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