What is the value?

[RadiumBall]

If sqrt(xy) = xy, what is the value of x + y?

(1) x = -1/2
(2) y is not equal to 0

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

(1) x = yx
(2) x^3 = 8

[Anurag@Gurome]

If sqrt(xy) = xy, what is the value of x + y?

(1) x = -1/2
(2) y is not equal to 0

√(xy) = xy or xy = (x^2)(y^2)

(1) x = -1/2 implies -y/2 = (y^2)/4or y = 0, -2
Since we don't know the exact value of y, so we cannot find x + y.
NOT SUFFICIENT.

(2) y is not equal to 0 implies y can take any value such that √(xy) = xy. But this is NOT SUFFICIENT to find the value of x + y.

Combining (1) and (2), we know that y is not 0, so y = -2. Hence, x + y = -1/2 - 2, which can be further solved.

The correct answer is C.

[RadiumBall]

Thanks Anurag.

Could you kindly also answer the other question. Actually I think the two are related and so posted them together.

[gig92]

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

(1) x = yx
(2) x^3 = 8

Stmnt1

x can be anything but y has to be 1 for x(y-1) = 0 to be true (x not equal to y)
so suffi

Stmnt 2
given x^3 = 8 also
x = +2 as given sqrt(x) = y; possible only when x > 0 which will give some value to y (y > 0 too).
so one can calculate y^3.
so suffi


IMO Ans: D

[clock60]

hi guys i have strange feelings concerning second problem, to me it is poorly constructed

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

according to the problem x and y can`t be 0
if x=0 then 0^1/2=0 and x does not equal y

and also x can`t be 1
if x=1, then 1^1/2=1, x=y=1 and again x does not equal y

now to the problem
(1) x-xy=0, x(1-y)=0, x=0 or y=1, but according to my above reasoning it is not possible either for x=0, or for y be 1
at least 1 st insuff
(2) x^3=8 only possible value for x=2 so we can calculate y^3 suff
but statements here contradict each other, we must verify the source
or i as usual missing something?

[Night reader]

only second problem (selected in bold)

Given: x <> y, x=y^2 (Since square roots can't be -ve). Find y^3-?

st(1) x=xy, As x=y^2, x cannot be 0, therefore cancel x on both sides (x is not equal to y) --> y=1, y^3=1 Sufficient;
st(2) x^3 = 8, x=2 and y^3=x*Sqrt(x) OR y^3= 2*Sqrt(2) Sufficient;

answer D is supplying this question with two answers y^3 = {1; 2*Sqrt(2)}

not conventional Gmat question?

If sqrt(xy) = xy, what is the value of x + y?

(1) x = -1/2
(2) y is not equal to 0

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

(1) x = yx
(2) x^3 = 8

[RadiumBall]

Yes the OA for 1 is C and D for 2. But yeah may be 2 is not conventional GMAT question which is why even I was not convinced.

Thanks anyway guys.