If a, b, and c are integers and ab^2/c . . .

[VJesus12]

If a, b, and c are integers and 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

The OA is A.

Experts, may you give me some help here please? It is a hard PS question to me.

[EconomistGMATTutor]

If a, b, and c are integers and 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

The OA is A.

Experts, may you give me some help here please? It is a hard PS question to me.

Hi VJesus12,
Let's take a look at your question.

The question says,
$$\frac{ab^2}{c}>0$$
and
$$\frac{ab^2}{c}=even$$
$$ab^2=c\times even$$
When any number is multiplied by an even number, it will result into an even number as well. Therefore,
$$ab^2=even$$
ab^2 can be even if a or b or both a and b are even.
Hence, ab will be even.
Therefore, I is true.

Let's check if II is true or not.
The question says that,
$$\frac{ab^2}{c}>0$$
Which can be true even b is negative, therefore, ab > 0 will not be true for b < 0.
Hence, II is not true.

Let's check if III is true or not.
c can not be even in all cases because the given statement can be true for c = 1 and i is not even.
Hence, III is not true.

It means only I is true.
Therefore, Option A is correct.

Hope that makes sense.
I am available if you'd like any follow up.

[Matt@VeritasPrep]

If we've got ab² / c = even, then we've also got

ab² = c * even

That means that either a or b is even, since a * b * b = even. Once a or b is even, we know that even * any integer = even, so ab MUST be even.

[Scott@TargetTestPrep]

If a, b, and c are integers and 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

The OA is A.

Experts, may you give me some help here please? It is a hard PS question to me.

We are given that (a*b^2)/c is a positive even integer. Therefore, a*b^2 must be even. (If a*b^2 is odd, (a*b^2)/c can't ever be even.)

Now recall that the product of an even number and any integer is even, so either a or b, or both, must be even. Thus we see that ab must be an even integer. However, ab DOES NOT have to be greater than zero, since a could be -2 and b could be 1. We could then let c = -1 to meet the requirement that (a*b^2)/c be a positive even integer. Finally, we see that c does not have to be even, since a could be -2, b could be 1, and c = -1. Thus, only Roman numeral I must be true.

Answer: A