CAT 2020 · Slot 2 — Data Interpretation & Logical Reasoning

Question 1

A chain of departmental stores has outlets in Delhi, Mumbai, Bengaluru and Kolkata. The sales are categorized by its three
departments – ‘Apparel’, ‘Electronics’, and ‘HomeDecor’. An Accountant has been asked to prepare a summary of the 2018 and
2019 sales amounts for an internal report. He has collated partial information and prepared the following table.
Sales Amounts (Crore Rupees)
Delhi Mumbai Bengaluru Kolkata
2018 2019 2018 2019 2018 2019 2018 2019
Apparels - - - - - - - 54
Electronics 78 98 82 102 90 70 80 100
HomeDecor - 100 - 72 - 80 - 54
The following additional information is known.
1. The sales amounts in the Apparel departments were the same for Delhi and Kolkata in2018.
2. The sales amounts in the Apparel departments were the same for Mumbai and Bengaluru in 2018. This sales amount
matched the sales amount in the Apparel department for Delhi in2019.
3. The sales amounts in the Home Decor departments were the same for Mumbai and Kolkata in 2018.
4. The sum of the sales amounts of four Electronics departments increased by the same amount as the sum of the sales
amounts of four Apparel departments from 2018 to 2019.
5. The total sales amounts of the four Home Decor departments increased by Rs 70 Crores from 2018 to 2019.
6. The sales amounts in the Home Decor departments of Delhi and Bengaluru each increased by Rs 20 Crores from 2018 to
2019.
7. The sales amounts in the Apparel departments of Delhi and Bengaluru each increased by the same amount in 2019 from
2018. The sales amounts in the Apparel departments of Mumbai and Kolkata also each increased by the same amount in 2019
from 2018.
8. The sales amounts in the Apparel departments of Delhi, Kolkata and Bengaluru in 2019 followed an Arithmetic Progression.
In HomeDecor departments of which cities were the sales amounts the highest in 2018and 2019, respectively?

1. Bengaluru and Delhi
2. Mumbai and Mumbai
3. Mumbai and Delhi
4. Delhi and Delhi

Correct answer: D · Delhi and Delhi

Question 2

What was the increase in sales amount, in Crore Rupees, in the Apparel department of Mumbai from 2018 to 2019?

1. 12
2. 8
3. 5
4. 10

Correct answer: A · 12

Question 3

Among all the 12 departments (i.e., the 3 departments in each of the 4 cities), what was the maximum percentage increase in
sales amount from 2018 to 2019?

1. 25
2. 28
3. 75
4. 50

Correct answer: D · 50

Question 4

What was the total sales amount, in Crore Rupees, in 2019 for the chain of departmental stores?

1. 600
2. 900
3. 150
4. 750

Correct answer: B · 900

Question 5

In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who
polled the highest number of votes, the first runner up was the one who polled the second highest number of votes, the
second runner up was the one who polled the third highest number of votes, and so on. There were no ties (in terms of number
of votes polled by the candidates) in any of the constituencies in this election.
In an electoral system, a security deposit is the sum of money that a candidate is required to pay to the election commission
before he or she is permitted to contest. Only the defeated candidates (i.e., one who is not the winning candidate) who fail to
secure more than one sixth of the valid votes polled in the constituency, lose their security deposits.
The following table provides some incomplete information about votes polled in four constituencies: A,B, C and D, in this
election.
Constituency
A B C D
No. of candidates contesting 10 12 5 8
Total No. of valid votes polled 5,00,000 3,25,000 6,00,030
No. of votes polled by the winning
2,75,000 48,750
candidate
No. of votes polled by the first runner
95,000 37,500
up
No. of votes polled by the second
30,000
runner up
% of valid votes polled by the third
10%
runner up
The following additional facts are known:
1. The first runner up polled 10,000 more votes than the second runner up in constituency A.
2. None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by any pair
of candidates in this constituency was at least 10,000.
3. The winning candidate in constituency D polled 5% of valid votes more than that of the first runner up. All the candidates
who lost their security deposits while contesting for this constituency, put together, polled 35% of the valid votes.
What is the percentage of votes polled in total by all the candidates who lost their security deposits while contesting for
constituency A?

Correct answer: 9

Question 6

How many candidates who contested in constituency B lost their security deposit?

