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Re: If x < 3, is (x + 1)/(x - 3) > 1/3?
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10 Feb 2017, 11:54
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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 question
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
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