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

Question

If  x = \frac{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

ScottTargetTestPrep · Accepted Answer

We are given that x = ½ and we must determine whether y = 1.
 
 Statement One Alone: 
 
y^2(x + ½) = 1
 
We can substitute ½ for x in the equation:
 
y^2(x + ½) = 1
 
y^2(1/2+ 1/2) = 1
 
y^2(1) = 1
 
y^2 = 1
 
y = 1 or y = -1
 
Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.
 
 Statement Two Alone: 
 
y(2x – 1) = 2x – y
 
We can substitute ½ for x in the equation:
 
y(2x – 1) = 2x – y
 
y(2(1/2) – 1) = 2(1/2) – y
 
y(1- 1) = 1 – y
 
y(0) = 1 – y
 
0 = 1 – y
 
y = 1
 
Statement two alone is sufficient to answer the question. 
 
Answer: B

shameekv · Answer

Hey Pradeep, Are you sure of the OA. And is the 1st statement Y*(X+\frac{1}{2}) = 1 ?? Because if that is so then it is sufficient. We can substitute value of X = 1/2 in this and we certainly get Y = 1. I don't believe there is any trick here? Can someone kick in here? And by the way about your query on \sqrt{Y^2} you can visit the following link where Bunuel has explained it very nicely. https://gmatclub.com/forum/confusion-on-square-roots-127807.html For this question my Answer would be D. Consider Kudos if the post helps. :-D

pradeepss · Answer

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.

shameekv · Answer

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".

Bunuel · Answer

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. Answer: B. Hope it's clear. P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rules 3 and 5. Thank you.

bumpbot · Answer

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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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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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