dvk007 wrote:

If a, b, and c are integers and \(\frac{ab^2}{c}\) is a positive even integer, which of the following must be true?

I. ab is even

II. ab > 0

III. c is even

A. I only

B. II only

C. I and II

D. I and III

E. I, II, and III

Statement I. ab is even

GIVEN: \(\frac{ab^2}{c}\) is an

even integer

This means we can say that \(\frac{ab^2}{c}\) = 2k (for some integer k)

Multiply both sides by c to get: \(ab^2 = 2kc\)

We can see that 2kc must be EVEN, which means ab^2 must be EVEN.

If ab^2 is EVEN, then either a or b must be EVEN, which means

ab must be EVENSo

statement I is trueCheck the answer choices....ELIMINATE B

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Statement II. ab > 0

Notice that, regardless of the value of b, we know that b² is POSITIVE (for all non-zero values of b)

This leads me to test some possible values...

If \(\frac{ab^2}{c}\) is a positive even integer, then it COULD be the case that a = 2, b = -1 and c = 1

Notice that \(\frac{ab^2}{c}=\frac{(2)(-1)^2}{1}=2\), which is a positive even integer

In this case, ab = (2)(-1) = -2

So, it is NOT true that ab > 0

So

statement II is NOT trueCheck the answer choices....ELIMINATE C and E

-------------------------------

Statement III. c is even

Notice that we can reuse the values we used above (a = 2, b = -1 and c = 1)

If c = 1, then c is NOT even

So

statement III is NOT trueCheck the answer choices....ELIMINATE D

The correct answer is A

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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