Is -3*x^3 <= -3?
1) -3x<3
2) x <0
OA B
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Is -3*x^3 <= -3?
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BTGmoderatorDC
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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
Brent Hanneson - Creator of GMATPrepNow.com
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fskilnik@GMATH
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$$ - 3{x^3}\,\,\mathop \leqslant \limits^? \,\, - 3\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( { - \frac{1}{3}} \right)} \,\,\,\,\,{x^3}\,\mathop \geqslant \limits^? \,\,1\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\root {3\,} \of {\,\,\,} } \,\,\,\boxed{\,\,x\,\mathop \geqslant \limits^? \,\,1\,\,}\,$$BTGmoderatorDC wrote:Is -3*x^3 <= -3?
1) -3x<3
2) x <0
Source: GMAT Prep
$$\left( 1 \right)\,\,\, - 3x < 3\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,x = 0\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,x = 1\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.$$
$$\left( 2 \right)\,\,\,x < 0\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle $$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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