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If y does not equal 0. Does x = 0 ?

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If y does not equal 0. Does x = 0 ? [#permalink] New post 06 Jan 2011, 05:32
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If y does not equal 0. Does x = 0 ?

(1) x^2 y = x^3 y
(2) x^2 / y = x^3 y
[Reveal] Spoiler: OA

Last edited by Bunuel on 25 Aug 2012, 08:56, edited 1 time in total.
OA added.
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Re: Algebra DS [#permalink] New post 06 Jan 2011, 05:45
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Expert's post
rxs0005 wrote:
If y <> = 0 Does x = 0

x^2 y = x^3 y

x^2 / y = x^3 y


Given: y\neq{0}. Question does x=0?

(1) x^2*y=x^3*y --> as y\neq{0} we can reduce by y --> x^2=x^3 --> x^2(x-1)=0 --> either x=0 or x=1. Not sufficient.

(2) x^2/y=x^3*y --> x^2=x^3y^2 --> x^2(xy^2-1)=0 --> either x=0 or xy^2=1 (depending on y x can be any positive number). Not sufficient.

(1)+(2) Both x=0 and x=1 (in this case y=1 or y=-1) satisfy the statements. Not sufficient.

Answer: E.
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Re: Algebra DS [#permalink] New post 07 Sep 2011, 04:19
**
Quote:
If y <> = 0 Does x = 0

(1) x^2 y = x^3 y

(2) x^2 / y = x^3 y


Very clear explanation, Bunuel. Thanks!
Initially, I had answer A and realised my mistake after reading Bunuel's solution. My error came from the fact that I cross-multiplied and eliminated as below:
Quote:
From Statement 1
--> x^2y=x^3y --> y/y = x^3/x^2 --> x = 1
Sufficient


Given y does not equal to zero, does x=0?

Statement 1
x^2y = x^3y --> x^3=x^2 --> 0 = x^2(x-1)
So, x=0 or x=1
Insufficient.

Statement 2
x^2/y = x^3y --> 0 = x^2(xy^2-1)
So, x=0 or xy^2=1 (i.e. x is not zero)
Insufficient.

Statement 1 + 2
x^2(x-1) = x^2(xy^2-1)
x-1 = xy^2-1
x(1-y^2) = 0
So, x = 0 or x does not equals to zero (when y^2=1)
Insufficient.

Answer: E
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Re: If y does not equal 0. Does x = 0 ? [#permalink] New post 26 Aug 2012, 09:55
Very nice explanation Bunuel , thanks a lot !

I was confused whether to choose D or E because i thought that in either of the options x is coming 0 (along with some other value)

But it suggests that the value is not sufficient in both the cases.
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please do clarify my quey [#permalink] New post 29 Dec 2012, 01:21
If y does not equal 0. Does x = 0 ?

(1) x^2 y = x^3 y
(2) x^2 / y = x^3 y

please do calrify my doubt :

Given:
y does not equal to zero, does x=0?

x^2y = x^3y

Here we are calculating as x^2y-x^3y
my question is
why can't we do as x^2y/x^3y

Please do clarify when what is the actual procedure and why can't do like this as mentioned later
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Re: please do clarify my quey [#permalink] New post 29 Dec 2012, 02:51
Expert's post
skamal7 wrote:
If y does not equal 0. Does x = 0 ?

(1) x^2 y = x^3 y
(2) x^2 / y = x^3 y

please do calrify my doubt :

Given:
y does not equal to zero, does x=0?

x^2y = x^3y

Here we are calculating as x^2y-x^3y
my question is
why can't we do as x^2y/x^3y

Please do clarify when what is the actual procedure and why can't do like this as mentioned later


Merging similar topics. Please refer to the solutions above.

Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule #3.

Next, I guess your question is why are not we dividing both parts of x^2*y = x^3*y by x^3*y to get x^2*y/(x^3*y) = 1. That's because x^3*y can be zero (in case y=0) and we cannot divide by 0.

Hope it's clear.
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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: please do clarify my quey   [#permalink] 29 Dec 2012, 02:51
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