Question 20, end of chapter CAT on Manhattan (DS)

[tex.boonjue]

If x is not equal to y and if sqrt(x) = y, what is the value of y^3 ?

(1) x = y^x

(2) x^3 = 8


I solved for x is in the original prompt: x = y^2

Plugged in the value of x into statement 1: y^2 = y^x so then x = 2

Then we have sqrt(2) = y , square both sides

and we get that y = plus or minus sqrt(2)

which will give different answers for when y is cubed, which is what the question is asking.


Can someone please explain where I went wrong? The answer is D by the way.

[jnelson0612]

If x is not equal to y and if sqrt(x) = y, what is the value of y^3 ?

(1) x = y^x

(2) x^3 = 8


I solved for x is in the original prompt: x = y^2

Plugged in the value of x into statement 1: y^2 = y^x so then x = 2

Then we have sqrt(2) = y , square both sides

and we get that y = plus or minus sqrt(2)

which will give different answers for when y is cubed, which is what the question is asking.


Can someone please explain where I went wrong? The answer is D by the way.

Ah yes, this is confusing and trips up many people. For GMAT purposes, the square root of any number is the positive root only, according to the GMAT. So the square root of 2 is only positive 1.4, not negative 1.4.

This is tricky because when something is squared, the result becomes positive whether or not the original number is positive or negative. This is why many students become confused. Let me give you some examples so things are clear:

1) If x^2=25, then x could be 5 or -5
BUT
2) The square root of 25 is ONLY the positive value, 5.

Just remember this and you will be fine!