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

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Joined: 07 Jun 2004
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Is x > 0 (1) x < x^2 (2) x^2 < x^3  [#permalink]

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24 Jan 2011, 06:42
4
2
00:00

Difficulty:

25% (medium)

Question Stats:

69% (01:17) correct 31% (01:27) wrong based on 108 sessions

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Is x > 0

(1) x < x^2
(2) x^2 < x^3
Math Expert
Joined: 02 Sep 2009
Posts: 58381
Re: Is x > 0 (1) x < x^2 (2) x^2 < x^3  [#permalink]

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24 Jan 2011, 07:37
1
rxs0005 wrote:
is x > 0

S1 x < x^2

S2 x^2 < x^3

Is x > 0?

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

(2) x^2 < x^3 --> x^2(x-1)>0 --> x>1. Sufficient.

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Re: Is x > 0 (1) x < x^2 (2) x^2 < x^3  [#permalink]

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24 Jan 2011, 06:59
(1) If x = 2, then $$x^2 = 4$$; here x > 0
If x = -2, then $$x^2 = (-2)^2 = 4$$; here x < 0
x may or may not be greater than 0. Hence, there is no unique answer.
So, statement 1 is NOT SUFFICIENT.

(2) $$x^2 < x^3$$ implies that x > 1, which implies x is always positive. So, x > 0.
So, statement 2 is SUFFICIENT.

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Re: Is x > 0 (1) x < x^2 (2) x^2 < x^3  [#permalink]

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17 Mar 2011, 22:56
Very easy. Question asks if x is positive ...fraction OR integer doesn't matter..
Statement 1 says that x is either a negative fraction OR a positive integer.
Statement 2 says that x is definitely a positive integer.
Hence B
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Re: Is x > 0 (1) x < x^2 (2) x^2 < x^3  [#permalink]

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18 Mar 2011, 00:09
(1)

x-x^2 < 0

x(1-x) < 0

=> x > 1 or x < 0, so not sufficient

(2)
x^2 < x^3

=> x is +ve as if x is -ve then, then x^3 will be -ve while x^2 will be still +ve and +ve can't be < -ve

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Re: Is x > 0 (1) x < x^2 (2) x^2 < x^3  [#permalink]

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29 Mar 2019, 05:04
Hello from the GMAT Club BumpBot!

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Re: Is x > 0 (1) x < x^2 (2) x^2 < x^3   [#permalink] 29 Mar 2019, 05:04
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