CAT 2020 · Slot 3 — Data Interpretation & Logical Reasoning

Question 1

Sixteen patients in a hospital must undergo a blood test for a disease. It is known that exactly one of them has the disease. The
hospital has only eight testing kits and has decided to pool blood samples of patients into eight vials for the tests. The patients
are numbered 1 through 16, and the vials are labelled A, B, C, D, E, F, G, and H. The following table shows the vials into which
each patient’s blood sample is distributed.
Patient Vials Patient Vials
1 B, D, F, H 9 A, D, F, H
2 B, D, F, G 10 A, D, F, G
3 B, D, E, H 11 A, D, E, H
4 B, D, E, G 12 A, D, E, G
5 B, C, F, H 13 A, C, F, H
6 B, C, F, G 14 A, C, F, G
7 B, C, E, H 15 A, C, E, H
8 B, C, E, G 16 A, C, E, G
If a patient has the disease, then each vial containing his/her blood sample will test positive. If a vial tests positive, one of the
patients whose blood samples were mixed in the vial has the disease. If a vial tests negative, then none of the patients whose
blood samples were mixed in the vial has the disease.
Suppose vial C tests positive and vials A, E and H test negative. Which patient has the disease?

1. Patient 14
2. Patient 8
3. Patient 6
4. Patient 2

Correct answer: C · Patient 6

Question 2

Suppose vial A tests positive and vials D and G test negative. Which of the following vials should we test next to identify the
patient with the disease?

1. Vial B
2. Vial E
3. Vial C
4. Vial H

Correct answer: B · Vial E

Question 3

Which of the following combinations of test results is NOT possible?

1. Vials A and E positive, vials C and D negative
2. Vial B positive, vials C, F and H negative
3. Vials A and G positive, vials D and E negative
4. Vials B and D positive, vials F and H negative

Correct answer: A · Vials A and E positive, vials C and D negative

Question 4

Suppose one of the lab assistants accidentally mixed two patients' blood samples before they were distributed to the vials.
Which of the following correctly represents the set of all possible numbers of positive test results out of the eight vials?

1. {5,6,7,8}
2. {4,5,6,7}
3. {4,5,6,7,8}
4. {4,5}

Correct answer: C · {4,5,6,7,8}

Question 5

XYZ organization got into the business of delivering groceries to home at the beginning of the last month. They have a two-day
delivery promise. However, their deliveries are unreliable. An order booked on a particular day may be delivered the next day or
the day after. If the order is not delivered at the end of two days, then the order is declared as lost at the end of the second
day. XYZ then does not deliver the order, but informs the customer, marks the order as lost, returns the payment and pays a
penalty for non-delivery.
The following table provides details about the operations of XYZ for a week of the last month. The first column gives the date,
the second gives the cumulative number of orders that were booked up to and including that day. The third column represents
the number of orders delivered on that day. The last column gives the cumulative number of orders that were lost up to and
including that day.
It is known that the numbers of orders that were booked on the 11th, 12th, and 13th of the last month that took two days to
deliver were 4, 6, and 8 respectively.
Orders
Cumulative Cumulative
Day delivered on
orders booked orders lost
day
13th 219 11 91
14th 249 27 92
15th 277 23 94
16th 302 11 106
17th 327 21 118
18th 332 13 120
19th 337 14 129
Among the following days, the largest fraction of orders booked on which day was lost?

1. 15th
2. 16th
3. 13th
4. 14th

Correct answer: A · 15th

Question 6

On which of the following days was the number of orders booked the highest?

1. 12th
2. 15th
3. 13th
4. 14th

Correct answer: C · 13th

Question 7

The delivery ratio for a given day is defined as the ratio of the number of orders booked on that day which are delivered on the
next day to the number of orders booked on that day which are delivered on the second day after booking. On which of the
following days, was the delivery ratio the highest?

1. 15th
2. 16th
3. 13th
4. 14th

Correct answer: D · 14th

Question 8

The average time taken to deliver orders booked on a particular day is computed as follows. Let the number of orders delivered
the next day be x and the number of orders delivered the day after be y. Then the average time to deliver order is (x+2y)/(x+y).
On which of the following days was the average time taken to deliver orders booked the least?

1. 15th
2. 13th
3. 14th
4. 16th

Correct answer: C · 14th

Question 9

A farmer had a rectangular land containing 205 trees. He distributed that land among his four daughters – Abha, Bina, Chitra
and Dipti by dividing the land into twelve plots along three rows (X,Y,Z) and four Columns (1,2,3,4) as shown in the figure
below:
The plots in rows X, Y, Z contained mango, teak and pine trees respectively. Each plot had trees in non-zero multiples of 3 or 4
and none of the plots had the same number of trees. Each daughter got an even number of plots. In the figure, the
number mentioned in top left corner of a plot is the number of trees in that plot, while the letter in the bottom right corner is
the first letter of the name of the daughter who got that plot (For example, Abha got the plot in row Y and column 1 containing
21 trees). Some information in the figure got erased, but the following is known:
1. Abha got 20 trees more than Chitra but 6 trees less than Dipti.
2. The largest number of trees in a plot was 32, but it was not with Abha.
3. The number of teak trees in Column 3 was double of that in Column 2 but was half of that in Column 4.
4. Both Abha and Bina got a higher number of plots than Dipti.
5. Only Bina, Chitra and Dipti got corner plots.
6. Dipti got two adjoining plots in the same row.
7. Bina was the only one who got a plot in each row and each column.
8. Chitra and Dipti did not get plots which were adjacent to each other (either in row / column / diagonal).
9. The number of mango trees was double the number of teak trees.
How many mango trees were there in total?

