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Is x^3/y = x + x/y?

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Is x^3/y = x + x/y? [#permalink] New post 21 Jun 2012, 00:55
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Is x^3/y = x + x/y?

(1) y = 8
(2) y = x^2 - 1
[Reveal] Spoiler: OA
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Re: Is x^3/y = x + x/y? [#permalink] New post 21 Jun 2012, 01:07
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Is x^3/y = x + x/y?

Is \frac{x^3}{y} = x + \frac{x}{y}? --> \frac{x^3}{y} = \frac{x(y+1)}{y}?

(1) y = 8. The question becomes: is \frac{x^3}{8} = \frac{9x}{8}? --> is x^3=9x? --> is x(x^2-9)=0? --> is x=0, x=3 or x=-3? We don't know that. Not sufficient.

(2) y = x^2 - 1. The question becomes: is \frac{x^3}{x^2-1} = \frac{x(x^2-1+1)}{x^2-1}? --> is \frac{x^3}{x^2-1} = \frac{x^3}{x^2-1}? The answer to this question is YES. Sufficient.

Answer: B.

Hope it's clear.
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Re: Is x^3/y = x + x/y? [#permalink] New post 21 Jun 2012, 01:57
Thanks a lot,that really helps.I cancelled the x in A,silly mistake.
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Re: Is x^3/y = x + x/y? [#permalink] New post 21 Jun 2012, 02:03
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shivanigs wrote:
Thanks a lot,that really helps.I cancelled the x in A,silly mistake.


Even if you could cancel x in (1) (for example if we were told that x\neq{0}) question would become: is x^2=9? Or is x=3 or x=-3? And since we don't know whether that's true, then the statement still would be insufficient.
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Re: Is x^3/y = x + x/y? [#permalink] New post 08 Aug 2012, 15:56
Bunuel wrote:

Even if you could cancel x in (1) (for example if we were told that x\neq{0}) question would become: is x^2=9? Or is x=3 or x=-3? And since we don't know whether that's true, then the statement still would be insufficient.


Why isn't this allowed?

x^3 = xy + x

\frac{x^3-x}{x}=y

x^2-1=y

:oops:
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Re: Is x^3/y = x + x/y? [#permalink] New post 08 Aug 2012, 16:07
superpus07 wrote:

x^3 = xy + x

\frac{x^3-x}{x}=y

x^2-1=y

:oops:


x^3 = xy + x
x^3=x(y+1)
x^2= y+1 = Statement 2 (Answer B)
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Re: Is x^3/y = x + x/y? [#permalink] New post 08 Aug 2012, 16:40
SOURH7WK wrote:
superpus07 wrote:

x^3 = xy + x

\frac{x^3-x}{x}=y

x^2-1=y

:oops:


x^3 = xy + x
x^3=x(y+1)
x^2= y+1 = Statement 2 (Answer B)


Sorry if I was unclear. I meant for statement 1. If you take this approach you get x^2-9=0 --> (x-3)(x+3). But according to the post above the potential x's should include a zero also. So this means that this approach is not allowed?
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Re: Is x^3/y = x + x/y? [#permalink] New post 09 Aug 2012, 02:01
Expert's post
superpus07 wrote:
SOURH7WK wrote:
superpus07 wrote:

x^3 = xy + x

\frac{x^3-x}{x}=y

x^2-1=y

:oops:


x^3 = xy + x
x^3=x(y+1)
x^2= y+1 = Statement 2 (Answer B)


Sorry if I was unclear. I meant for statement 1. If you take this approach you get x^2-9=0 --> (x-3)(x+3). But according to the post above the potential x's should include a zero also. So this means that this approach is not allowed?


We cannot divide x^3=9x by x because x can be zero and division by zero is not allowed.

Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero.

So, if you divide (reduce) x^3=9x by x, you assume, with no ground for it, that x does not equal to zero thus exclude a possible solution (notice that x=0 satisfies x^3=9x).

Hope it's clear.
_________________

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: Is x^3/y = x + x/y?   [#permalink] 09 Aug 2012, 02:01
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