gmat focus DS -3

[abhasjha]

[GMATinsight]

Question : Is -3x^3 < -3?
Question : Is 3x^3 > 3?
Question : Is x^3 > 1? which is possible only if x>1

Question Rephrased : Is x > 1?

Statement 1) -3x<3
i.e. 3x>-3
i.e. x >-1 therfore, x may or may not be greater than 1

INSUFFICIENT

Statement 2) x<0
therefore, x is certainly Lesser than 1

SUFFICIENT

Answer: Option B

[Brent@GMATPrepNow]

Is -3x³ < -3?

1) -3x < 3
2) x < 0

IMPORTANT CONCEPT: If we divide both sides of an inequality by a NEGATIVE value, we must REVERSE the direction of the inequality sign.

Target question: Is -3x³ < -3?
This is a great candidate for rephrasing the target question.
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Take -3x³ < -3 and divide both sides by -3 to get x³ > 1
NOTE: x³ > 1 ONLY IF x > 1
Now rephrase the target question as....
REPHRASED target question: Is x > 1?

Statement 1: -3x < 3
Divide both sides by -3 to get: x > -1
There are several values of that satisfy this condition. Here are two:
Case a: x = 2, in which case x > 1
Case b: x = 0, in which case x < 1
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x < 0
In other words, x is negative
If x is negative, then we can be certain that x is NOT greater than or equal to 1.
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

For even more information on rephrasing the target question, you can read this article I wrote for BTG: https://www.beatthegmat.com/mba/2014/06/ ... t-question