If x > 4, is (5x − 2)

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If x > 4, is (5x − 2)

by Brent@GMATPrepNow » Mon Jan 09, 2017 1:02 pm
Just made this is up.
Estimated difficulty level: 650
If x > 4, is (5x − 2)/(10 - 3x) > −2 ?

1) x > 20
2) x < 40
Answer: A
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by melguy » Mon Jan 09, 2017 11:35 pm
Statement 1

x = 21

5x21 - 2
------------- > -2
10 - 3x21

103
------------- > -2
-53

Less than -2 > -2 Yes

As we keep on adding the same values (positive large numbers greater than 20) to numerator and denominator the value will get closer to -1 i.e the value will keep on increasing. As a result the value will always be greater than -2.

Sufficient

Statement 2

x = 0

-2
----- > -2 No
10

x = 3

13
----- > -2 Yes
1

Answer A

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by Brent@GMATPrepNow » Tue Jan 10, 2017 10:50 am
Nice work, melguy!
I like how you combined plugging in x-values with some number sense to arrive at the correct answer.

Here's another approach:
Brent@GMATPrepNow wrote: If x > 4, is (5x − 2)/(10 - 3x) > −2 ?

1) x > 20
2) x < 40
Target question: Is (5x − 2)/(10 - 3x) > −2 ?

This is a great 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 we're told that x > 4, we can be certain that (10-3x) will be a NEGATIVE value for all permissible values of x.
So, let's take (5x − 2)/(10 - 3x) > −2 and multiply both sides by (10-3x)
We get: (5x − 2) < −2(10 - 3x) [aside: since we multiplied both sides by a NEGATIVE value, we REVERSED the inequality sign]
Simplify to get: 5x − 2 < −20 + 6x
Subtract 5x from both sides: −2 < −20 + x
Add 20 to both sides: 18 < x
Great! We can now REPHRASE the target question...

REPHRASED target question: Is x > 18?

Statement 1: x > 20
Well, if x > 20, we can be certain that x > 18
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: x < 40
There are several values of x that satisfy statement 2. Here are two:
Case a: x = 39, in which case x > 18
Case b: x = 10, in which case x < 18
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
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