* inequality problem--is this correct

[wignewton]

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?

[andrew.k.john]

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).

[Ben Ku]

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.