Brent@GMATPrepNow wrote:If x < 3, is (x + 1)/(x - 3) > 1/3?
(1) x < 2
(2) x > -1
Given: x < 3
Target question: Is (x + 1)/(x - 3) > 1/3?
This is a good candidate for
rephrasing the target question.
Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Since x < 3, we know that (x - 3) will always be NEGATIVE.
So, let's take
(x + 1)/(x - 3) > 1/3, and multiply both sides by (x - 3)
We get:
x + 1 < (1/3)(x - 3) [ASIDE: since we multiplied both sides by a NEGATIVE value, we REVERSED the inequality sign]
Now take
x + 1 < (1/3)(x - 3) and multiply both sides by 3 to get:
3(x + 1) < x - 3
Expand to get:
3x + 3 < x - 3
Subtract x from both sides:
2x + 3 < -3
Subtract 3 from both sides:
2x < -6
Divide both sides by 2 to get:
x < -3
This equivalent inequality is much easier to work with. So, ....
REPHRASED target question: Is x < -3?
Statement 1: x < 2
There are several values of x that satisfy statement 1. Here are two:
Case a: x = -7, in which case
x < -3
Case b: x = 0, in which case
x > -3
Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x > -1
If x is greater than -1, then we can be
100% certain that
x IS NOT less than -3
Since we can answer the
REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer:
B
Cheers,
Brent