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If m and n are integers, is |m - n|= |m| - |n|?

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If m and n are integers, is |m - n|= |m| - |n|?

by Max@Math Revolution » Sat Oct 01, 2016 12:59 am
If m and n are integers, is |m - n|= |m| - |n|?
1) m>n
2) m+2n>0
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Source: — Data Sufficiency |
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by Max@Math Revolution » Sun Oct 02, 2016 11:59 pm
==> If you modify the original condition and the problem, and square the bothe sides, you get (|m - n|)^2= (|m| - |n|)^2?. From m^2-2mn+n^2=m^2+n^2-2|mn|?, you get rid of m^2 and n^2, you -2mn=-2|mn|?, mn=|mn|?. In other words, you get mn≥0?. However, there is no information regarding mn≥0 for 1) and 2), the answer is E.

Answer: E
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