Consider each choice. (A) is possible; for instance, 6 + 7 + 8 = 21. (B) is impossible, so it is correct. An integer with only even prime factors cannot have 7 as a prime factor; if it doesn't have 7 as a prime factor, it can't yield an integer when divided by 7.

(C) is possible: If either of the odd integers is 7 or divisible by 7, the result is also divisible by 7. (D) is possible: for example, 56 is divisible by both 7 and 8. Finally, many even integers are divisible by 7 (28, 42, etc.), so (E) is possible as well. (B) is the correct choice.