Question

How many people (from the group surveyed) read both Indian Express and Times of India?
I. Out of total of 200 readers, 100 read Indian Express, 120 read Times of India and 50 read Hindu.
II. Out of a total of 200 readers, 100 read Indian Express, 120 read Times of India and 50 read neither.

• A. If the question can be answered with the help of statement I alone.
• B. If the question can be answered with the help of statement II alone.
• C. If both the statement I and statement II are needed to answer the question.
• D. If the question cannot be answered even with the help of both the statements.

Hint:

To find number of people who read both sets, use: $|A \cap B| = |A| + |B| - |A \cup B|$. Reading "neither" helps find $|A \cup B|$.

Answer 1

The Correct Option is B

Let the total number of readers be 200. Let us define: Let: \[ A = \text{Number of people who read Indian Express} = 100
B = \text{Number of people who read Times of India} = 120
x = \text{Number of people who read both papers} \] From set theory: \[ \text{Number of people who read either Indian Express or Times of India}
= A + B - x = \text{Number who read at least one} \] From Statement I: We are given: - 100 read Indian Express - 120 read Times of India - 50 read Hindu But Hindu readership doesn't help in calculating the overlap between Indian Express and Times of India. So we cannot determine $x$ from Statement I alone. From Statement II: - 100 read Indian Express - 120 read Times of India - 50 read neither So, number of people who read at least one of the two = 200 - 50 = 150 Apply formula: \[ x = A + B - (\text{Number who read at least one}) = 100 + 120 - 150 = 70 \] Thus, Statement II alone is sufficient to answer the question.