Question

If the average of p numbers is q² and that of q numbers is p², then the average of (p+q) numbers is:

• A. \(\frac{p}{q}\)​
• B. \(pq\)
• C. \(p+q\)
• D. \(p−q\)

Answer 1

The Correct Option is B

If the average of \( p \) numbers is \( q^2 \), then the sum of these numbers is \( p \cdot q^2 \).

If the average of \( q \) numbers is \( p^2 \), then the sum of these numbers is \( q \cdot p^2 \).

The total sum of \( p + q \) numbers is the sum of these two sums: \( p \cdot q^2 + q \cdot p^2 \).

Factoring the total sum yields \( pq(q + p) \).

The average of \( p + q \) numbers is the total sum divided by \( p + q \).

Therefore, the average is \( \frac{pq(q + p)}{p+q} \).

Assuming \( p+q eq 0 \), we can simplify this expression by canceling \( p+q \) from the numerator and the denominator.

This results in an average of \( pq \).