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Is -3*x^3 <= -3?
1) -3x<3
2) x <0
OA B
Source: GMAT Prep
1) -3x<3
2) x <0
OA B
Source: GMAT Prep
Target question: Is (-3)(x³) ≤ -3?BTGmoderatorDC wrote:Is (-3)(x³) ≤ -3?
1) -3x < 3
2) x < 0
This is a good candidate for rephrasing the target question.
Take: (-3)(x³) ≤ -3?
Divide both sides by -3 to get: x³ ≥ 1 [since we divided an inequality by NEGATIVE value, we had to REVERSE the inequality symbol]
Under what circumstance will x³ be greater than or equal to 1?
Well, x³ EQUALS 1 when x = 1
So, x³ will be greater than or equal to 1, when x ≥ 1
We're now ready to go....
REPHRASED target question: Is x ≥ 1?
Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Statement 1: -3x < 3
Divide both sides by -3 to get: x > -1
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 2, in which case, the answer to the REPHRASED target question is YES, it IS the case that x ≥ 1
Case b: x = 0, in which case, the answer to the REPHRASED target question is NO, it is NOT the case that x ≥ 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x < 0
Perfect!
If x is NEGATIVE then x CANNOT be greater than or equal to 1
So, the answer to the REPHRASED target question is NO, it is NOT the case that x ≥ 1
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
