CAT 2024 DILR Slot 2 Paper With Answers & Explanation
Question Numbers (1 to 4):
The above is a schematic diagram of walkways (indicated by all the straight-lines) and lakes(3 of them, each in the
shape of rectangles – shaded in the diagram) of a gated area.
Different points on the walkway are indicated by letters (A through P) with distances being OP = 150 m, ON = MN =
300 m, ML = 400 m, EL = 200 m, DE = 400 m.
The following additional information about the facilities in the area is known.
1. The only entry/exit point is at C.
2. There are many residences within the gated area; all of them are located on the path AH and ML with four of them being at A, H, M, and L.
3. The post office is located at P and the bank is located at B.
Q. 1 One resident whose house is located at L, needs to
visit the post office as well as the bank. What is the
minimum distance (in m) he has to walk starting
from his residence and returning to his residence
after visiting both the post office and the bank?
[Note: In actual paper CAT 2024, two options (3) and (4) i.e., 3000 were same.]
Q. 2 One person enters the gated area and decides to
walk as much as possible before leaving the area
without walking along any path more than once and
always walking next to one of the lakes. Note that
he may cross a point multiple times. How
much distance (in m) will he walk within the gated
area?
Q. 3 One resident takes a walk within the gated area
starting from A and returning to A without going
through any point (other than A) more than once.
What is the maximum distance (in m) she can walk
in this way?
Q. 4 Visitors coming for morning walks are allowed to enter
as long as they do not pass by any of the residences
and do not cross any point (except C) more than
once.What is the maximum distance (in m) that such
a visitor can walk within the gated area?
Question Numbers (5 to 8): An online e-commerce firm receives daily integer product ratings from 1 through 5 given
by buyers. The daily average is the average of the ratings given on that day. The cumulative average is the average of
all ratings given on or before that day.
The rating system began on Day 1, and the cumulative averages were 3 and 3.1 at the end of Day 1 and Day 2,
respectively. The distribution of ratings on Day 2 is given in the figure below.
The following information is known about ratings on Day 3.
1. 100 buyers gave product ratings on Day 3.
2. The modes of the product ratings were 4 and 5.
3. The numbers of buyers giving each product rating are non-zero multiples of 10.
4. The same number of buyers gave product ratings of 1 and 2, and that number is half the number of buyers who
gave a rating of 3.
Question Numbers (9 to 12): The two plots below give the following information about six firms A, B, C, D, E, and F
for 2019 and 2023.
PAT: The firm’s profits after taxes in Rs. crores,
ES: The firm’s employee strength, that is the number of employees in the firm, and
PRD: The percentage of the firm’s PAT that they spend on Research and Development (R&D).
In the plots, the horizontal and vertical coordinates of point representing each firm gives their ES and PAT values
respectively. The PRD values of each firm are proportional to the areas around the points representing each firm. The
areas are comparable between the two plots, i.e., equal areas in the two plots represent the same PRD values for the
two years.
Q. 9 Assume that the annual rate of growth in PAT over
the previous year (ARG) remained constant over the
years for each of the six firms. Which among the
firms A, B, C, and E had the highest ARG?
Since we are given that the annual growth rate
should be taken as constant, we can simply
compare the changes in the firm’s PAT in 2019
and 2023 and compare them.
Firm A: 3000 to 3900; an increase of 900
Firm B: 2800 to 3800; an increase of 1000
Firm C: 2400 to 3000; an increase of 600
Firm E: 2400 to 3500; an increase of 1100
The growth is highest for firm E.
Q. 10 The ratio of the amount of money spent by Firm C on
R&D in 2019 to that in 2023 is closest to
Question Numbers (13 to 17): Eight gymnastics players numbered 1 through 8 underwent a training camp where
they were coached by three coaches - Xena, Yuki, and Zara. Each coach trained at least two players.Yuki trained only
even numbered players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the
players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest
rating and 7 the highest.
The following additional information is known.
1. Xena trained more players than Yuki.
2. Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and
Player-5 were all different.
3. Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique
rating.
4. The average of the ratings of all the players was 4.
5. Player-2 got the highest rating.
6. The average of the ratings of the players trained by Yuki was twice that of the player strained by Xena and two more
than that of the players trained by Zara.
7. Player-4’s rating was double of Player-8's and less than Player-5’s.
Q. 13 What best can be concluded about the number of
players coached by Zara?
Player-1, player-3, player-4 and player-8 were
coached by Xena.
Question Numbers (18 to 22): The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid
based on the conditions below.
1. Numbers in any row appear in an increasing order from left to right.
2. Numbers in any column appear in a decreasing order from top to bottom.
3. 1 is placed either in the same row or in the same column as 10.
4. Neither 2 nor 3 is placed in the same row or in the same column as 10.
5. Neither 7 nor 8 is placed in the same row or in the same column as 9.
6. 4 and 6 are placed in the same row.
Q. 18 What is the row number which has the least sum of
numbers placed in that row?
