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# If n ≠ 0, is m/n > 0 ? (1) n^m = 1 (2) m|n| < 0

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Re: If n ≠ 0, is m/n > 0 ? (1) n^m = 1 (2) m|n| < 0 [#permalink]
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(1): Case1: n=1,m=1
Case2: n=-1,m=2
so not sufficient
(2): m|n|<0 means m has to be negative
m=-1,n=-1
m=-1,n=1
not sufficient
Combining Both
no solution
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Re: If n ≠ 0, is m/n > 0 ? (1) n^m = 1 (2) m|n| < 0 [#permalink]
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If n≠0n≠0, is m/n>0 ?

(1) n^m=1
Here either M can be zero or n can be 1 or -1 (but only -1 if m is even). So this is insufficient.

(2) m|n|<0

Here we know that m<0, so m must be negative. We also know that m cannot be zero. But alone, this is insufficient because n could be just about any number other than zero.

Combined

Combined, we know first that m is not zero and m must be equal to a negative number, but we do not know what exact value it will have. We also know that |n| is equal to one. But do we know whether n is negative? We need to know whether n is negative to know whether the fraction m/n is > 0 or not.

Can n be 1? Yes. 1^m is always going to be equal to 1. Can n be equal to -1? It's a bit more complicated. If m is an even number, then n can be negative. But if m is an odd number, then then n cannot be negative. Recall from above that we do not know what value m has beyond being less than zero, so we must conclude the statements, even combined, are insufficient to determine whether m/n>0.
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Re: If n ≠ 0, is m/n > 0 ? (1) n^m = 1 (2) m|n| < 0 [#permalink]
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Re: If n ≠ 0, is m/n > 0 ? (1) n^m = 1 (2) m|n| < 0 [#permalink]
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