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If |A|<|B|, which of the following numbers is always -ve

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by guerrero » Wed Jun 19, 2013 3:44 am
If |A|<|B|, which of the following numbers is always negative?

A. A/B - B/A
B. A-B/A+B
C. A^B - B^A
D. A B/A-B
E. B-A/B

What could be the best approach ?


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by GMATGuruNY » Wed Jun 19, 2013 4:06 am
guerrero wrote:If |A|<|B|, which of the following numbers is always negative?

A. A/B - B/A
B. A-B/A+B
C. A^B - B^A
D. A B/A-B
E. B-A/B
|A| and |B| are both NONNEGATIVE.
Thus, we can safely square both sides of |A|<|B|, knowing that the direction of the inequality will not change:
|A|² < |B|²
A² - B² < 0.
(A+B)(A-B) < 0.

For the resulting inequality to hold true, A+B and A-B must be DIFFERENT SIGNS.
Thus, answer choice B -- (A-B)/(A+B) -- must always be negative.

The correct answer is B.
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