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banksy
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If x is not equal to 1, is x^2/(x-1) greater than x? 18 Feb 2011, 11:58
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47% (02:02) correct 53% (02:03) wrong based on 90 sessions

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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.
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E
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If x is not equal to 1, is x^2/(x-1) greater than x? 18 Feb 2011, 12:18
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banksy
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.
Show more

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.

Answer: E.
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If x is not equal to 1, is x^2/(x-1) greater than x? 10 Apr 2014, 22:43
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banksy
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.

Answer: E.
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Hi Bunuel,
will you explain this step ?

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

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

Answer: E.
Hi Bunuel,
will you explain this step ?

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

thanks.
Show more

\(\frac{x}{x-1}>0\) --> 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 \(x>1\).

Theory on 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
everything-is-less-than-zero-108884.html
graphic-approach-to-problems-with-inequalities-68037.html

All DS Inequalities Problems to practice: search.php?search_id=tag&tag_id=184
All PS Inequalities Problems to practice: search.php?search_id=tag&tag_id=189

700+ Inequalities problems: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope this helps.
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If x is not equal to 1, is x^2/(x-1) greater than x? 01 Aug 2022, 08:27
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