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Is x odd?

This topic has 1 member reply

Is x odd?

Post Fri Nov 03, 2017 9:08 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Is x odd?

    (1) x/2 is not an integer

    (2) 2x + 3 is odd.

    The OA is C.

    I don't have clear why that is the correct answer. Please, can any expert assist me with this DS question? Thanks.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!

    Top Member

    Post Fri Nov 03, 2017 11:15 pm
    Question: Is x odd?

    Statement 1: x/2 is not an integer

    Possibilities:

    x is odd. For example, x = 3. 3/2 = 1.5, which is not an integer.

    x is a fraction. For example, x = 1/2. (1/2)/2 = 1/4, which is not an integer.

    Two different possibilities.

    Insufficient.

    (2) 2x + 3 is odd.

    Possibilities:

    x is even. For example, x = 2. 2(2) + 3 = 7, which is odd.

    x is odd. For example, x = 1. 2(1) + 3 = 5, which is odd.

    Two different possibilities.

    Insufficient.

    Statements Combined:

    We have three possibilities from the two statements.

    x is odd.

    x is even.

    x is a fraction.

    If we can eliminate two, we will have sufficient information.

    If we plug an even number into the expression from Statement 1 we get the following.

    Even Number/2 = Integer

    This is contrary to Statement 1. So, x cannot be even.

    Statement 2 combines 2x + 3 to get an odd number. Since even + odd = odd, 2x must be even.

    There is no way to multiply a fraction by 2 to get an even number. Consider the following examples.

    2 * 1/2 = 1

    2 * 1/3 = 2/3

    2 * 1 1/2 = 3

    So, x cannot be a fraction.

    Therefore, x must be odd.

    Sufficient.

    The correct answer is C.

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