Square root and exponents

[aidaait]

Hello

I'm having trouble with a Data Sufficiency question in the Number Properties question bank :

If x is not equal to y and if sqrt(x)=y, what is the value of y3 ?

(1) x = yx

(2) x3 = 8


According to the explanation, each statement allows to find that x=2 so each statement is sufficient because we can find y from x.



Finding that x=2 is ok.
But to me, finding x isn't sufficient to find y because we don't know the sign of y (The square root of x can be either >0 or <0)... So we don't know the sign of y3

I know it's a common trap in the GMAT which is why I had answered that Statements (1) and (2) TOGETHER are NOT sufficient.

Can anyone help me with this one so I know how to answer next time I'm faced with this type of question?

Thx

[mba.dream.2013]

1 is not sufficient as the only possible values for that equation is x = 0 => y = 0 or x =1 => y = 1 and it's already stated that x is NOT equal to y

2. x^3 = 8 => x = 2

if y^2 = x and if you know x, you cannot determine y as you don't know the sign of y. Here is the case is different. Remember in GMAT there is a difference between unsquaring and taking sq. rt.

sqrt (2) is a constant and is always equal to 1.4 and hence you can can determine y. So Answer is B

[das.sk.82]

1 is not sufficient as the only possible values for that equation is x = 0 => y = 0 or x =1 => y = 1 and it's already stated that x is NOT equal to y

sqrt(x) = y

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

for example x=4, y=2
4=2*2 --> condition is OK.

also, x=4 y=-2
4 != -2*2 --> condition is not OK.

Thus <1> it is insufficient IMO.

I hope it is clearer!

[700+]

Finding that x=2 is ok.
But to me, finding x isn't sufficient to find y because we don't know the sign of y (The square root of x can be either >0 or <0)... So we don't know the sign of y3

As far as I know, in GMAT the square root will always be positive. For e.g.,
if x = sq rt (4), then x = +2.

At the same time,
if x^2 = 4, then x = +2 or -2

Now, if x^3 = 8, then x would be only +2.

In this case, from Statement 2
y^3 = sq rt (8). So y would be positive.

[RonPurewal]

i'm going to lock this thread, for two reasons:

1/ the problem has been copied incorrectly; the way the problem currently reads in the original post, it is self-contradictory.
specifically, the statement "x = yx", with the attached condition that √x = y, gives only two possibilities: (0, 0) and (1, 1). but that contradicts the stated fact that x ≠ y.

2/ this problem is not from the GMAT PREP software, so this is the wrong folder for it anyway.

----

@ mbadream2013

1 is not sufficient as the only possible values for that equation is x = 0 => y = 0 or x =1 => y = 1 and it's already stated that x is NOT equal to y

no. if you find a self-contradiction in the problem, that means that the problem hasn't been copied correctly!
NO data sufficiency problem will EVER have "no solution"!

if you see a problem with no solution on a forum, then the original poster has probably just mistranscribed the problem. (if you think you see a problem with no solution on the actual test, then that means YOU are making a mistake.)