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# If n and k are integers and (-2)n^5 > 0, is k^37 < 0?

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If n and k are integers and (-2)n^5 > 0, is k^37 < 0? [#permalink]

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04 Mar 2012, 22:11
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If n and k are integers and (-2)n^5 > 0, is k^37 < 0?

(1) (nk)^z > 0, where z is an integer that is not divisible by two
(2) k < n
[Reveal] Spoiler: OA
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Re: If n and k are integers and (-2)n^5 > 0, is k^37 < 0? [#permalink]

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05 Mar 2012, 00:56
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If n and k are integers and (-2)n^5 > 0, is k^37 < 0?

First of all: $$(-2)*n^5>0$$ --> reduce by negative -2 and flip the sign: $$n^5<0$$ --> $$n<0$$;
Next: "is $$k^{37}<0$$" basically means whether $$k<0$$.

So the question becomes: If n and k are integers and $$n<0$$ is $$k<0$$?

(1) (nk)^z > 0, where z is an integer that is not divisible by two --> $$(nk)^{odd} > 0$$ --> $$nk> 0$$ --> $$n$$ and $$k$$ have the same sign and since $$n<0$$ then $$k<0$$. Sufficient.

(2) k < n --> since given that $$n<0$$ then $$k<n<0$$. Sufficient.

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Re: If n and k are integers and (-2)n^5 > 0, is k^37 < 0? [#permalink]

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22 Jun 2012, 14:54
Expert's post
Bunuel I find this question on the net.......I would like to know if you think that is a good question and if it is elaborate in a good manner.

It is important to practice.

Thanks
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Re: If n and k are integers and (-2)n^5 > 0, is k^37 < 0? [#permalink]

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23 Jun 2012, 03:58
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carcass wrote:
Bunuel I find this question on the net.......I would like to know if you think that is a good question and if it is elaborate in a good manner.

It is important to practice.

Thanks

Though the question is testing basic concepts usual for the GMAT, I still wouldn't call that question very elegant.
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Re: If n and k are integers and (-2)n^5 > 0, is k^37 < 0? [#permalink]

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11 Mar 2013, 18:37
What about the possibility that Z is equal to 0. In that case 1) would be insufficient.
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Re: If n and k are integers and (-2)n^5 > 0, is k^37 < 0? [#permalink]

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11 Mar 2013, 21:47
Expert's post
thekid1998 wrote:
What about the possibility that Z is equal to 0. In that case 1) would be insufficient.

Z can't be zero as it is mentioned that z is not divisible by 2.
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Re: If n and k are integers and (-2)n^5 > 0, is k^37 < 0? [#permalink]

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12 Mar 2013, 07:26
Another great DS problem that helps pinpoint the need to stay alert at the sign of the base of the exponent and whether the power itself is odd or even.

Let's begin by understanding the problem.

We have $$-2*(n)^5 > 0$$. Since the power is odd and the end result is positive despite multiplying the expression $$n^5$$ by (-2), then this states that n is negative.
So we want to see whether $$k^(37)<0$$, which is translated to : is k negative ? since 37 is an odd number !

Statement 1 : $$(nk)^z > 0$$, where z is an integer that is not divisible by two

Since z is odd and the expression is positive, we can assume that the base, nk, is positive. And seeing as n is negative, we can say that k is also negative. And since 37 is an odd power, then $$k^(37)$$ is negative. So statement 1 is sufficient.

Statement 2 : $$k < n$$

Since n is negative, it naturally follows that k is also negative. And since 37 is an odd power, then $$k^(37)$$ is negative. So statement 2 is sufficient.

The correct answer is, therefore, D !

Hope that helped .
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Re: If n and k are integers and (-2)n^5 > 0, is k^37 < 0? [#permalink]

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26 Jun 2015, 02:20
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Re: If n and k are integers and (-2)n^5 > 0, is k^37 < 0?   [#permalink] 26 Jun 2015, 02:20
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