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CAT 2024 Slot 2 DILR · Set 3 of 5Data InterpretationModerate DifficultyQ10–Q13 · 2 MCQ + 2 TITA

CAT 2024 Slot 2 DILR Set 3: Bar Graphs (4 Questions) with Solutions

The Bar Graphs set from the official CAT 2024 Slot 2 DILR paper: the caselet, all 4 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2024 Slot 2 DILR · Questions 10–13
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.
Official Reference Chart - CAT 2024 Slot 2 Official Reference Chart - CAT 2024 Slot 2

In the exam this set competed with 4 others for 40 minutes. Budget about 8 minutes if you attempt it.

Q10. Bar Graphs

TITA · +3 / 0
How many buyers gave ratings on Day 1?
Correct Answer
150
Step-by-step solution
📌 Core Concept
Use the Day 2 bar chart to get the Day 2 total and sum of ratings, then use the Day 2 cumulative average to find the Day 1 count.
🔢 Step-by-Step Solution
1
Reading the chart, Day 2 has 5, 10, 5, 20 and 10 buyers giving ratings 1, 2, 3, 4 and 5. That is 50 buyers.
2
Sum of Day 2 ratings =5(1)+10(2)+5(3)+20(4)+10(5)=5+20+15+80+50=170= 5(1)+10(2)+5(3)+20(4)+10(5) = 5+20+15+80+50 = 170.
3
Let nn be the number of buyers on Day 1. The Day 1 average is 3, so the Day 1 sum is 3n3n.
4
The cumulative average after Day 2 is 3.1, so 3n+170n+50=3.1\dfrac{3n+170}{n+50}=3.1.
5
Then 3n+170=3.1n+1553n+170 = 3.1n+155, so 0.1n=150.1n = 15 and n=150n=150.
Quick Check
Day 1 sum is 450, so the two-day sum is 620 over 200 buyers, which is 3.1.
Correct Answer: 150

Q11. Bar Graphs

MCQ · +3 / −1
What is the daily average rating of Day 3?
  1. A) 3.6
  2. B) 3.4
  3. C) 3.0
  4. D) 3.2
Correct Answer
A) 3.6
Step-by-step solution
📌 Core Concept
The Day 3 distribution is fixed by the mode and multiple-of-10 conditions. The daily average then follows from it.
🔢 Step-by-Step Solution
1
Let xx be the number of buyers giving rating 1. By clue 4, rating 2 also has xx buyers and rating 3 has 2x2x buyers.
2
Ratings 4 and 5 together have 100−4x100-4x buyers (clue 1).
3
Clue 2 says 4 and 5 are both modes, so they have equal counts of 50−2x50-2x each.
4
A mode must exceed the count for rating 3, so 50−2x>2x50-2x > 2x, which gives x<12.5x<12.5.
5
By clue 3, xx is a non-zero multiple of 10, so x=10x=10.
6
The distribution for ratings 1 to 5 is 10, 10, 20, 30, 30. These add up to 100.
7
Sum of ratings =10+20+60+120+150=360= 10+20+60+120+150 = 360, so the daily average is 360100=3.6\dfrac{360}{100}=3.6.
Why Not the Others
3.4 is the Day 2 average, not Day 3.
3.0 and 3.2 do not match the sum of 360 on 100 buyers.
Correct Answer: A

Q12. Bar Graphs

TITA · +3 / 0
What is the median of all ratings given on Day 3?
Correct Answer
4
Step-by-step solution
📌 Core Concept
The median of 100 ratings is the average of the 50th and 51st ratings when they are arranged in order. Use the cumulative counts.
🔢 Step-by-Step Solution
1
The Day 3 distribution for ratings 1 to 5 is 10, 10, 20, 30, 30. This comes from the mode and multiple-of-10 conditions, which force x=10x=10.
2
The cumulative counts are 10 for rating 1, 20 for ratings up to 2, and 40 for ratings up to 3.
3
Rating 4 covers positions 41 to 70.
4
The 50th and 51st ratings both lie in this range, so both are 4.
5
The median is 4+42=4\dfrac{4+4}{2}=4.
Correct Answer: 4

Q13. Bar Graphs

MCQ · +3 / −1
Which of the following is true about the cumulative average ratings of Day 2 and Day 3?
  1. A) 1. The cumulative average of Day 3 decreased from Day 2.
  2. B) 2. The cumulative average of Day 3 increased by more than 8% from Day 2.
  3. C) 3. The cumulative average of Day 3 increased by less than 5% from Day 2.
  4. D) 4. The cumulative average of Day 3 increased by a percentage between 5% and 8% from Day 2.
Correct Answer
D) 4. The cumulative average of Day 3 increased by a percentage between 5% and 8% from Day 2.
Step-by-step solution
📌 Core Concept
Compare the cumulative average after Day 2 (3.1) with the cumulative average after Day 3. Then find the percentage change.
🔢 Step-by-Step Solution
1
After Day 2 there are 150+50=200150+50=200 buyers with an average of 3.1. The sum is 620.
2
On Day 3 there are 100 buyers with a sum of 360. The distribution 10, 10, 20, 30, 30 comes from the mode and multiple-of-10 conditions.
3
After Day 3 there are 300 buyers with a sum of 620+360=980620+360=980. The cumulative average is 980300≈3.267\dfrac{980}{300}\approx 3.267.
4
The change is 3.267−3.1≈0.1673.267-3.1 \approx 0.167.
5
As a percentage of 3.1, this is 0.1673.1×100≈5.4%\dfrac{0.167}{3.1}\times 100 \approx 5.4\%.
6
This lies between 5% and 8%.
Why Not the Others
A is wrong because the average rose from 3.1 to about 3.27.
B is wrong because 5.4% is not more than 8%.
C is wrong because 5.4% is not less than 5%.
Correct Answer: D
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CAT 2024 Slot 2 DILR at a Glance

Sets in this section5
Questions in this section22
Section time40 minutes
Convenor IIMIIM Calcutta

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