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BrentGMATPrepNow
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If x > 4, is (5x - 2)/(10 - 3x) > -2? 09 Jan 2017, 13:56
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A
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35% (medium)

Question Stats:

71% (01:36) correct 29% (02:26) wrong based on 76 sessions

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If x > 4, is \(\frac{5x - 2}{10 - 3x} > -2\)?

1) x > 20
2) x < 40

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vitaliyGMAT
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If x > 4, is (5x - 2)/(10 - 3x) > -2? 09 Jan 2017, 14:56
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If x > 4, is \(\frac{5x - 2}{10 - 3x} > -2\)?

1) x > 20
2) x < 40

I'm not sure whether my solution is correct or not.

\(\frac{5x - 2}{10 - 3x} > -2\)

\(\frac{5x - 2}{3x - 10} < 2\)

x>4 ---> (3x - 10) > 0

5x - 2 < 2(3x - 10)

5x - 2 < 6x - 20

x > 18

(1) x > 20 Sufficient.

(2) x < 40. x can be either 4<x<18 or 18<x<40. Insufficient.

Answer A.
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If x > 4, is (5x - 2)/(10 - 3x) > -2? 09 Jan 2017, 15:05
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If x > 4, is \(\frac{5x - 2}{10 - 3x} > -2\)?

1) x > 20
2) x < 40

I'm not sure whether my solution is correct or not.

\(\frac{5x - 2}{10 - 3x} > -2\)

\(\frac{5x - 2}{3x - 10} < 2\)

x>4 ---> (3x - 10) > 0

5x - 2 < 2(3x - 10)

5x - 2 < 6x - 20

x > 18

(1) x > 20 Sufficient.

(2) x < 40. x can be either 4<x<18 or 18<x<40. Insufficient.

Answer A.

Perfect!
You've taken the target question,"Is \(\frac{5x - 2}{10 - 3x} > -2\)?", and REPHRASED it as "Is x > 18?"

Cheers,
Brent
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If x > 4, is (5x - 2)/(10 - 3x) > -2? 10 Jan 2017, 01:51
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Such questions can be solved using the concept of Quadratic Inequalities.

https://gmatclub.com/forum/inequalities-quadratic-inequalities-231326.html#p1781849

While solving inequalities it also always helps to keep the right hand side equal to 0.

Simplifying the target question \(\frac{(5x-2)}{(10-3x)}\) > -2

\(\frac{(5x-2)}{(10-3x)}\) + 2 > 0 -----> \(\frac{(-x+18)}{(10-3x)}\) > 0

Multiplying both the numerator and denominator by -1 and keeping the inequality sign the same we get

\(\frac{(x-18)}{(3x-10)}\) > 0

This can be rewritten as (x-18)(3x-10) > 0

The critical points here are 18 and 10/3, plotting them on the number line and considering the positive regions we get

Attachment:
Capture 9.PNG
Capture 9.PNG [ 1.41 KiB | Viewed 2263 times ]

The solutions here are x > 18 and x < 10/3. We ignore the solution of x < 10/3 since we have the constraint x > 4. So the question can be rephrased as 'Is x > 18'

Statement 1 : x > 18

Clearly sufficient

Statement 2 : x < 40

Insufficient since x can be greater than 18 or less than 18. Insufficient.

Answer : A
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If x > 4, is (5x - 2)/(10 - 3x) > -2? 10 Jan 2017, 11:52
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If x > 4, is \(\frac{5x - 2}{10 - 3x} > -2\)?

1) x > 20
2) x < 40


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

This is a great candidate for rephrasing the target question.

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

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