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Master | Next Rank: 500 Posts
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by topspin360 » Sat Oct 12, 2013 10:05 am
Hi All,

I know how to solve the following intuitively. But I'm trying to solve it algebraically.

x^3 > x^2?

Using algebra, I simplify the question and end up with: x<0 OR x>1? Which is obviously wrong. Can someone please show me how to simplify it using algebra?

Just FYI, answer choices are:
1) x > 0
2) x^2 > x

but answer choices are irrelevant at this point. I just want to focus on the question stem. Thanks.
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by GMATGuruNY » Sat Oct 12, 2013 12:36 pm
Is x^3 > x^2 ?

(1) x > 0
(2) x^2 > x
Since x³ > x² only if x≠0, we can rephrase the question stem by dividing by x², which must be a POSITIVE value:
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: x^2 > 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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by topspin360 » Sat Oct 12, 2013 2:19 pm
GMATGuruNY wrote:
Is x^3 > x^2 ?

(1) x > 0
(2) x^2 > x
Since x³ > x² only if x≠0, we can rephrase the question stem by dividing by x², which must be a POSITIVE value:
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: x^2 > 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.
Great explanation Mitch. what if I wanted to go the where I set it up as x^3 - x^2 > 0? How does that work? Just wondering for problems where I cant divide by x^2.
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by GMATGuruNY » Sat Oct 12, 2013 2:55 pm
topspin360 wrote: Great explanation Mitch. what if I wanted to go the where I set it up as x^3 - x^2 > 0? How does that work? Just wondering for problems where I cant divide by x^2.
Use the CRITICAL POINT approach. Check my posts here:

https://www.beatthegmat.com/inequalities-t115175.html
https://www.beatthegmat.com/inequality-c ... 89518.html
https://www.beatthegmat.com/manhattan-ad ... 66829.html
https://www.beatthegmat.com/number-t233111.html
https://www.beatthegmat.com/knewton-q-t89317.html
https://www.beatthegmat.com/which-is-true-t89111.html
https://www.beatthegmat.com/inequality-c ... 89518.html
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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.

For more information, please email me (Mitch Hunt) at [email protected].
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