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Difficulty: EasyLogical Venn Diagrams

In a survey of 8080 state administrative officers, 5050 officers read Newspaper X, 4040 officers read Newspaper Y, and 1515 officers read both newspapers. How many officers read only Newspaper X?

  1. 35Answer
  2. B
    50
  3. C
    25
  4. D
    65

Answer

35 officers read only Newspaper X.
The total number of officers who read Newspaper X is 50. Since 15 of these officers also read Newspaper Y, subtracting the overlapping group (15) from the total Newspaper X group (50) gives 35 officers who read strictly Newspaper X.

Step-by-Step Solution

1
Identify the total count of readers for Newspaper X and the intersection count of readers who read both newspapers.
Total readers of Newspaper X = 50, Readers of both Newspaper X and Y = 15.
The group reading Newspaper X consists of those reading Newspaper X only and those reading both newspapers.
2
Subtract the intersection count from the total count of Newspaper X readers.
50 - 15 = 35.
Using set theory, n(Only X) = n(X) - n(X ∩ Y).

Key Concept

Two-set Venn diagram region calculation: n(Only A) = n(A) - n(A ∩ B)
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Topics

Logical Venn Diagrams

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