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# If x = 1/2, is y equal to 1? (1) y^2(x + 1/2) = 1 (2) y(2x - 1) = 2x

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Re: If x = 1/2, is y equal to 1? (1) y^2(x + 1/2) = 1 (2) y(2x - 1) = 2x [#permalink]
Shameek,

You have the correct expression for 1.
I read in MGMAT guides as follow:
if square of Y = 1, then Y = + or - 1. GMAT approach is, if Y = 1 then square of Y = 1 and if Y = -1 the square if Y is still 1.

Hope that helps.
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Re: If x = 1/2, is y equal to 1? (1) y^2(x + 1/2) = 1 (2) y(2x - 1) = 2x [#permalink]
Shameek,

You have the correct expression for 1.
I read in MGMAT guides as follow:
if square of Y = 1, then Y = + or - 1. GMAT approach is, if Y = 1 then square of Y = 1 and if Y = -1 the square if Y is still 1.

Hope that helps.

First of all I would like to know where does square of Y comes into picture in this question. If you open the 1st statement's expression you get

$$X*Y + (\frac{Y}{2}) = 1$$

which will be $$\frac{Y}{2} + \frac{Y}{2} = 1$$

i.e. Y = 1 - Hence Sufficient

For the second statement :-
Y*(2X-1) = 2X - Y

2XY - Y = 2X - Y

i.e. 2XY - 2X = 0

i.e. 2X(Y-1) = 0

either X = 0 or Y = 1

Given that $$X = \frac{1}{2}$$ we are left with Y = 1

And yes $$\sqrt{Y^2} = |Y|$$; and therefore 2 solutions for Y.

But why are you concerned with it for this question? I don't get that.

Also according to me the answer should be "D" not "B".
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Re: If x = 1/2, is y equal to 1? (1) y^2(x + 1/2) = 1 (2) y(2x - 1) = 2x [#permalink]
2
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If x = 1/2, is y equal to 1?

(1) y^2(x + 1/2) = 1
(2) y(2x - 1) = 2x - y

why is GMAT so biased on sqr(y) = 1. I mean, why sqroot(y) not equal to 1, instead it is + or - 1? for GMAT \sqrt{1} = 1

NOTE: edited the first statement.

If x = 1/2, is y equal to 1?

(1) y^2(x + 1/2) = 1 --> substitute: $$y^2=1$$ --> $$y=-1$$ or $$y=1$$. Not sufficient.

(2) y(2x - 1) = 2x - y --> substitute: $$0=1-y$$ --> $$y=1$$. Sufficient.

Hope it's clear.

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Re: If x = 1/2, is y equal to 1? (1) y^2(x + 1/2) = 1 (2) y(2x - 1) = 2x [#permalink]
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Re: If x = 1/2, is y equal to 1? (1) y^2(x + 1/2) = 1 (2) y(2x - 1) = 2x [#permalink]
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