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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] New post 18 Feb 2011, 10:58
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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] New post 18 Feb 2011, 11:18
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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.

Answer: E.
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Re: If x is not equal to 1, is x^2/(x-1) greater than x? [#permalink] New post 06 Feb 2014, 12:42
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Re: 217. If x is not equal to 1, is greater than x? (1) x is [#permalink] New post 10 Apr 2014, 21:43
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.

Answer: E.

Hi Bunuel,
will you explain this step ?

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

thanks.
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Re: 217. If x is not equal to 1, is greater than x? (1) x is [#permalink] New post 11 Apr 2014, 01:54
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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.

Answer: E.

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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: 217. If x is not equal to 1, is greater than x? (1) x is   [#permalink] 11 Apr 2014, 01:54
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