Question

How many people watch program P?
Statement A
A. The number watching Q is $1000$; the number watching both P and Q is $100$.
Statement B
B. The number of people watching either P or Q or both is $1500$.

• A. The question can be answered by one of the statements alone but not by the other.
• B. The question can be answered by using either statement alone.
• C. The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
• D. The question cannot be answered even by using both statements together.

Hint:

Use the union formula for two sets: $|A \cup B| = |A| + |B| - |A \cap B|$.

Answer 1

The Correct Option is C

From A alone: Not enough to find P. From B alone: Not enough to find P. Combining: From union formula $|P \cup Q| = |P| + |Q| - |P \cap Q|$, $1500 = P + 1000 - 100 \Rightarrow P = 600$. Thus both statements are required.