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CAT 2024 Slot 3 — DILR Question 1

TablesEasy
Passage / Data

Answer the following questions based on the information given below.

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.

Bar chart of Kid and Elder subscriber percentages in 2023 and 2024

Category (% of total subscribers)20232024
Kid15%20%
Elder20%30%
Others (balance)65%50%

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 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.

How many subscribers belonged to the ‘Others’ category in 2024?

Answer & solution

  • A

    65000

  • B

    Cannot be determined

  • 55000

  • D

    45000

Solution

Easy

The chart gives percentages of the total subscriber base. Use Facts 3 and 4 (which mix 2023 counts) to pin down the 2023 total, then scale by 10% for 2024.

Percent of total subscribers — Kid: 2023 = 15%, 2024 = 20%; Elder: 2023 = 20%, 2024 = 30%; Others = balance (2023 = 65%, 2024 = 50%).

Let the 2023 total be TT. In 2023: Kid one-app = 10,000; Elder multiple = 15,000; Kid-multiple = Elder-one-app (Fact 3).

1

Find the 2023 total TT. Kid 2023 =0.15T=0.15T so Kid-multiple =0.15T−10000=0.15T-10000. Elder 2023 =0.20T=0.20T so Elder-one-app =0.20T−15000=0.20T-15000. Fact 3 equates them.

0.15T−10000=0.20T−15000(Fact 3)⇒ 5000=0.05T⇒ T=100000\begin{aligned} &0.15T-10000 = 0.20T-15000 \quad\text{(Fact 3)}\\ &\Rightarrow\ 5000 = 0.05T\\ &\Rightarrow\ T = 100000 \end{aligned}
2

Build the 2024 counts. Total grows 10% to 110,000 (Fact 1); apply the 2024 percentages.

Total2024=1.1×100000=110000⇒ Kid=20%=22000,Elder=30%=33000(from chart)⇒ Others=110000−22000−33000=55000\begin{aligned} &\text{Total}_{2024}=1.1\times100000=110000\\ &\Rightarrow\ \text{Kid}=20\%=22000,\quad \text{Elder}=30\%=33000 \quad\text{(from chart)}\\ &\Rightarrow\ \text{Others}=110000-22000-33000=55000 \end{aligned}
Others in 2024=55000\text{Others in 2024}=55000
CAT 2024 Slot 3 DILR Q1: How many subscribers belonged to the ‘Others’ category in 2024? — Solution | TheCATExam