests are compounded annually, then find the value of

X+Y

TITA Answer:

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Official Convenor Answer Key: 4000

Question 14 of 34

CAT 2018 Slot 2QAModern Math • LogarithmsModerate

The smallest integer

n

for which

4^n > 17^{19}

holds, is closest to

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Official Convenor Answer Key: A

Question 15 of 34

CAT 2018 Slot 2QAGeometry • TrianglesModerate

A triangle

ABC

has area 32sq units and its side

BC

, of length 8 units, lies on the line

\mathrm{x}=4

. Then the shortest possible distance between

A

and the point

(0,0)

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Official Convenor Answer Key: C

Question 16 of 34

CAT 2018 Slot 2QAModern Math • Set TheoryModerate

For two sets

A

and

B

, let

A \Delta B

denote the set of elements which belong to

A

B

but not both. If

P=\{1,2,3,4\}, Q=\{2,3,5,6\},, R=\{1,3,7,8,9\}, S= \{2,4,9,10\}

, then the number of elements in

(P \Delta Q) \Delta(R \Delta S)

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Official Convenor Answer Key: A

Question 17 of 34

CAT 2018 Slot 2QAModern Math • LogarithmsModerate

p^3 = q^4 = r^5 = s^6 , then the value of

\log_s(pqr)$ is equal to

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Official Convenor Answer Key: D

Question 18 of 34

CAT 2018 Slot 2QAArithmetic • Mixture & AlligationModerate

There are two drums, each containing a mixture of paints

A

and

B

. In drum

1, \mathrm{~A}

and B are in the ratio

18: 7

. The mixtures from drums 1 and 2 are mixed in the ratio

3: 4

and in this final mixture,

A

and

B

are in the ratio

13: 7

. In drum

2

, then

A

and

B

were in the ratio

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Official Convenor Answer Key: A

Question 19 of 34

CAT 2018 Slot 2QAArithmetic • Ratio, Proportion & VariationModerate

The scores of Amal and Bimal in an examination are in the ratio

11:14

. After an appeal, their scores increase by the same amount and their new scores are in the ratio

47 : 56

. The ratio of Bimal's new score to that of his original score is

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Official Convenor Answer Key: D

Question 20 of 34

CAT 2018 Slot 2QAArithmetic • Mean, Median & ModeModerate

The arithmetic mean of

x, y

and

z

80

, and that of

x, y, z, u

and

v

75

, where

u=(x+y) / 2

and

v=(y+z) / 2

. If

x \geq

z , then the minimum possible value of

x

TITA Answer:

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Official Convenor Answer Key: 105

Question 21 of 34

CAT 2018 Slot 2QAArithmetic • Mixture & AlligationEasy

The strength of a salt solution is

p\%

100 \mathrm{ml}

of the solution contains p grams of salt. If three salt solutions

A, B, C

are mixed in the proportion

1: 2: 3

, then the resulting solution has strength

20 \%

. If instead the proportion is

3: 2: 1

, then the resulting solution has strength

30 \%

. A fourth solution,

D

, is produced by mixing

B

and

C

in the ratio

2: 7

. The ratio of the strength of

D

to that of

A

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Official Convenor Answer Key: C

Question 22 of 34

CAT 2018 Slot 2QAArithmetic • Time, Speed & DistanceModerate

Points

A

and

B

are

150 \mathrm{~km}

apart. Cars 1 and 2 travel from

A

B

, but car 2 starts from

A

when car 1 is already

20 \mathrm{~km}

away from

A

. Each car travels at a speed of

100 \mathrm{kmph}

for the first

50 \mathrm{~km}

, at

50 \mathrm{kmph}

for the next

50 \mathrm{~km}

, and at

25 \mathrm{kmph}

for the last

50 \mathrm{~km}

. The distance, in km, between car 2 and

B

when car 1 reaches

B

TITA Answer:

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Official Convenor Answer Key: 5

Question 23 of 34

CAT 2018 Slot 2QAAlgebra • Minima & MaximaModerate

Let

f(x)=

max{

5x , 52-2x^2

}, where

x

is any positive real number. Then the minimum possible value of

f(x)

TITA Answer:

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Official Convenor Answer Key: 20

Question 24 of 34

CAT 2018 Slot 2QAModern Math • LogarithmsModerate

\dfrac{1}{\log _{2} 100}-\dfrac{1}{\log _{4} 100}+\dfrac{1}{\log _{5} 100}-\dfrac{1}{\log _{10} 100}+\dfrac{1}{\log _{20} 100}-\dfrac{1}{\log _{25} 100}+\dfrac{1}{\log _{50} 100}= \ ?

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Official Convenor Answer Key: D

Question 25 of 34

CAT 2018 Slot 2QAAlgebra • Progression & SeriesModerate

Let

t_1, t_2, \dots

be real numbers such that

t_1 + t_2 +\dots+ t_n = 2n^2 + 9n + 13

, for every positive integer

n\ge2

. If

t_k =103

, then

k

equals

TITA Answer:

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Official Convenor Answer Key: 24

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Frequently Asked Questions about CAT 2018 Slot 2 QA Questions & Answer Key

How many questions were asked in CAT 2018 Slot 2 QA?

CAT 2018 Slot 2 QA contained 34 questions convened by IIM Calcutta. 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 2018 Slot 2 QA?

Achieving a 99.0th percentile in QA required approximately 28–31 marks (~10 net correct), reflecting the standard cat difficulty profile.

Can I practice other sections of CAT 2018 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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CAT 2018 Slot 2 QA Questions & Answer Key

CAT Direct Answer Fact Sheet & Citation Summary

CAT 2018 Slot 2 QA Answer Key

QA

Attempt under official TCS iON 40-Min countdown timer

Official Exam Questions & Explanations (25 of 34)

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Frequently Asked Questions about CAT 2018 Slot 2 QA Questions & Answer Key

How many questions were asked in CAT 2018 Slot 2 QA?

What score was required for a 99th percentile in CAT 2018 Slot 2 QA?

Can I practice other sections of CAT 2018 Slot 2?

Related CAT Papers & Topic Mastery Hubs

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