Correct answer: 11

Question 7

What BEST can be concluded about the number of votes polled by the winning candidate in constituency C?

1. 1,40,010
2. between 1,40,005 and 1,40,010
3. less than 2,00,010
4. 1,40,006

Correct answer: D · 1,40,006

Question 8

What was the number of valid votes polled in constituency D?

1. 1,25,000
2. 1,50,000
3. 1,75,000
4. 62,500

Correct answer: C · 1,75,000

Question 9

The winning margin of a constituency is defined as the difference of votes polled by the winner and that of the first runner up.
Which of the following CANNOT be the list of constituencies, in increasing order of winning margin?

1. D, B, C, A
2. B, D, C, A
3. B, C, D, A
4. D, C, B, A

Correct answer: C · B, C, D, A

Question 10

For all the four constituencies taken together, what was the approximate number of votes polled by all the candidates who lost
their security deposit expressed as a percentage of the total valid votes from these four constituencies?

1. 38.25%
2. 23.54%
3. 23.91%
4. 32.00%

Correct answer: C · 23.91%

Question 11

Twenty five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must
contain exactly one bead. Each bead is coloured either Red, Blue or Green.
While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed:
1. Two adjacent beads along the same row or column are always of different colours.
2. There is at least one Green bead between any two Blue beads along the same row or column.
3. There is at least one Blue and at least one Green bead between any two Red beads along the same row or column.
Every unique, complete arrangement of twenty five beads is called a configuration.
The total number of possible configurations using beads of only two colors is:

Correct answer: 2

Question 12

Twenty five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must
contain exactly one bead. Each bead is coloured either Red, Blue or Green.
While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed:
1. Two adjacent beads along the same row or column are always of different colours.
2. There is at least one Green bead between any two Blue beads along the same row or column.
3. There is at least one Blue and at least one Green bead between any two Red beads along the same row or column.
Every unique, complete arrangement of twenty five beads is called a configuration.
What is the maximum possible number of Red beads that can appear in any configuration?

Correct answer: 9

Question 13

Twenty five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must
contain exactly one bead. Each bead is coloured either Red, Blue or Green.
While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed:
1. Two adjacent beads along the same row or column are always of different colours.
2. There is at least one Green bead between any two Blue beads along the same row or column.
3. There is at least one Blue and at least one Green bead between any two Red beads along the same row or column.
Every unique, complete arrangement of twenty five beads is called a configuration.
What is the minimum number of Blue beads in any configuration?

Correct answer: 6

Question 14

Twenty five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must
contain exactly one bead. Each bead is coloured either Red, Blue or Green.
While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed:
1. Two adjacent beads along the same row or column are always of different colours.
2. There is at least one Green bead between any two Blue beads along the same row or column.
3. There is at least one Blue and at least one Green bead between any two Red beads along the same row or column.
Every unique, complete arrangement of twenty five beads is called a configuration.
Two Red beads have been placed in ‘second row, third column’ and ‘third row, second column’. How many more Red beads can
be placed so as to maximise the number of Red beads used in the configuration?

Correct answer: 6

Question 15

The Humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students - A,
B, C, D, E, F, G and H. Four of them are from Economics, three from Sociology and one from Anthropology department. Each
student is guided by one among P, Q, R, S and T. Two students are guided by each of P, R and T, while one student is guided by
each of Q and S. Each student is guided by a guide belonging to their department.
Each seminar is to be scheduled in one of four consecutive 30-minute slots starting at 9:00am, 9:30 am, 10:00 am and 10:30 am
on the same day. More than one seminars can be scheduled in a slot, provided the guide is free. Only three rooms are available
and hence at the most three seminars can be Scheduled in a slot. Students who are guided by the same guide must be
scheduled in consecutive slots.
The following additional facts are also known.
1. Seminars by students from Economics are scheduled in each of the four slots.
2. A’s is the only seminar that is scheduled at 10:00 am. A is guided by R.
3. F is an Anthropology student whose seminar is scheduled at 10:30 am.
4. The seminar of a Sociology student is scheduled at 9:00 am.
5. B and G are both Sociology students, whose seminars are scheduled in the same slot. The seminar of an Economics student,
who is guided by T, is also scheduled in the same slot.
6. P, who is guiding both B and C, has students scheduled in the first two slots.
7. A and G are scheduled in two consecutive slots.
Which one of the following statements is true?

