Which of the following CANNOT yield an integer when divided by 10 ?

SOLUTION

Which of the following CANNOT yield an integer when divided by 10 ?

(A) The sum of two odd integers
(B) An integer less than 10
(C) The product of two primes
(D) The sum of three consecutive integers
(E) An odd integer

In order an integer to be divisible by 10=2*5, the integer must be divisible by 2 (and 5), so it must be even, thus an odd integer is never divisible by 10 (or another way, an integer to be divisible by 10 its units digit must be 0, thus it must be even).

To discard other options:
(A) The sum of two odd integers. Not true: for example, 5+5=10 --> 10 IS divisible by 10.
(B) An integer less than 10. Not true: for example 0 IS divisible by 10.
(C) The product of two primes. Not true: 2*5=10 --> 10 IS divisible by 10.
(D) The sum of three consecutive integers. Not true: for example, -1+0+1=0 --> 0 IS divisible by 10.

Answer: E.