Question 17

Explanation

To solve this problem, we need to understand the statistical properties regarding data transformation. Remember the key principles:

1. Mean changes according to all arithmetic operations (multiplication, division, addition, subtraction).
2. Range changes only with multiplication or division, but remains unchanged with addition or subtraction.

First, let's find the value of $p$ using the range information. Since the initial range of $6$ becomes $9$ after being multiplied by $p$, we have:

Next, we find the value of $q$ using the mean information. The mean is affected by both the multiplication by $p$ and the subtraction by $q$.

Finally, calculate the requested value using $p$ and $q$.

Thus, the value of $2p + q$ is $7$.