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# If x is not equal to 1, is x^2/(x-1) greater than x?

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If x is not equal to 1, is x^2/(x-1) greater than x? [#permalink]

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18 Feb 2011, 11:58
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If x is not equal to 1, is x^2/(x-1) greater than x?

(1) x is not an integer.
(2) x is positive.
[Reveal] Spoiler: OA
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Re: 217. If x is not equal to 1, is greater than x? (1) x is [#permalink]

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18 Feb 2011, 12:18
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banksy wrote:
217. If x is not equal to 1, is x^2/(x-1) greater than x?
(1) x is not an integer.
(2) x is positive.

Is $$\frac{x^2}{x-1}>x$$ --> is $$\frac{x^2}{x-1}-x>0$$? --> is $$\frac{x^2-x^2+x}{x-1}>0$$ --> is $$\frac{x}{x-1}>0$$ --> is $$x<0$$ or $$x>1$$?

(1) x is not an integer --> clearly insufficient: for example if $$x=1.5$$ the the answer will be YES but if $$x=0.5$$ then the answer will be NO.

(2) x is positive. Also not sufficient.

(1)+(2) The values of $$x$$ from (1) also satisfy (2) (x can be positive fraction from the range (0,1) or some non integer more than 1) thus even taken together statements are not sufficient.

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Re: If x is not equal to 1, is x^2/(x-1) greater than x? [#permalink]

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06 Feb 2014, 13:42
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Re: 217. If x is not equal to 1, is greater than x? (1) x is [#permalink]

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10 Apr 2014, 22:43
Bunuel wrote:
banksy wrote:
217. If x is not equal to 1, is x^2/(x-1) greater than x?
(1) x is not an integer.
(2) x is positive.

Is $$\frac{x^2}{x-1}>x$$ --> is $$\frac{x^2}{x-1}-x>0$$? --> is $$\frac{x^2-x^2+x}{x-1}>0$$ --> is $$\frac{x}{x-1}>0$$ --> is $$x<0$$ or $$x>1$$?

(1) x is not an integer --> clearly insufficient: for example if $$x=1.5$$ the the answer will be YES but if $$x=0.5$$ then the answer will be NO.

(2) x is positive. Also not sufficient.

(1)+(2) The values of $$x$$ from (1) also satisfy (2) (x can be positive fraction from the range (0,1) or some non integer more than 1) thus even taken together statements are not sufficient.

Hi Bunuel,
will you explain this step ?

x/x-1 > 0 translating to x>1 or x<0 ?

thanks.
Math Expert
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Posts: 38908
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Kudos [?]: 106225 [1] , given: 11618

Re: 217. If x is not equal to 1, is greater than x? (1) x is [#permalink]

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11 Apr 2014, 02:54
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vishalrastogi wrote:
Bunuel wrote:
banksy wrote:
217. If x is not equal to 1, is x^2/(x-1) greater than x?
(1) x is not an integer.
(2) x is positive.

Is $$\frac{x^2}{x-1}>x$$ --> is $$\frac{x^2}{x-1}-x>0$$? --> is $$\frac{x^2-x^2+x}{x-1}>0$$ --> is $$\frac{x}{x-1}>0$$ --> is $$x<0$$ or $$x>1$$?

(1) x is not an integer --> clearly insufficient: for example if $$x=1.5$$ the the answer will be YES but if $$x=0.5$$ then the answer will be NO.

(2) x is positive. Also not sufficient.

(1)+(2) The values of $$x$$ from (1) also satisfy (2) (x can be positive fraction from the range (0,1) or some non integer more than 1) thus even taken together statements are not sufficient.

Hi Bunuel,
will you explain this step ?

x/x-1 > 0 translating to x>1 or x<0 ?

thanks.

$$\frac{x}{x-1}>0$$ --> transition pints are at 0 and 1:

If x is greater than 1, then $$\frac{x}{x-1}=\frac{positive}{positive}=positive$$, thus in this case $$\frac{x}{x-1}>0$$;

If 0<x<1, then $$\frac{x}{x-1}=\frac{positive}{negative}=negative$$, thus in this case $$\frac{x}{x-1}<0$$;

If x is less than 0, then $$\frac{x}{x-1}=\frac{negative}{negative}=positive$$, thus in this case $$\frac{x}{x-1}>$$;

As you can see the inequality holds true for $$x<0$$ and $$x>1$$.

Hope this helps.
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Re: 217. If x is not equal to 1, is greater than x? (1) x is   [#permalink] 11 Apr 2014, 02:54
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# If x is not equal to 1, is x^2/(x-1) greater than x?

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