varun289 wrote:268. Which of the following CANNOT yield an integer when divided by 7 ?
(A) The sum of three consecutive integers
(B) An integer with only even prime factors
(C) The product of two odd integers
(D) An integer divisible by 8
(E) An even integer

Reword question as "Which of the following CANNOT by divisible by 7?"

We'll eliminate every answer choice that CAN yield an integer when divided by 7.

A) If the 3 consecutive integers are 6, 7, 8 then the sum (21) IS divisible by 7. Eliminate A.
B) For integer N to be divisible by 7, then 7 must be somewhere in the prime factorization of N. If all of the prime factors of the number are even, then 7 cannot be in the prime factorization, which
means this number CANNNOT be divisible by 7.
The correct answer is B . . . take it and move on.

Just for "fun" we'll examine the remaining answer choices.
C) If the numbers are 1 and 7, then the product (7) IS divisible by 7. Eliminate C.
D) If the number is 56, then it IS divisible by 7. Eliminate D.
E) If the number is 14, then it IS divisible by 7. Eliminate E.

Cheers,
Brent