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# If -10 < k < 10, is k > 0 ?

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Re: If -10 < k < 10, is k > 0 ? [#permalink]
Given -10 < k <10 , is k>0

This is simple if we think the question in terms of sign of k rather than its values

(1) 1/k > 0
1/k is +ve this means k is +ve Sufficient

(2) k^2 > 0
k^2 is +ve means, k could either be +ve or -ve
Insufficient.

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Re: If -10 < k < 10, is k > 0 ? [#permalink]
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Shiv636 wrote:
If -10 < k < 10, is k > 0 ?

(1) 1/k > 0
(2) k^2 > 0

If -10 < k < 10, is k > 0 ?
(1) 1/k > 0
It means K cannot be negative because 1 divided by a negative number will yield negative number and by definition -ve<0
so k will always be greater than 0
K>0 yes
SUFFICIENT

(2) k^2 > 0
Squaring a term takes away its polarity so k can be both negative and positive
If k is -ve then 1/-ve will be <0 ; hence the answer will be NO
if k is +ve then 1/+ve will be >0 ; hence answer will be YES
INSUFFICIENT

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Re: If -10 < k < 10, is k > 0 ? [#permalink]
Hi experts,
Could you please look into my question.
As per statement 1) 1/k>0. What I learnt from previous questions is that we cannot decide whether 1/k is positive or negative in such cases. The sign could be negative or positive. Then how can we conclude that k>0. Moreover, it is nowhere mentioned that k is a positive integer.

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Re: If -10 < k < 10, is k > 0 ? [#permalink]
Ben10512 wrote:
Hi experts,
Could you please look into my question.
As per statement 1) 1/k>0. What I learnt from previous questions is that we cannot decide whether 1/k is positive or negative in such cases. The sign could be negative or positive. Then how can we conclude that k>0. Moreover, it is nowhere mentioned that k is a positive integer.

Posted from my mobile device

1/k > 0 directly tells us that 1/k is positive (1/k is more than 0). 1/k to be positive k has to be positive. It's that simple. Also, k can be any positive number integer or not.

I think you should brush up basics on inequalities. Check the links below.

9. Inequalities

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
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Re: If -10 < k < 10, is k > 0 ? [#permalink]
If -10 < k < 10, is k > 0 ?

(1) 1/k > 0 --> suff: 1/k > 0 => k/k^2>0 => k > 0
(2) k^2 > 0 --> insuff: k^2 > 0 => k > 0 or k < 0

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Re: If -10 < k < 10, is k > 0 ? [#permalink]
Shiv636 wrote:
If -10 < k < 10, is k > 0 ?

(1) 1/k > 0
(2) k^2 > 0

Asked: If -10 < k < 10, is k > 0 ?

(1) 1/k > 0
k>0 and k<>0
SUFFICIENT

(2) k^2 > 0
|k|>0
$$k \neq 0$$
k may be positive or negative
NOT SUFFICIENT

IMO A
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Re: If -10 < k < 10, is k > 0 ? [#permalink]
Shiv636 wrote:
If -10 < k < 10, is k > 0 ?

(1) 1/k > 0
(2) k^2 > 0

S1: well 1/k > 0 is possible ONLY when k>0. if k<0, this would've been a negative number. Sufficient. Keep A and D, strike off BCE.
S2. square (or for that matter any even powers) will always be positive, no matter the sign of k. Therefore B is not sufficient.

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Re: If -10 < k < 10, is k > 0 ? [#permalink]
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Re: If -10 < k < 10, is k > 0 ? [#permalink]
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