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# OA says that (2) is insufficiente because it leaves the

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Intern
Joined: 19 Jan 2009
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OA says that (2) is insufficiente because it leaves the  [#permalink]

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02 Feb 2009, 04:51
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OA says that (2) is insufficiente because it leaves the original equation in (y-1)(y-1) = 1 but does not give the value of y.
But (y-1)(y-1) (y-1)^2 = y^2 + 1^2 - 2y. Then, y^2 + 1^2 - 2y = 1; y^2 - 2y = 0; y(y -2) = 0; y = 0 or y = 2, and in both cases (x-1)(y-1) for x= y gives 1=1, so (2) is sufficient, making the final answer D vs OA = A

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Joined: 29 Aug 2007
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Re: OG DS equations - disagreement with OG explanation  [#permalink]

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02 Feb 2009, 08:55
jairus wrote:
OA says that (2) is insufficiente because it leaves the original equation in (y-1)(y-1) = 1 but does not give the value of y.

But (y-1)(y-1) (y-1)^2 = y^2 + 1^2 - 2y. Then, y^2 + 1^2 - 2y = 1; y^2 - 2y = 0; y(y -2) = 0; y = 0 or y = 2, and in both cases (x-1)(y-1) for x= y gives 1=1, so (2) is sufficient, making the final answer D vs OA = A

How did you get the red part, which you need to prove?
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Joined: 04 Jan 2009
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Re: OG DS equations - disagreement with OG explanation  [#permalink]

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02 Feb 2009, 10:08
jairus wrote:
OA says that (2) is insufficiente because it leaves the original equation in (y-1)(y-1) = 1 but does not give the value of y.
But (y-1)(y-1) (y-1)^2 = y^2 + 1^2 - 2y. Then, y^2 + 1^2 - 2y = 1; y^2 - 2y = 0; y(y -2) = 0; y = 0 or y = 2, and in both cases (x-1)(y-1) for x= y gives 1=1, so (2) is sufficient, making the final answer D vs OA = A

So you have no disagreement with A being suff.
Let us look at B.
x=y =>(x-1)*(y-1) is (x-1)^2 = x^2-2x+1. This is one only if x==0 and x==2. Hence, not suff.

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Re: OG DS equations - disagreement with OG explanation &nbs [#permalink] 02 Feb 2009, 10:08
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