Eliminating Answer Choices

Here's a great example of eliminating answer choices.

Add 8x to 2x and then subtract 5 from the sum. If x is a positive integer, the result must be an integer multiple of
A. 2
B. 5
C. 8
D. 10
E. 15


Well, if 10 is a correct answer, then 5 would be correct, too. You can't have two correct answers. So 10 could not possibly be an answer. The same goes for 15. So two answers are eliminated.

There are two ways to do this:
Add 8x and 2x and you get 10x, a multiple of 10. If you subtract 5, it's no longer a multiple of 10, but it's a still a multiple of 5.

OR
substitute for x. Let's make x=4.
8x plus 2x = 40. Subtract 5, and you get 35, which is a multiple of 5.

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