Which of the following is the sum of three consecutive integers?
(A) 17
(B) 11
(C) 25
(D) 21
(E) 8
Given three consecutive integers, the smallest integer is one less than the middle integer and the largest integer is one more than the middle integer.

For example, 10, 11 and 12 are three consecutive integers, and 10 is one less than the middle integer 11 , and 12 is one more than 11 .

So, the sum of the smallest and largest integers is twice the middle integer.

(In the example, $10+12=2 \times 11$.)

Then, the sum of three consecutive integers is equal to 3 times the middle integer and so the sum of three consecutive integers is a multiple of 3 .

Of the answers given, the only number that is a multiple of 3 is 21 .

Alternately, we could use trial and error to solve this problem to find that $6+7+8=21$.

ANSWER: (D)