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 \(x + 1.\)
Answer:
A
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
Answer: A
Cheers,
Brent
