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

This topic has 2 expert replies and 0 member replies

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

Post Wed Nov 08, 2017 7:44 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Wed Nov 08, 2017 12:22 pm
    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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    GMAT/MBA Expert

    Post Thu Nov 09, 2017 7:12 pm
    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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