The sum of seven consecutive positive integers is always
(A) odd
(B) a multiple of 7
(D) a multiple of 4
(E) a multiple of 3

![](https://cdn.mathpix.com/cropped/2024_04_20_6027bc27089ed4fc493cg-101.jpg?height=214&width=266&top_left_y=262&top_left_x=1423)
The sum of seven consecutive positive integers is always
(A) odd
(B) a multiple of 7
(D) a multiple of 4
(E) a multiple of 3
(C) even

## Solution

The easiest way to do this is to start with $1+2+3+4+5+6+7=28$. If we consider the next possibility, $2+3+4+5+6+7+8=35$, we notice that the acceptable sums are one of,
$\{28,35,42,49, \ldots\}$. Each one of these numbers is a multiple of 7 .

ANSWER: (B)