If x 4, is (5x - 2)/(10 - 3x) -2?

Question

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

1) x > 20
2) x < 40

* kudos for all correct solutions

vitaliyGMAT · Answer

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

BrentGMATPrepNow · Answer

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

Cheers,
Brent

CrackverbalGMAT · Answer

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 [ 1.41 KiB | Viewed 2737 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

BrentGMATPrepNow · Answer

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) 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 RELATED VIDEOS https://www.youtube.com/watch?v=MyG1K3ee69w https://www.youtube.com/watch?v=Od98BOicIq4

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If x > 4, is (5x - 2)/(10 - 3x) > -2?

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