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MGMAT Number Properties QB #17

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cindyqtran
 Post subject: MGMAT Number Properties QB #17
 Post Posted: Sun Sep 30, 2007 2:35 am 
Is |a| + |b| > |a + b| ?

(1) a^2 > b^2

(2) |a| × b < 0

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I thought the answer was B because the question does not ask for a specific value. (2) states that b is negative, therefore the question stem will always be correct.


OA is E
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Guest
 Post subject:
 Post Posted: Sun Sep 30, 2007 2:38 am 
nvm...it doesn't work when both a and b are negative.
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Kishore
 Post subject: drive from the property of the question
 Post Posted: Fri Oct 12, 2007 7:54 am 
Note that |a|+|b| > |a+b| does not hold if both a and b are negative or a and b are both positive, in which case |a|+|b| = |a+b|; None of the conditions stated above hint us that a and b are otherwise. So the answer is E.
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RonPurewal
 Post subject:
 Post Posted: Wed Oct 24, 2007 5:19 am 
Offline
ManhattanGMAT Staff


Posts: 6765
Here's a more concise explanation.

The inequality in the question stem is equivalent to "Do a and b have different signs?" This is not easy to see, but play around with some specific positive and negative numbers and you'll notice the emerging pattern.

Statement 2 says that b is negative
Statement 1 says NOTHING about the signs of the two numbers

Even when the two statements are taken together, we don't know whether the signs of a and b match, because the sign of a is still completely undetermined. Therefore, the answer is E.
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