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
Algebra.Com
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): You can put this solution on YOUR website!
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
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