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Mathematical operation

Expert replies
by alexi_laiho » Wed Aug 06, 2008 5:29 am
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
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Source: — Data Sufficiency |

by bha » Wed Aug 06, 2008 5:38 am
I think answer is 'A'. What is the OA?
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by alexi_laiho » Wed Aug 06, 2008 6:23 am
Yes the OA is A...can you provide the explanation?
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by bha » Wed Aug 06, 2008 7:25 am
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..
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