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# Is x^3 > x^2? (1) x > 0 (2) x^2 > x

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Is x^3 > x^2? (1) x > 0 (2) x^2 > x [#permalink]  06 May 2012, 18:29
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Is x^3 > x^2?

(1) x > 0
(2) x^2 > x
[Reveal] Spoiler: OA
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Joined: 16 Sep 2011
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Concentration: Strategy, Operations
Schools: ISB '15
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Re: Inequalities [#permalink]  06 May 2012, 20:23
pgmat wrote:
Is x^3 > x^2?
1. x > 0
2. x^2 > x

Can some one explain how to solve this?

I hope yo know the basic structure of DS questions? You need to first check the suffecieny of statement 1...then for statement 2....and if neither is insuffecient on its own...then test for suffeciency together etc...

St1: X>0
his means x could be a number like 1/2 (which between 0 and 1) or could be a number like 2 (>1)...
for x=1/2, $$x^3<x^2$$ as 1/8<1/4
for x=2, $$X^3>X^2$$ as 8>4.
As both cases are possible, statement 1 alone is not suffecient to say if $$x^3>x^2$$ or not

St2: this says x^2>x => x(x-1)>0 =>x>1 or x<0 =>x could be numbers like -1/2,-2, 2
for x =-1/2, x^3<x^2
for x= -2, x^3<x^2
for x= 2, X^3>x^2....
hence not suffecient to say if$$x^3$$ is greater than$$X^2$$ or not

St1 and St2 together: X>0 AND (X>1 or X<0)....only numbers satisfying both cases (or in other words only common area for both cases on number line) is for x>1....for all x greater than 1. x^3>x^2...so suffecient to say YES to the question asked.
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Re: Is x^3 > x^2? (1) x > 0 (2) x^2 > x [#permalink]  06 May 2012, 22:42
Expert's post
Is x^3 > x^2?

Is $$x^3>x^2$$? --> since $$x^2$$ cannot be negative we can safely reduce by it: is $$x>1$$?

(1) x > 0. Not sufficient.
(2) x^2 > x --> $$x(x-1)>0$$ --> $$x<0$$ or $$x>1$$. Not sufficient.

(1)+(2) Intersection of the ranges from (1) and (2) is $$x>1$$, so the answer to the question is YES. Sufficient.

Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.
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Re: Is x^3 > x^2? (1) x > 0 (2) x^2 > x [#permalink]  14 Mar 2013, 02:18
Bunuel wrote:
Is x^3 > x^2?

Is $$x^3>x^2$$? --> since $$x^2$$ cannot be negative we can safely reduce by it: is $$x>1$$?

Hi Bunuel,

In this case, we dont know if x is not equal to zero. Without knowing that can we divide the eqn by x^2 which will also be zero?

Thanks,
Jaisri
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Re: Is x^3 > x^2? (1) x > 0 (2) x^2 > x [#permalink]  14 Mar 2013, 02:23
Expert's post
Jaisri wrote:
Bunuel wrote:
Is x^3 > x^2?

Is $$x^3>x^2$$? --> since $$x^2$$ cannot be negative we can safely reduce by it: is $$x>1$$?

Hi Bunuel,

In this case, we dont know if x is not equal to zero. Without knowing that can we divide the eqn by x^2 which will also be zero?

Thanks,
Jaisri

If x=0, then x^3>x^2 won't hold true. Or in another way: is $$x^3>x^2$$? --> is $$x^2(x-1)>0$$? is $$x>1$$?
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Re: Is x^3 > x^2? (1) x > 0 (2) x^2 > x [#permalink]  14 Mar 2013, 03:11
Thanks for your reply! I am getting the bigger picture of how you do things now. Thanks again!
Re: Is x^3 > x^2? (1) x > 0 (2) x^2 > x   [#permalink] 14 Mar 2013, 03:11
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