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# What is Y? 1. y^3 + 2y = y + 2y^2 2. y^2 = y

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Manager
Joined: 08 Sep 2010
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What is Y? 1. y^3 + 2y = y + 2y^2 2. y^2 = y [#permalink]

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04 Jul 2011, 08:02
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Question Stats:

83% (01:53) correct 17% (01:34) wrong based on 6 sessions

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What is Y?

1. y^3 + 2y = y + 2y^2

2. y^2 = y
[Reveal] Spoiler: OA

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Manager
Joined: 29 Jun 2011
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Re: What is y ? [#permalink]

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04 Jul 2011, 08:08
easy :
take statement 2 : y^2 = y => y = 0 or 1 => statement is not sufficient
take statement 1 : y^3 + 2y = y + 2y^2 => y = 0 or 1 => statement is not sufficient
take both together : y = 0 or y =1 => statements is not sufficient together
Ans E

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Re: What is y ? [#permalink]

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04 Jul 2011, 08:09
(1) says :

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

=> y^3 - 2y^2 + y = 0

=> y(y^2 - 2y + 1) = 0

=> y(y-1)^2 = 0

So y = 0, or y = 1

Insufficient

(2) says :

y^2 = y

=> y(y-1) = 0

=> y = 0 or y = 1

Insufficient

(1) + (2)

y = 0 or y = 1

Insufficient

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Re: What is y ? [#permalink]

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04 Jul 2011, 08:14
puneetj wrote:
What is Y?

1. y^3 + 2y = y + 2y^2

2. y^2 = y

1. y^3 + 2y = y + 2y^2
y^3 + 2y - y - 2y^2 = 0
y(y^2 + 1 - 2y) = 0
y = 0 or y-1=0 => y=1

Cant conclude

2. y^2 - y = 0
y(y-1) = 0
y = 0 or y-1=0 => y=1

Cant conclude

Together also can't conclude hence E.

We cannot cancel y on both side as it not known whether it is -ve or +ve.
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Re: What is y ? [#permalink]

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04 Jul 2011, 08:16
Thanks...i realize my mistake. Did not pay attention to the 1st equation...

This is what I did..

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

Then cancelled the y on both sides ....big mistake
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Re: What is y ?   [#permalink] 04 Jul 2011, 08:16
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