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# If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3

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Joined: 02 Sep 2009
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If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3  [#permalink]

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09 Dec 2019, 00:32
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If k is a non zero integer, is $$k > 0$$?

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

(2) $$k > k^3$$

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If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3  [#permalink]

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Updated on: 11 Dec 2019, 20:44
For any integer k < 0, the first option holds true. Sufficient.

For any integer k < -1 , the second option holds true. Sufficient

Originally posted by BinitKhadka on 09 Dec 2019, 01:04.
Last edited by BinitKhadka on 11 Dec 2019, 20:44, edited 1 time in total.
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Re: If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3  [#permalink]

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09 Dec 2019, 07:30
2) K is an integer so K<0. answer should be D
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Re: If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3  [#permalink]

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09 Dec 2019, 08:33
1
Bunuel wrote:
If k is a non zero integer, is $$k > 0$$?

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

(2) $$k > k^3$$

Are You Up For the Challenge: 700 Level Questions

Statement 1:
The absolute values give us the regions we should check. There are three cases, k > 4, 0 < k < 4, and k < 0. If k > 4, the equation is k - 4 = k + 4 which has no solution. If 0 < k < 4, we get 4 - k = k + 4 and k = 0, which isn't within the region but plugging in k = 0 tells us it's a viable solution. Therefore there are no positive k solutions, k cannot be positive. Sufficient.

Statement 2:
Whenever we are comparing powers of a single variable, we should check the 4 regions: k < -1, -1 < k < 0, 0 < k < 1, and k > 1. We can check the regions by picking a point in the region and if the point satisfies the inequality, the entire region is a solution set. For example, k = 0.5 satisfies this inequality so 0 < k < 1 is a solution set. By plugging in k = -2, we can see the same is true for k < -1. So we can have positive k or negative k, insufficient.

Ans: A
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Re: If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3  [#permalink]

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12 Jan 2020, 01:24
1
Hi chetan2u ,

Although i did arrive at D , I could not algebraically solve the first equation as the equation got very messy and time consuming to solve. So i substitutd numbers to reach the correct answer.

Could you please show us the correct approach to move with the first stsatement ?

Regards
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Re: If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3  [#permalink]

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12 Jan 2020, 02:51
1
ShankSouljaBoi If k is a non zero integer, is $$k > 0$$?

(1) $$|k - 4| = |k| + 4$$
Now both sides are positive, so you can square two sides
$$k^2-8k+16=k^2+8|k|+16......|k|=-k$$. This will be true ONLY when k is negative.
OR
Logically if you see what is happening to two sides.
The right side is adding two quantities but the left will add only when k and -4 have same sign, so k has to be 0 or <0
Suff

(2) $$k > k^3$$
$$k(1-k^2)>0$$..
If k>0, 1-k^2>0....k^2<1...-1<k<1 but no integer value exists as k is non zero.
When k<0, 1-k^2<0....k^2>1...k<-1
Suff

D
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Re: If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3  [#permalink]

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26 Jan 2020, 06:44
how did u solve k^2>1 and k^2<1 ?
Re: If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3   [#permalink] 26 Jan 2020, 06:44
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