CAT 2024 Slot 3 DILR Question & Solution
Data Set
Over the top (OTT) subscribers of a platform are segregated into three categories: i) Kid, ii)Elder, and iii) Others. Some of the subscribers used one app and the others used multiple apps to access the platform. The figure below shows the percentage of the total number of subscribers in 2023 and 2024 who belong to the ‘Kid’ and ‘Elder’ categories.
The following additional facts are known about the numbers of subscribers.
1. The total number of subscribers increased by 10% from 2023 to 2024.
2. In 2024, 1/2 of the subscribers from the ‘Kid’ category and 2/3 of the subscribers from the ‘Elder’ category subscribers use one app.
3. In 2023, the number of subscribers from the ‘Kid’ category who used multiple apps was the same as the number of subscribers from the ‘Elder’ category who used one app.
4. 10,000 subscribers from the ‘Kid’ category used one app and 15,000 subscribers from the ‘Elder’ category used multiple apps in 2023.
Question 1
How many subscribers belonged to the ‘Others’ category in 2024?
Solution:
Reading the bar graphs, we can find the distribution of the subscribers as:
Taking clue one into consideration, let's take the total number of subscribers in 2023 as 100x and in 2204 as 110x
This would give the split of subscribers as follows:
Clue 2 says that half of 22x, which is 11x and 2/3 of 33x, which is 22x, used one app, given that in 2024, out of 55x, 33x used one app.
Clues 3 and 4 are to be used with each other.
Clue 4 says that out of 15x kids, 10,000 used one app, and out of 20x Elders, 15,000 used multiple apps.
Clue 3 says that the kids who used multiple apps (15x - 10000) were the same as Elders who used one app (20x - 15000)
Equating these two we get:
15x- 10000 = 20x - 15000
5x = 5000
x = 1000
The first question asks about the number of others in 2024, which is 55x, or simply 55,000
Therefore, Option C is the correct answer.
Question 2
What percentage of subscribers in the ‘Kid’ category used multiple apps in 2023?
Solution:
Reading the bar graphs, we can find the distribution of the subscribers as:
Taking clue one into consideration, let's take the total number of subscribers in 2023 as 100x and in 2204 as 110x
This would give the split of subscribers as follows:
Clue 2 says that half of 22x, which is 11x and 2/3 of 33x, which is 22x, used one app, given that in 2024, out of 55x, 33x used one app.
Clues 3 and 4 are to be used with each other.
Clue 4 says that out of 15x kids, 10,000 used one app, and out of 20x Elders, 15,000 used multiple apps.
Clue 3 says that the kids who used multiple apps (15x - 10000) were the same as Elders who used one app (20x - 15000)
Equating these two, we get:
15x- 10000 = 20x - 15000
5x = 5000
x = 1000
There are 15x, that is, 15,000 kids in 2023, of which we are given that 10,000 use one app.
So, 5,000 use multiple apps.
The percentage of kids using multiple apps in 2023 would hence be $\frac{5000}{15000}\times\ 100=\frac{100}{3}=33.33\%$
Therefore, Option A is the correct answer.
Question 3
What was the percentage increase in the number of subscribers in the ‘Elder’ categoryfrom 2023 to 2024?
Solution:
Reading the bar graphs, we can find the distribution of the subscribers as:
Taking clue one into consideration, let's take the total number of subscribers in 2023 as 100x and in 2204 as 110x
This would give the split of subscribers as follows:
Clue 2 says that half of 22x, which is 11x and 2/3 of 33x, which is 22x, used one app, given that in 2024, out of 55x, 33x used one app.
Clues 3 and 4 are to be used with each other.
Clue 4 says that out of 15x kids, 10,000 used one app, and out of 20x Elders, 15,000 used multiple apps.
Clue 3 says that the kids who used multiple apps (15x - 10000) were the same as Elders who used one app (20x - 15000)
Equating these two, we get:
15x- 10000 = 20x - 15000
5x = 5000
x = 1000
In 2023, there were 20,000 elders; in 2024, there were 33,000 elders.
The increase in percentage would be $\frac{33000-20000}{20000}\times\ 100=\frac{13}{20}\times\ 100=65\%$
Therefore, Option C is the correct answer.
Question 4
What could be the minimum percentage of subscribers who used multiple apps in 2024?
Solution:
Reading the bar graphs, we can find the distribution of the subscribers as:
Taking clue one into consideration, let's take the total number of subscribers in 2023 as 100x and in 2204 as 110x
This would give the split of subscribers as follows:
Clue 2 says that half of 22x, which is 11x and 2/3 of 33x, which is 22x, used one app, given that in 2024, out of 55x, 33x used one app.
Clues 3 and 4 are to be used with each other.
Clue 4 says that out of 15x kids, 10,000 used one app, and out of 20x Elders, 15,000 used multiple apps.
Clue 3 says that the kids who used multiple apps (15x - 10000) were the same as Elders who used one app (20x - 15000)
Equating these two, we get:
15x- 10000 = 20x - 15000
5x = 5000
x = 1000
In clue 2, we were given that 33000 kids and elders out of 55000 kids and elders use one app, showing that 22000 use multiple apps. To minimize the total usage of multiple apps, we can assume that all 55000 other subscribers use one app.
Giving the percentage of multiple app users as: $\frac{22,000}{110,000}\times\ 100=\frac{100}{5}=20\%$
Therefore, Option B is the correct answer.