1. 49
2. 84
3. 98
4. 126

Correct answer: C · 98

Question 10

Which of the following is the correct sequence of trees received by Abha, Bina, Chitra and Dipti in that order?

1. 50, 69, 30, 56
2. 54, 57, 34, 60
3. 44, 87, 24, 50
4. 60, 39, 40, 66

Correct answer: A · 50, 69, 30, 56

Question 11

How many pine trees did Chitra receive?

1. 18
2. 30
3. 21
4. 15

Correct answer: A · 18

Question 12

Who got the plot with the smallest number of trees and how many trees did that plot have?

1. Dipti, 6 trees
2. Bina, 3 trees
3. Bina, 4 trees
4. Abha, 4 trees

Correct answer: B · Bina, 3 trees

Question 13

Which of the following statements is NOT true?

1. Chitra got 12 mango trees
2. Bina got 32 pine trees
3. Abha got 41 teak trees
4. Dipti got 56 mango trees

Correct answer: B · Bina got 32 pine trees

Question 14

Which column had the highest number of trees?

1. 4
2. 3
3. Cannot be determined
4. 2

Correct answer: A · 4

Question 15

The Hi-Lo game is a four-player game played in six rounds. In every round, each player chooses to bid Hi or Lo. The bids are
made simultaneously. If all four bid Hi, then all four lose 1 point each. If three players bid Hi and one bids Lo, then the players
bidding Hi gain 1 point each and the player bidding Lo loses 3 points. If two players bid Hi and two bid Lo, then the players
bidding Hi gain 2 points each and the players bidding Lo lose 2 points each. If one player bids Hi and three bid Lo, then the
player bidding Hi gains 3 points and the players bidding Lo lose 1 point each. If all four bid Lo, then all four gain 1 point each.
Four players Arun, Bankim, Charu, and Dipak played the Hi-Lo game. The following facts are known about their game:
1. At the end of three rounds, Arun had scored 6 points, Dipak had scored 2 points, Bankim and Charu had scored -2 points
each.
2. At the end of six rounds, Arun had scored 7 points, Bankim and Dipak had scored -1 point each, and Charu had scored -5
points.
3. Dipak’s score in the third round was less than his score in the first round but was more than his score in the second round.
4. In exactly two out of the six rounds, Arun was the only player who bid Hi.
What were the bids by Arun, Bankim, Charu and Dipak, respectively in the first round?

1. Hi, Lo, Lo, Hi
2. Hi, Lo, Lo, Lo
3. Hi, Hi, Lo, Lo
4. Lo, Lo, Lo, Hi

Correct answer: A · Hi, Lo, Lo, Hi

Question 16

In how many rounds did Arun bid Hi? (in numerical value)

Correct answer: 4

Question 17

In how many rounds did Bankim bid Lo? (in numerical value)

Correct answer: 4

Question 18

In how many rounds did all four players make identical bids? (in numerical value)

Correct answer: 2

Question 19

In how many rounds did Dipak gain exactly 1 point? (in numerical value)

Correct answer: 1

Question 20

In which of the following rounds, was Arun DEFINITELY the only player to bid Hi?

1. Second
2. Third
3. Fourth
4. First

Correct answer: A · Second

Question 21

A survey of 600 schools in India was conducted to gather information about their online teaching learning processes (OTLP).
The following four facilities were studied.
F1: Own software for OTLP
F2: Trained teachers for OTLP
F3: Training materials for OTLP
F4: All students having Laptops
The following observations were summarized from the survey.
1. 80 schools did not have any of the four facilities – F1, F2, F3, F4.
2. 40 schools had all four facilities.
3. The number of schools with only F1, only F2, only F3, and only F4 was 25, 30, 26 and 20 respectively.
4. The number of schools with exactly three of the facilities was the same irrespective of which three were considered.
5. 313 schools had F2.
6. 26 schools had only F2 and F3 (but neither F1 nor F4).
7. Among the schools having F4, 24 had only F3, and 45 had only F2.
8. 162 schools had both F1 and F2.
9. The number of schools having F1 was the same as the number of schools having F4.
What was the total number of schools having exactly three of the four facilities?

1. 64
2. 50
3. 200
4. 80

Correct answer: C · 200

Question 22

What was the number of schools having facilities F2 and F4?

1. 185
2. 95
3. 45
4. 85

Correct answer: A · 185

Question 23

What was the number of schools having only facilities F1 and F3? (in numerical value)

Correct answer: 42

Question 24

What was the number of schools having only facilities F1 and F4? (in numerical value)

Correct answer: 20