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I disagree with explanations given above. Here is my approach:
Stmt (1) indicates that x=y otherwise x^6-y^6=0 does not hold true. Hence, x^3-y^3 is always equal to zero. SUFF.
Stmt (2) is clearly INSUFF because there is no inf. about x.
If my approach is wrong, I would appreciate any other explanations.
Yes, your approach is wrong: \(x^6-y^6=0\) implies that either \(x=y\) or \(x=-y\), for example \(1^6-1^6=0\) and also \(1^6-(-1)^6=0\). To see this algebraically you could rewrite \(x^6-y^6=0\) as \((x^3-y^3)(x^3+y^3)=0\) --> either \(x^3=y^3\), or \(x^3=-y^3\) --> so either \(x=y\) or \(x=-y\). OR \(x^6-y^6=0\) --> \(x^6=y^6\) --> \(x^2=y^2\) --> \(x=y\) or \(x=-y\).
Now, if \(x=y\) then \(x^3-y^3=0\) for any values of \(x\) and \(y\) BUT of \(x=-y\) then \(x^3-y^3=2x^3\) and we need the value of \(x\) (or \(y\)) the get the single numerical value of \(2x^3\). So statement (1) is not sufficient.
(2) y=0 --> clearly insufficient.
(1)+(2) \(y=0\), so \(x=0\) too (as \(x^6-y^6=0\)) and \(x^3-y^3=0\). Sufficient.
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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1- xˆ6 - yˆ6 = 0 As we have an even number (6) it means that X and Y can be either negative or positive. For example. X=3 Y=-3 If we put this values on the equations, then its going to be valid (equal 0)
However, if we put the same numbers on x^3 - yˆ3 we are going to have: 27 - ( -27) = 54
Therefore number 1 is not valid.
2-> This information alone doesn't help anything, we don't know about the X.
If we use both of them together, we are going to know that the only value will be 0. Therefore C
What is the value of x^3 - y^3 ?
30 Nov 2015, 18:45