## Is the number $$x$$ positive?

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### Is the number $$x$$ positive?

by Gmat_mission » Fri Aug 20, 2021 12:11 pm

00:00

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## Global Stats

Is the number $$x$$ positive?

(1) On the number line, $$0$$ is closer to $$x - 1$$ than to $$x.$$
(2) On the number line, $$0$$ is closer to $$x$$ than to $$x + 1.$$

Source: Manhattan GMAT

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### Re: Is the number $$x$$ positive?

by [email protected] » Tue Aug 24, 2021 5:55 am

00:00

A

B

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D

E

## Global Stats

Gmat_mission wrote:
Fri Aug 20, 2021 12:11 pm
Is the number $$x$$ positive?

(1) On the number line, $$0$$ is closer to $$x - 1$$ than to $$x.$$
(2) On the number line, $$0$$ is closer to $$x$$ than to $$x + 1.$$

Source: Manhattan GMAT
One approach is the sketch the cases on a number line.

First, recognize that x-1 will always be to the left of x.

Second, recognize that there are 3 possible ways to place x-1 and x with relation to zero.

Target question: Is x positive?

Statement 1: On the number line, 0 is closer to x – 1 than to x.
If zero is closer to x-1 than to x, then we can rule out case #2, leaving us with cases #1 and #3 as possible scenarios.
If case #1 is true, we can see that x must be positive
If case #3 is true, we can see that x must be positive
Since both possible cases yield the same answer to the target question, we can answer the target question with certainty.
So, statement 1 is SUFFICIENT

Statement 2: On the number line, 0 is closer to x than to x + 1.
Recognize that x+1 will always be to the right of x.
Also recognize that there are 3 possible ways to place x and x+1 with relation to zero.

If zero is closer to x than to x+1, then we can rule out case #2, leaving us with cases #1 and #3 as possible scenarios.
If case #1 is true, we can see that x is negative
If case #3 is true, we can see that x is positive
Since the two possible cases yield different answers to the target question, we cannot answer the target question with certainty.
So, statement 2 is NOT SUFFICIENT