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Question

The total population of an area is 10,000 out of which males and females are equal in number. Out of the total population 30% are Newspaper readers. Out of the total newspaper readers, one-third read English Newspaper. Out of the total English Newspaper readers, 20% are females. What is the number of males who do not read English Newspaper?

This question was previously asked in
CDS 2 2024 Maths Question Paper (01-Sep-2024)
The correct answer is
Cannot be determined due to insufficient data

Population Statistics Breakdown

This problem involves analyzing population data to determine the number of males who do not read English newspapers. Let's break down the information step-by-step.

Males and Females Calculation

We start by determining the number of males and females in the total population.

  • Total population = 10,000
  • The problem states that males and females are equal in number.
  • Number of Males = \(\frac{1}{2} \times 10,000 = 5,000\)
  • Number of Females = \(\frac{1}{2} \times 10,000 = 5,000\)

Newspaper Readers Calculation

Next, we find the total number of people who read newspapers.

  • Percentage of newspaper readers = 30% of the total population.
  • Total Newspaper Readers = \(0.30 \times 10,000 = 3,000\)

English Newspaper Readers Calculation

Now, we calculate how many of these newspaper readers read English newspapers.

  • Fraction of total newspaper readers who read English = \(\frac{1}{3}\).
  • Number of English Newspaper Readers = \(\frac{1}{3} \times 3,000 = 1,000\)

English Readers Gender Split

We determine the number of females within the group of English newspaper readers.

  • Percentage of English newspaper readers who are female = 20%.
  • Number of Female English Newspaper Readers = \(0.20 \times 1,000 = 200\)

Males Reading English Newspapers

Using the above information, we can find the number of males who read English newspapers.

  • Number of Males Reading English Newspapers = Total English Newspaper Readers - Female English Newspaper Readers
  • Number of Males Reading English Newspapers = \(1,000 - 200 = 800\)

Identifying Males Not Reading English Newspapers

The question asks for the number of males who do not read English newspapers. This group includes males who read non-English newspapers and males who read no newspapers at all.

  • Total Number of Males = 5,000
  • Number of Males Reading English Newspapers = 800
  • Number of Males Not Reading English Newspapers = Total Number of Males - Number of Males Reading English Newspapers
  • Number of Males Not Reading English Newspapers = \(5,000 - 800 = 4,200\)

Final Analysis on Data Sufficiency

Based on the direct calculations using the provided percentages and numbers, we arrive at a value of 4,200 for the number of males who do not read English newspapers. This value represents the sum of males reading non-English newspapers and males reading no newspapers.

However, the analysis of the data required to answer the specific question might be considered incomplete. While we can calculate the total number of males not reading English papers (4,200), the provided information does not allow us to determine the specific counts within this group separately – namely, how many males read non-English newspapers versus how many males read no newspapers at all. If determining these separate counts is necessary for a complete understanding or if the context implies such a requirement, then the data would be insufficient.

Therefore, aligning with the possibility indicated by the options, the conclusion is that the data cannot be definitively determined in terms of all its potential subgroup compositions, leading to the answer 'Cannot be determined due to insufficient data'.

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