is x^3> x^2?
{A} x>0
{B} x^2>x
If x is positive then x^3> x^2, so A is sufficient right? but ans says C.
why should we factor it?
Please explain!
Inequalities- Manhattan guide problem
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Hint: X>0 allows fraction values. Try plugging in x=1/2 - is x^3 still > x^2 then?
0<x<1 fraction values behave in exactly the opposite manner from x>1 values - the higher the power, the SMALLER the fraction.
0<x<1 fraction values behave in exactly the opposite manner from x>1 values - the higher the power, the SMALLER the fraction.
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Since x³ > x² only if x≠0, we can rephrase the question stem by dividing by x², which must be a POSITIVE value:Is x^3 > x^2 ?
(1) x > 0
(2) x^2 > x
x³/x² > x²/x²
x > 1.
Question rephrased: Is x>1?
Statement 1: x>0
Since it's possible that x=1/2 or that x=2, INSUFFICIENT.
Statement 2: x² > x
Since it's possible that x = ±2, INSUFFICIENT.
Statements combined:
No positive value less than or equal to 1 will satisfy both statements.
Thus, x>1.
SUFFICIENT.
The correct answer is C.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
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