If x is not equal to 0, is |x| less than 1?
1) x/|x| < x
(2) |x| > x
OAC
If x is not equal to 0
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- GMATGuruNY
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I posted a solution here:
https://www.beatthegmat.com/if-x-is-not- ... 65585.html
https://www.beatthegmat.com/if-x-is-not- ... 65585.html
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I unlock the best way for YOU to solve problems.
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- ceilidh.erickson
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For |x| to be less than 1, x must be greater than -1 and less than 1.rsarashi wrote:If x is not equal to 0, is |x| less than 1?
1) x/|x| < x
(2) |x| > x
OAC
Target question: -1 < x < 0 ?
(1) x/|x| < x
- If x is positive, then x/|x| = 1. So 1 < x. This would give us a "no" answer to the question.
- If x is negative, then x/|x| = -1. So -1 < x. But since x is negative, we can add: -1 < x < 0. This would give is a "yes" answer to the question.
If we get a "no" answer when x < 0 and a "yes" answer when x > 0, this is insufficient.
(2) |x| > x
If x were positive, it would be equal to |x|. So this is telling us that x must be negative. However, just knowing that it is negative is not enough to tell us whether |x| < 1. Insufficient.
Together:
Statement 2 tells us that x must be negative, so x/|x| = -1 ---> -1 < x < 0. This would give is a "yes" answer to the question.
Sufficient.
The answer is C.
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This question comes from Manhattan Prep CATs.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education