Question

A total of 200 people were surveyed for newspaper readership. It was found that 100 people read publication X, 120 people read publication Y and 50 people do not read either X or Y. What is the total number of people who read either publication X or publication Y but not both?

Answer 1

Correct Answer: 80

To solve the problem, we need to determine the number of people who read either publication X or publication Y but not both. We will use the principle of inclusion-exclusion from set theory.

Let's define:
- \( A \) as the set of people who read publication X
- \( B \) as the set of people who read publication Y

We are given:
- \( |A| = 100 \) (people who read X)
- \( |B| = 120 \) (people who read Y)
- 50 people do not read either X or Y
- Total surveyed = 200

First, calculate the number of people who read X or Y (or both):
total\_read = 200 - 50 = 150

Using the formula for the union of two sets, we have:
\[ |A \cup B| = |A| + |B| - |A \cap B| \]
Substitute the known values to find \(|A \cap B|\):
\[ 150 = 100 + 120 - |A \cap B| \]
Solve for \(|A \cap B|\):
\[ |A \cap B| = 100 + 120 - 150 = 70 \]

Now, we need to find how many people read either X or Y but not both:
\[ (|A| - |A \cap B|) + (|B| - |A \cap B|) = (100 - 70) + (120 - 70) = 30 + 50 = 80 \]

Thus, the total number of people who read either publication X or Y but not both is 80. This value is well within the expected range of 80,80 as provided.