The sum of five consecutive integers is 75 . The sum of the largest and smallest of these five integers is
(A) 15
(B) 25
(C) 26
(D) 30
(E) 32

## Part B: Each correct answer is worth 6.
The sum of five consecutive integers is 75 . The sum of the largest and smallest of these five integers is
(A) 15
(B) 25
(C) 26
(D) 30
(E) 32

## Solution

There are a variety of ways of approaching this problem. The easiest is to represent the integers as $x-2, x-1, x, x+1$, and $x+2$.

Thus, $(x-2)+(x-1)+x+(x+1)+(x+2)=75$

$$
5 x=75
$$

$$
x=15
$$

The five consecutive integers are 13, 14, 15, 16, and 17.

The required sum is $13+17=30$.

ANSWER: (D)

## Part B