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10 Feb 2017, 09:16
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B
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Difficulty:
55%
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Question Stats:
60% (01:54) correct
40%
(02:07)
wrong
based on 269
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If x < 3, is \(\frac{x + 1}{x - 3}\) > 1/3?
(1) x < 2
(2) x > -1
*Kudos for all correct solutions
(1) x < 2
(2) x > -1
*Kudos for all correct solutions
10 Feb 2017, 12:54
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GMATPrepNow
If x < 3, is \(\frac{x + 1}{x - 3}\) > 1/3?
(1) x < 2
(2) x > -1
(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
Answer: B
RELATED VIDEOS FROM OUR COURSE
General Discussion
(x + 1)/(x - 3) - 1/3 > 0?
2(x + 3)/3(x -3) > 0? --> We have to find out whether the expression (x + 3)/(x - 3) is positive.
St1: x < 2 --> The expression can be positive, negative or zero.
Insufficient.
St2: x > -1 --> -1 < x < 3 --> Numerator is always positive and denominator is always negative. So the expression is negative.
Sufficient.
Answer: B
2(x + 3)/3(x -3) > 0? --> We have to find out whether the expression (x + 3)/(x - 3) is positive.
St1: x < 2 --> The expression can be positive, negative or zero.
Insufficient.
St2: x > -1 --> -1 < x < 3 --> Numerator is always positive and denominator is always negative. So the expression is negative.
Sufficient.
Answer: B
