Mathematical operation

[alexi_laiho]

If * denotes a mathematical operation, does X* Y = Y * X for all X and Y?
(A) For all X and Y, X * Y = 2 (X^2 + Y^2)
(B) For all Y, 0 * Y = 2Y^2

1. statement (A) alone is sufficient but statement (B) alone is not
2. statement (B) alone is sufficient but statement (A) alone is not
3. both (A) and (B) together are sufficient but none of them alone is sufficient
4. both statements independently are sufficient
5. both (A) and (B) together are not sufficient

[bha]

I think answer is 'A'. What is the OA?

[alexi_laiho]

Yes the OA is A...can you provide the explanation?

[bha]

We have to prove that for all all values of X and Y, X* Y = Y * X i.e if values of X & Y are interchanged, result should still be same...
Stmt1: X * Y = 2 (X^2 + Y^2)...Y*X= 2((Y^2 + X^2)= 2 (X^2 + Y^2)= X*Y....sufficient
stmt2: 0 * Y = 2Y^2..Y*0 = 0 <> 2Y^2...not sufficient..