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Something Wrong with the question???

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ronnie1985 GMAT Destroyer!
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Something Wrong with the question??? Post Wed May 23, 2012 11:51 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Is 1/(a-b)<(b-a)?
    1. a<b
    2. 1<|a-b|

    The question is 1<(b-a)(a-b)
    Now (b-a)*(a-b) = -1(a-b)*(a-b) = -(a-b)^2

    hence the question asks if 1 < a negative number which is absurd.

    The OA is (A)

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    Stuart Kovinsky GMAT Instructor
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    Post Wed May 23, 2012 2:03 pm
    ronnie1985 wrote:
    Is 1/(a-b)<(b-a)?
    1. a<b
    2. 1<|a-b|

    The question is 1<(b-a)(a-b)
    Now (b-a)*(a-b) = -1(a-b)*(a-b) = -(a-b)^2

    hence the question asks if 1 < a negative number which is absurd.

    The OA is (A)
    Hi!

    Remember - when inequalities and variables are involved, you have to be very careful with your manipulations!

    You cannot simply cross-multiply by a-b, since it's possible that a-b is negative. If a-b IS negative, then when you cross multiply you get:

    Is 1/(a-b)<(b-a)?
    Is 1 > (b-a)(a-b)?
    Is 1 > -1(a-b)(a-b)?
    Is 1 > -(a-b)^2?

    So, if a-b is positive, you get a "NO" answer to the question; if a-b is negative you get a "YES" answer to the question.

    Since (1) tells us that a-b<0, it's sufficient to answer the question. (2) doesn't tell us anything about the sign of (a-b), so it's insufficient. Choose (A)!

    * * *

    As an aside, if you ever wonder whether a question is valid, make sure you include the source! (Even better, always include the source.)

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