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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, 23:23
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Question Stats:

50% (01:40) correct 50% (00:41) wrong based on 1 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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Re: What is the value of y? [#permalink] New post 04 Dec 2012, 23:30
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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Kudos if u like :)

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Re: What is the value of y? [#permalink] New post 05 Dec 2012, 00:42
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, 02:02
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, 02:04
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.
_________________

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

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. NEW!!!

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. NEW!!!


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Manager
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User avatar
Joined: 04 Oct 2011
Posts: 228
Location: India
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Kudos [?]: 17 [0], given: 44

Re: What is the value of y? [#permalink] New post 05 Dec 2012, 03:44
MacFauz wrote:
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...



Thanks MacFauz....

Actually, i forgot this rule :oops:
_________________

GMAT - Practice, Patience, Persistence
Kudos if u like :)

Manager
Manager
User avatar
Joined: 04 Oct 2011
Posts: 228
Location: India
Concentration: Entrepreneurship, International Business
GMAT 1: 440 Q33 V13
GMAT 2: 0 Q0 V0
GPA: 3
Followers: 0

Kudos [?]: 17 [0], given: 44

Re: What is the value of y? [#permalink] New post 05 Dec 2012, 03:45
Bunuel wrote:
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.



Thanks Bunuel....
made me clear...
_________________

GMAT - Practice, Patience, Persistence
Kudos if u like :)

Re: What is the value of y?   [#permalink] 05 Dec 2012, 03:45
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