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simple absolute value problem

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simple absolute value problem

by topspin360 » Sun Aug 12, 2012 12:44 pm
Is |a| > |b|?

(1) b < -a

(2) a < 0

So the question is really asking if a is farther from 0 than b. It could also be translated to the following two equations:
a > b, or a < -b.

now first choice is -a > b which can easily be translated to a < -b. And that should satisfy our requirement mentioned above.

OA is E. How come first choice doesn't work?

Thanks.
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Source: — Data Sufficiency |
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by GMATGuruNY » Sun Aug 12, 2012 3:13 pm
topspin360 wrote:Is |a| > |b|?

(1) b < -a

(2) a < 0

So the question is really asking if a is farther from 0 than b. It could also be translated to the following two equations:
a > b, or a < -b.

now first choice is -a > b which can easily be translated to a < -b. And that should satisfy our requirement mentioned above.

OA is E. How come first choice doesn't work?

Thanks.
If a=-2 and b=-1, both statements are satisfied:
(1) b < -a
-1 < -(-2)
-1 < 2.

(2) a < 0
-2<0.

In this case, |a| > |b|.

If a=-1 and b=-2, both statements are satisfied:
(1) b < -a
-2 < -(-1)
-2 < 1.

(2) a < 0
-1<0.

In this case, |a| < |b|.

Thus, the two statements combined are INSUFFICIENT.

The correct answer is E.

You're overlooking a crucial aspect here: EACH SIDE of the inequality contains an absolute value.
Is |a| > |b|?
YES, if a>0, b>0, and a>b.
YES, if a<0, b>0, and -a>b.
YES, if a>0, b<0, and a>-b.
YES, if a<0, b<0, and a<b.
A messy business.
Plugging in values seems easier and more efficient.
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