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# Is x between 0 and 1? (1) x^2 is less than x. (2) x^3 is

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Manager
Joined: 25 Apr 2007
Posts: 50
Followers: 1

Kudos [?]: 2 [0], given: 0

Is x between 0 and 1? (1) x^2 is less than x. (2) x^3 is [#permalink]  27 Oct 2007, 12:57
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Is x between 0 and 1?
(1) x^2 is less than x.
(2) x^3 is positive.

If X^2 < X then X can be either -ve of or a fraction. So INSUFF but the answer key says A.

Manager
Joined: 19 Aug 2007
Posts: 170
Followers: 1

Kudos [?]: 17 [0], given: 0

theres no negative value of x for which x^2 < x holds. because a negative number squared will be positive, while x was negative.

same is the case with a fraction.

the only time when x^2 can be less than x is between 0 and 1
SVP
Joined: 29 Aug 2007
Posts: 2497
Followers: 57

Kudos [?]: 556 [0], given: 19

Re: DS Value of X [#permalink]  27 Oct 2007, 13:10
johnbaker wrote:
Is x between 0 and 1?
(1) x^2 is less than x.
(2) x^3 is positive.

If X^2 < X then X can be either -ve of or a fraction. So INSUFF but the answer key says A.

hmm....

A. it is A as x^2 is less than x is true only when x is a +ve fraction.
SVP
Joined: 01 May 2006
Posts: 1805
Followers: 8

Kudos [?]: 99 [0], given: 0

(A) too

I suggest to draw in an XY plane y = x, y = x^2 and y = x^3... x^2 less than x implies that the curve x^2 is below the line y=x. ... It's fast and avoid any doubt.

I will do it with algebra

Stat1
x^2 < x
<=> x^2 - x < 0
<=> x*(x-1) < 0 >>> it's only true for x between the roots of the expression x*(x-1).... So, 0 < x < 1

SUFF.

Stat2
x^3 > 0
<=> x > 0

INSUFF.
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