13. If a is an even integer and b is an odd integer, which of the following cannot be an even integer?

(A) ab
(B) a/b
(C) b/a
(D) a^b
(E) a^2b + 1

The correct answer is (C), with the following explanation:

(C) NOT EVEN: An odd number is never divisible by an even number. By definition, an odd number is not divisible by 2 and an even number is. The quotient of an odd number divided by an even number will not be an integer, let alone an even integer.

I understand the explanation, but I just wanted to point out that what threw me off here was a statement made in the MGMAT Number Properties Strategy Guide. In Chapter 2 on Odds & Evens on p. 25:

"There are no guaranteed outcomes in division because the division of two integers may not yield an integer result (if the numerator is smaller than the denominator)."

Based on that statement I mistakenly eliminated (B) and (C) because I thought "there are no guaranteed outcomes regarding even/odds in division." However, now I know that there IS at least one guaranteed outcome: "An odd number divided by an even number NEVER produces an integer."

I only wanted to point all this out so that maybe in future editions the statement on page 25 might be clarified a bit, as follows:

"There are no guaranteed outcomes in division when it comes to a quotient being odd or even because the division of two integers may not yield an integer result (if the numerator is smaller than the denominator). Note, however, that when an odd integer is divided by an even integer, the result will NEVER be an integer.

Had the statement been worded this way, I would've answered the Question Bank problem with no difficulty. The language also might not be so strong as to mislead weak minds like mine. :wink: Just a suggestion...[/i]

"An odd number divided by an even number NEVER produces an integer."

Oops, I meant to say integer in that statement instead of "number."

you are of course correct.
in writing the text for that section, we face a tradeoff between precision and wordiness. i see your point, but, at the same time, the more precisely edited text is much more difficult to read and process than is the original version.

in any case, i'm glad you figured it out; i'll raise this issue later for consideration.