Number property Homework question

[raajpagare]

I have a question for this problem in number property homework

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

(1) x = y^x

(2) x^3 = 8

My Solution

sq_rt(x)=y
i.e. x=y^2

Now

(1) x=y^x

y^2=y^x

i.e x=2

therefore y^3=y^2*y=2*sq_rt(2) =2* (+- 1.41)

this gives 2 values which means its INSufficeint

Same way

(2) x^3=8 i.e x=2 and we can deduce the same thing from top
y^3=y^2*y=2*sq_rt(2) again insufficient


But in the solution they considered both A and B to be sufficient. How can that be?

[loving.achin]

Actually your logic is perfectly valid, but there is a slight twist added to the same for GMAT.

Quoting from Chapter 6 in Number properties guide :-
`` Unlink even exponents, which yield both a positive and negative number, roots have only one solution. When we take an even root(a square root, a 4th root ...) a radical sign means ONLY the nonnegative root of a number. Thus 4^.5 only means a positive 2. "

Hence,
(1) x = y^.5 => x=2 => y = 2^.5 => sqrt(2) SUFFICIENT
(2) x = 8^.33=> x=2=> y = 2^.5 => sqrt(2) SUFFICIENT

I hope it clears your doubt.

Thanks
Achin

[mschwrtz]

Exactly right loving.achin, ty.