Which of the following cannot yield an integer when divided by 12?

STRATEGY: Find counter-examples that allow us to eliminate four of the five answer choices.
A. The sum of 5 consecutive integers
10 + 11 + 12 + 13 + 14 = 60, and 60 divided by 12 equals 5 (which is an integer)

B. An integer less than 12
-12 is less than 12, and -12 divided by 12 equals -1 (which is an integer)

C. The product of three primes
(2)(2)(3) = 12, and 12 divided by 12 equals 1 (which is an integer)

D. The product of two odd integers
Unable to find a counterexample for this answer choice. Skip for now.

E. A multiple of 5
60 is a multiple of 5, and 60 divided by 12 equals 5 (which is an integer)

Answer: D

ALTERNATE APPROACH
In order for a number to yield an integer when divided by 12, that number must be a multiple of 12.
Numbers that are multiples of 12 include the following: ...-24, -12, 0, 12, 24, 36,...
You'll notice that, since 12 is an even integer, all multiples of 12 are also EVEN.
Since the product of two odd integers is always ODD, it's impossible for the product of two odd integers to be a multiple of 12.
Answer: D