1. Two seminars are scheduled in the first slot.
2. Only one seminar is scheduled in the second slot.
3. Three seminars are scheduled in the first slot.
4. Three seminars are scheduled in the last slot.

Correct answer: A · Two seminars are scheduled in the first slot.

Question 16

Who all are NOT guiding any Economics students?

1. Q, R and S
2. P, Q and R
3. P, R and S
4. P, Q and S

Correct answer: D · P, Q and S

Question 17

Which of the following statements is necessarily true?

1. Q is guiding G
2. H is an Economics student.
3. S is guiding F.
4. B is scheduled in the first slot.

Correct answer: B · H is an Economics student.

Question 18

If D is scheduled in a slot later than Q's, then which of the following two statement(s) is (are) true?
(i) E and H are guided by T.
(ii) G is guided by Q.

1. Only (ii)
2. Neither (i) nor (ii)
3. Only (i)
4. Both (i) and (ii)

Correct answer: D · Both (i) and (ii)

Question 19

If E and Q are both scheduled in the same slot, then which of the following statements BEST describes the relationship between
D, H, and T?

1. Exactly one of D and H is guided by T.
2. Both D and H are guided by T.
3. At least one of D and H is guided by T.
4. Neither D nor H is guided by T.

Correct answer: C · At least one of D and H is guided by T.

Question 20

If D is scheduled in the slot immediately before Q’s, then which of the following is NOT necessarily true?

1. G is guided by Q.
2. E is guided by R.
3. F is guided by S.
4. D is guided by T.

Correct answer: B · E is guided by R.

Question 21

A shopping mall has a large basement parking lot with parking slots painted in it along a single row. These slots are quite
narrow; a compact car can fit in a single slot but an SUV requires two slots. When a car arrives, the parking attendant guides the
car to the first available slot from the beginning of the row into which the car can fit.
For our purpose, cars are numbered according to the order in which they arrive at the lot. For example, the first car to arrive is
given a number 1, the second a number 2, and so on. This numbering does not indicate whether a car is a compact or an SUV.
The configuration of a parking lot is a sequence of the car numbers in each slot. Each single vacant slot is represented by letter
V.
For instance, suppose cars numbered 1 through 5 arrive and park, where cars 1, 3 and 5 are compact cars and 2 and 4 are SUVs.
At this point, the parking lot would be described by the sequence 1, 2, 3, 4, 5. If cars 2 and 5 now vacate their slots, the parking
lot would now be described as 1, V, V, 3, 4. If a compact car (numbered 6) arrives subsequently followed by an SUV (numbered
7), the parking lot would be described by the sequence 1, 6, V, 3, 4, 7.
Answer the following questions INDEPENDENTLY of each other.
Initially cars numbered 1, 2, 3, and 4 arrive among which 1 and 4 are SUVs while 2 and3 are compact cars. Car 1 then leaves,
followed by the arrivals of car 5 (a compact car) and car 6 (an SUV). Car 4 then leaves. Then car 7 (an SUV) and car 8 (a compact
car)arrive. At this moment, which among the following numbered car is parked next to car3?

1. 8
2. 5
3. 6
4. 7

Correct answer: D · 7

Question 22

Suppose eight cars have arrived, of which two have left. Also suppose that car 4 is a compact and car 7 is an SUV. Which of the
following is a POSSIBLE current configuration of the parking lot?

1. 8, 2, 3, V, 6, 5, 7
2. V, 2, 3, 7, 5, 6, 8
3. 8, 2, 3, V, 5, 7, 6
4. 8, 2, 3, V, 5, 6, 7

Correct answer: D · 8, 2, 3, V, 5, 6, 7

Question 23

Suppose the sequence at some point of time is 4, 5, 6, V, 3. Which of the following is NOT necessarily true?

1. Car 4 is a compact
2. Car 1 is an SUV
3. Car 3 is an SUV
4. Car 5 is a compact

Correct answer: C · Car 3 is an SUV

Question 24

Suppose that car 4 is not the first car to leave and that the sequence at a time between the arrival of the car 7 and car 8 is V, 7,
3, 6, 5. Then which of the following statements MUST be false?

1. Car 2 is a compact
2. Car 7 is a compact
3. Car 4 is an SUV
4. Car 6 is a compact

Correct answer: D · Car 6 is a compact