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

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

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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.

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Quote:
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.

_________________
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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.

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