GMATPrepNow wrote:
If x < 3, is \(\frac{x + 1}{x - 3}\) > 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: See below for a video with tips on rephrasing the target questionSince 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 - 3Expand to get:
3x + 3 < x - 3Subtract x from both sides:
2x + 3 < -3Subtract 3 from both sides:
2x < -6Divide both sides by 2 to get:
x < -3This 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 < -3Case b: x = 0, in which case
x > -3Since 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 -3Since we can answer the
REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer: B
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