What is the value of x – y?

Question

(1) x + y = 3y – x
(2) x + y = x^3 + y^3

Source:   Nova GMAT  
Difficulty Level:   600

Luckisnoexcuse · Answer

(1) is sufficient since multiple values of (x,y) like (0,0), (1,1), (-1,-1) satisfy the equation and yield same result for x-y which is 0

(2) is also sufficient since same set of values satisfy the equation and yield same result for x-y

hence (D)

please correct me if i am wrong

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pushpitkc · Answer

(1) x + y = 3y – x
Rewriting this equation, we get x=y. 
Whatever the value of x and y, x-y is always 0.Hence sufficient.

(2) x + y = x^3 + y^3
This is possible when both x and y are 1 and if x=1 and y = -1.
Adding both these values will not yield an unique answer.
Hence insufficient. (Option A)

Luckisnoexcuse · Answer

please correct if i am wrong

-1-(-1) =0

and 
1-1 =0

hence unique answers

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pushpitkc · Answer

This is what i meant. if x=1,y=-1, we get x-y = 2
But if x and y are 1, their difference is 0.

Corrected the solution! Hope that helps

utkarshthapak · Answer

Statement 1 will give x = y. regardless of the value of x and y, answer will be zero. Sufficient.

Statement 2 x + y = x^3 + y^3. (x + y) = (x+y)(x^2 + y^2 - xy) or x^2 + y^2 = 1 + xy. This option doesn't lead anywhere. Insufficient.

Option A should be correct.

What is the value of x – y?

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