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Source: — Data Sufficiency |
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by sanju09 » Mon Jul 26, 2010 5:24 am
mathewmithun wrote:If x + y^2= ( x + y ^2) ^2, what is the value of y?

( 1) x = y ^2
( 2) xy ^2 = 0


I feel E is the answer but some can help me to cross verify...

If x + y^2 = (x + y ^2) ^2, then

x + y^2 = x^2 + 2 x y^2 + y ^4

(1) When x = y ^2, x + y^2 = x^2 + 2 x y^2 + y ^4 becomes

y^2 + y^2 = y^4 + 2 y^4 + y ^4, or

2 y^2 = 5 y^4

It's a 4-degree in y, no unique y can be known. Insufficient

(2) When x y ^2 = 0, at least either x or y is 0; moreover we can have

x + y^2 = x^2 + y ^4

if x is 0, and y is not, we get 2 non zero values for y, otherwise y is 0. Insufficient

When taken together, we realize that [spoiler]y is 0.

C[/spoiler]
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by kvcpk » Mon Jul 26, 2010 5:28 am
mathewmithun wrote:If x + y^2= ( x + y ^2) ^2, what is the value of y?

( 1) x = y ^2
( 2) xy ^2 = 0


I feel E is the answer but some can help me to cross verify...
x + y^2= ( x + y ^2) ^2

x = y ^2
Replace in the above
2x = 4x^2
x=0 or x=1/2
when x=0, y=0, when x=1/2, y=1/sqrt(2)
2 values for Y, hence INSUFF

xy ^2 = 0
means either x=0 or y=0 or both are 0

Doesnt give any info about y exactly.
INSUFF

Combining:

x = y^2 and xy^2 = 0
By substituting, x^2 = 0 -> x=0
we get y=0
SUFF

pick C
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