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

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Question 321687: The sum of seven consecutive positive integers is always
(A) odd (B) a multiple of 7 (C) even (D) a multiple of 4 (E) a multiple of 3
Answer by solver91311(24713) (Show Source):
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Let represent the 7 integers where .

The sum of the 7 integers is then:

where is an arbitrary positive integer.

If is the th even integer, then , therefore and is even, hence is odd.

If is the th odd integer, then , therefore and is odd, hence is even.

Which is to say that answers A, C, and D can be excluded.

is only divisible by 3 if is divisible by 3. Exclude answer E.

Evenly divisible by 7 regardless of the value of x. Answer B.

John