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What is the value of y?

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Manager
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What is the value of y? [#permalink] New post 04 Dec 2012, 22:23
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Difficulty:

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Question Stats:

54% (01:50) correct 46% (01:10) wrong based on 50 sessions
What is the value of y?

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

(2) y^2=y
[Reveal] Spoiler: OA

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Joined: 04 Oct 2011
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Kudos [?]: 26 [0], given: 44

Re: What is the value of y? [#permalink] New post 04 Dec 2012, 22:30
shanmugamgsn wrote:
What is the value of y?

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

(2)y^2=y



My choice was A..
I did this way can any one correct me if im wrong??

(2) INSUFFICIENT :
y^2-y=0
y(y-1)
So y=0 or y=1

(1) i felt this is SUFFICIENT:
y^3+2y=y+2y^2
divide by y on both sides
y^2+2=1+2y
y^2-2y+1=0
(y-1)^2=0
So solution will be y=1

Is there any mistakes in my calculation?
If y this soln is wrong???
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Re: What is the value of y? [#permalink] New post 04 Dec 2012, 23:42
shanmugamgsn wrote:
shanmugamgsn wrote:
What is the value of y?

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

(2)y^2=y



My choice was A..
I did this way can any one correct me if im wrong??

(2) INSUFFICIENT :
y^2-y=0
y(y-1)
So y=0 or y=1

(1) i felt this is SUFFICIENT:
y^3+2y=y+2y^2
divide by y on both sides
y^2+2=1+2y
y^2-2y+1=0
(y-1)^2=0
So solution will be y=1

Is there any mistakes in my calculation?
If y this soln is wrong???


At first glance of the equation given in Statement 1, you should be able to see that 0 is a solution to the equation. Every expression contains a y term and hence 0 will satisfy the equation. Your first step is dividing by y. Since y is an unknown variable, that step cannot be allowed. As the famous mems of the internet go No one except Chuck Norris can divide by 0. :P...
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Re: What is the value of y? [#permalink] New post 05 Dec 2012, 01:02
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What is the value of y?

(1) y^3+2y=y+2y^2 --> y^3-2y^2+y=0 --> y(y^2-2y+1)=0 --> y(y-1)^2=0 --> y=0 or y=1. Not sufficient.

(2) y^2=y --> y(y-1)=0 --> y=0 or y=1. Not sufficient.

(1)+(2) y=0 or y=1. Not sufficient.

Answer: E.
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Re: What is the value of y? [#permalink] New post 05 Dec 2012, 01:04
Expert's post
shanmugamgsn wrote:
shanmugamgsn wrote:
What is the value of y?

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

(2)y^2=y



My choice was A..
I did this way can any one correct me if im wrong??

(2) INSUFFICIENT :
y^2-y=0
y(y-1)
So y=0 or y=1

(1) i felt this is SUFFICIENT:
y^3+2y=y+2y^2
divide by y on both sides
y^2+2=1+2y
y^2-2y+1=0
(y-1)^2=0
So solution will be y=1

Is there any mistakes in my calculation?
If y this soln is wrong???


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

So, if you divide (reduce) y^3+2y=y+2y^2 by y, you assume, with no ground for it, that y does not equal to zero thus exclude a possible solution (notice that both y=1 AND y=0 satisfy the equation).

Hope it's clear.
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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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What is the value of y? [#permalink] New post 06 May 2014, 05:48
What is the value of y?
(1) y^3+2y=y+2y^2

(2) y2=y

official ans. is E. But I got A. Please someone explain issue in following logic

y^3+2y = y+2y^2

y(Y^2+2) = y(1+2y)

now cancel y on both sides

y^2+2 = 1+2y
Y^2-2y+1 = 0

solving this I will get (y-1) = 0 so y =1

or we can see b^2-4ac = 0 so it has one root.

Please clarify

Thanks
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Re: What is the value of y? [#permalink] New post 06 May 2014, 07:22
Expert's post
PathFinder007 wrote:
What is the value of y?
(1) y^3+2y=y+2y^2

(2) y2=y

official ans. is E. But I got A. Please someone explain issue in following logic

y^3+2y = y+2y^2

y(Y^2+2) = y(1+2y)

now cancel y on both sides

y^2+2 = 1+2y
Y^2-2y+1 = 0

solving this I will get (y-1) = 0 so y =1

or we can see b^2-4ac = 0 so it has one root.

Please clarify

Thanks


Merging similar topics. Please refer to the discussion above.

Your doubt is addressed here: what-is-the-value-of-y-143619.html#p1150937

Hope it 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: What is the value of y?   [#permalink] 06 May 2014, 07:22
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