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

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by VJesus12 » Tue Jun 05, 2018 1:41 am

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Difficulty—

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

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

The OA is the option A.

I don't know how to use the first statement to solve this DS question? Can anyone give me some help here? Thanks in advance.
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Tue Jun 05, 2018 4:30 am
VJesus12 wrote:If -10 < k < 10, is k > 0?

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

The OA is the option A.

I don't know how to use the first statement to solve this DS question? Can anyone give me some help here? Thanks in advance.
1/k > 0 implies that the expression on the Right Hand Side (1/k) is positive.

Since 1/k is positive, k is positive or greater than 0.

Hope this helps!

-Jay
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by Brent@GMATPrepNow » Tue Jun 05, 2018 7:06 am
VJesus12 wrote:If -10 < k < 10, is k > 0?

(1) 1/k > 0
(2) k² > 0
Target question: Is k > 0

Given: -10 < k < 10

Statement 1: 1/k > 0
In other words, 1/k is POSITIVE
Since 1 is positive, we can write: POSITIVE/k = POSITIVE
From this, we can conclude that k must be POSITIVE
So, the answer to the target question is YES, it is the case that k > 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: k² > 0
There are several values of k that satisfy statement 2. Here are two:
Case a: k = 1. In this case, the answer to the target question is YES, it IS the case that k > 0
Case b: k = -1. In this case, the answer to the target question is NO, it is NOT the case that k > 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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