CAT 2024 Slot 3 DILR Set 2 Q5–Q8

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2024 Slot 3, with 4 questions (Charts & Tables). Answers are CAT's official key.

The set

This set relies on a figure in the original paper, which is not reproduced here. The questions and answers are 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.

[Figure in the original paper]

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 5

How many subscribers belonged to the 'Others' category in 2024?
  1. A
    Cannot be determined
  2. B
    65000
  3. C
    45000
  4. D
    55000

Answer: (D) 55000 Charts & Tables MCQ

Solution

  1. Let the 2023 total be \(T\): Kid \(= 0.15T\), Elder \(= 0.20T\). With \(x\) = Kid multi-app = Elder one-app: \(0.15T = 10000 + x\) and \(0.20T = x + 15000\).
  2. Subtracting: \(0.05T = 5000 \Rightarrow T = 100000\), so Kid \(= 15000\), Elder \(= 20000\), \(x = 5000\).
  3. 2024 total \(= 110000\): Kid \(= 20\% = 22000\), Elder \(= 30\% = 33000\), Others \(= 55000\).
  4. Others in 2024 \(= 110000 - 22000 - 33000 = 55000\).

Question 6

What percentage of subscribers in the 'Kid' category used multiple apps in 2023?
  1. A
    33.33%
  2. B
    25.50%
  3. C
    50.00%
  4. D
    5.00%

Answer: (A) 33.33% Charts & Tables MCQ

Solution

  1. Let the 2023 total be \(T\): Kid \(= 0.15T\), Elder \(= 0.20T\). With \(x\) = Kid multi-app = Elder one-app: \(0.15T = 10000 + x\) and \(0.20T = x + 15000\).
  2. Subtracting: \(0.05T = 5000 \Rightarrow T = 100000\), so Kid \(= 15000\), Elder \(= 20000\), \(x = 5000\).
  3. Kid multi-app 2023 \(= \frac{5000}{15000} = 33.33\%\).

Question 7

What was the percentage increase in the number of subscribers in the 'Elder' category from 2023 to 2024?
  1. A
    60%
  2. B
    65%
  3. C
    40%
  4. D
    50%

Answer: (B) 65% Charts & Tables MCQ

Solution

  1. Let the 2023 total be \(T\): Kid \(= 0.15T\), Elder \(= 0.20T\). With \(x\) = Kid multi-app = Elder one-app: \(0.15T = 10000 + x\) and \(0.20T = x + 15000\).
  2. Subtracting: \(0.05T = 5000 \Rightarrow T = 100000\), so Kid \(= 15000\), Elder \(= 20000\), \(x = 5000\).
  3. 2024 total \(= 110000\): Kid \(= 20\% = 22000\), Elder \(= 30\% = 33000\), Others \(= 55000\).
  4. Elder: \(20000 \to 33000\), increase \(\frac{13000}{20000} = 65\%\).

Shortcut. Elder share goes 20% to 30% of a total that grows 1.1 times: \(1.5 \times 1.1 = 1.65\).

Question 8

What could be the minimum percentage of subscribers who used multiple apps in 2024?
  1. A
    16.5%
  2. B
    20.0%
  3. C
    10.0%
  4. D
    22.00%

Answer: (B) 20.0% Charts & Tables MCQ

Solution

  1. Let the 2023 total be \(T\): Kid \(= 0.15T\), Elder \(= 0.20T\). With \(x\) = Kid multi-app = Elder one-app: \(0.15T = 10000 + x\) and \(0.20T = x + 15000\).
  2. Subtracting: \(0.05T = 5000 \Rightarrow T = 100000\), so Kid \(= 15000\), Elder \(= 20000\), \(x = 5000\).
  3. 2024 total \(= 110000\): Kid \(= 20\% = 22000\), Elder \(= 30\% = 33000\), Others \(= 55000\).
  4. 2024 multi-app: Kid \(\frac12 \times 22000 = 11000\), Elder \(\frac13 \times 33000 = 11000\); Others can all use one app.
  5. Minimum \(= \frac{22000}{110000} = 20\%\).

Same concept in other years

See every question on Sales/revenue DI with percentage shares across segments and years.

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