Re: If n ≠ 0, is m/n > 0 ? (1) n^m = 1 (2) m|n| < 0
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02 Sep 2020, 12:11
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.