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* inequality problem--is this correct

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wignewton
 Post subject: * inequality problem--is this correct
 Post Posted: Sun Jun 28, 2009 1:46 am 
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Students


Posts: 10
If –2<a<11 and 3<b<12, then which of the following is NOT true?
(A) 1<a+b<23
(B) -14<a-b<8
(C) -7<b-a<14
(D) 1<b+a<23
(E) -24<ab<132

Answer listed as C. Using the methods from the Manhattan books, C does not look to be valid. How is this problem done?
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andrew.k.john
 Post subject: Re: inequality problem--is this correct
 Post Posted: Sat Jul 04, 2009 2:55 am 
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Hi Wig.

To prove that C is the correct answer, let's use special cases of a and b. If b is close to it's lowest possible number, lets say 3.1, and a is close to it's highest number, 10.9, then what is b-a.

3.1-10.9 = -7.8.

This falls outside of the range outlined in answer (c).

The way the GMAT wants you to approach this problem is to calculate the extremes. In this case, (c) would be TRUE if we said -8 < b-a < 14. The limits of this inequality can be calculated by taking the (lowest b - highest a) < b-a < (highest b - lowest a).
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Ben Ku
 Post subject: Re: inequality problem--is this correct
 Post Posted: Fri Jul 31, 2009 12:44 am 
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ManhattanGMAT Staff


Posts: 753
Hi,

Just a reminder that this folder is reserved for questions specifically from Manhattan GMAT's Strategy Guides and its accompanying materials. Can you provide a source for your question? Thanks.

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Ben Ku
Instructor
ManhattanGMAT
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