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 \(x + 1.\)
Answer: A
Source: Manhattan GMAT
Is the number \(x\) positive?
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One approach is the sketch the cases on a number line.Gmat_mission wrote: ↑Fri Aug 20, 2021 12:11 pmIs 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 \(x + 1.\)
Answer: A
Source: Manhattan GMAT
First, recognize that x1 will always be to the left of x.
Second, recognize that there are 3 possible ways to place x1 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 x1 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
Answer: A
Cheers,
Brent