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Integers a and b are such that a -b...

This topic has 1 expert reply and 0 member replies

Integers a and b are such that a -b...

Post Tue Sep 12, 2017 11:18 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Integers a and b are such that a - b > 0. Is |a| > |b| ?

    (1) ab > 0
    (2) a + b = 12

    The OA is B.

    Why is B the answer?

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    Post Tue Sep 19, 2017 4:31 am
    Vincen wrote:
    Integers a and b are such that a - b > 0. Is |a| > |b| ?

    (1) ab > 0
    (2) a + b = 12

    The OA is B.

    Why is B the answer?
    Given that a - b > 0 => a > b.

    We have to determine whether |a| > |b|.

    Statement 1: ab > 0

    => Either a and b both are positive or both are negative.

    Case 1: Say a = 3 and b = 2 (a > b), then |3| > |2|. The answer is Yes.
    Case 2: Say a = -2 and b = -3 (a > b), then |-2| < |-3| => 2 < 3. The answer is No.

    Insufficient.

    Statement 2: a + b = 12

    Had a = b, then a = b = 6. But we know that a > b, thus a > 6 and b < 6. This means that |a| > |b|. Sufficient.

    If you try to increase the value of |b| so that it may be greater than |a|, it is not possible.

    Say b = -10, thus |b| = 10.

    From a + b = 12, we get a +(-10) = 12 => a - 10 = 12 => a = 22.

    Thus, |a| > |b|. The answer is Yes.

    The correct answer: B

    Hope this helps!

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    Thanked by: Vincen

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