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Given k is a nonzero integer, is k > 0 ?

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Given k is a nonzero integer, is k > 0 ? [#permalink]

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18 Sep 2016, 22:57
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Given k is a nonzero integer, is $$k > 0$$ ?

(1) $$|k-4| =| k| +4$$

(2) $$k>k^3$$
[Reveal] Spoiler: OA

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Re: Given k is a nonzero integer, is k > 0 ? [#permalink]

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19 Sep 2016, 01:14
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STAT1: |k-4| = |k| + 4

|k| + 4 will be a positive number and the absolute values of k and 4 will be added up.
|k-4| = |k + (-4)| this will give us the sum of absolute values of k and 4 only when k and -4 add up and this is possible only when k is also negative.
=> k < 0
=> SUFFICIENT

STAT2: k > k^3
=> possible values of k which will satisfy this statement are k<0 and k being a positive fraction. But k is a non-zero integer so k<0 is theonly solution
=> SUFFICIENT

Hope it helps!
GMATantidote wrote:
Given k is a nonzero integer, is $$k > 0$$ ?

1) $$|k-4| =| k| +4$$

2) $$k>k^3$$

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Re: Given k is a nonzero integer, is k > 0 ? [#permalink]

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19 Sep 2016, 01:49
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GMATantidote wrote:
Given k is a nonzero integer, is $$k > 0$$ ?

1) $$|k-4| =| k| +4$$

2) $$k>k^3$$

k is a non zero integer so the values it can take are ... -2, -1, 1, 2, 3, ...
Is k > 0?

1) $$|k-4| =| k| +4$$
According to the definition of absolute values,
|k - 4| = k - 4 if (k - 4) >= 0
|k - 4| = -(k - 4) = -k + 4 if (k - 4) < 0

Note that the the right hand side is |k| + 4. This can be equal to the second case only and that too when k < 0. So we know that k must be negative. We can answer the question with 'No'.
Sufficient.

2) $$k>k^3$$
On the number line, where is x greater than x^3? When either 0 < x< 1 or x < -1.
Here, since k must be an integer, it will not lie between 0 and 1. So k must be less than -1 i.e. k must be negative. We can answer the question with 'No'.
Sufficient.

P.S. - You must know the relation between x, x^2 and x^3 on the number line.
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Re: Given k is a nonzero integer, is k > 0 ? [#permalink]

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08 Dec 2017, 08:10
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Re: Given k is a nonzero integer, is k > 0 ?   [#permalink] 08 Dec 2017, 08:10
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