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a)X Y X = X, in this case, if X is -1 then Y is 1, and if X is 1 then y is 1. Hence, xy can have 2 values .. xy =-1 or xy =1

b) Y X Y=Y, the same as above. Y can be -1, or 1, and x is 1, therefore XY can be -1, or 1.

If x is other -1 and y is 1, then only one statement is satisfied. (Statement - A). And if y is -1 and x is 1, then it satisfies statement B.

Combining both, there is only one value, that is if X is 1, and y is 1 only then both satifies both the statments. If either of them is -1 or if both are -1, we do not satisfy both statements.

Answer is C.
Correct me, if wrong.
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Giving another SHOT

Last edited by carsen on 07 Jul 2004, 04:30, edited 1 time in total.

in part A if x =-1 then y = -1 and not 1 similarly in part B if y =-1 then x = -1 and not 1

1.xyx=x
2.yxy=y

If we substitute the values as mentioned by you...

If X is -1, then Y=-1, then we get the anser for statement A as -1
Statement 1 = -1 x -1 x -1 = -1 (this violate the original equation)

The same case for Statement 2.
If y=-1, and X=-1, then the final result will be -1 (-1 x -1 x -1 =-1). This again will violate the original statement 2.

Hence, if x is -1, then y has to 1, to satisfy statment 1, and similarly, for statement b, if y is -1, then x has to be 1 to satisfy the original statement 2.

Combing both, only one value can satisfy both equations, that is when, x is 1, and y is 1. Hence the answer is C.

I hope, i have explained better in here. If not, let me know, or perhaps, correct me, if my focus is wrong.
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You know, I got my mind fixed to this equation instead ..

1.xyx=x => my mind got fixed to this equation as xyx=1
2.yxy=y => my mind got fixed this equation as yxy=1

My mistake. I did crap on the above explaination, with the misinterptn. Sorry about girl. I need to re-read the whole thing again. Thanks for correcting me.

The answer is E. (Man, i need to focus, and I have just 2 weeks to go).
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From 1) x = 0 OR xy = 1. Not sufficient. Rule out A and D.
From 2) y = 0 OR xy = 1. Again Not sufficient. Rule out B.
Combining the 2. xy = 1 OR xy = 0 (since x and y can both be 0). Again Not sufficient. Rule out C.

(1) xyx = x --> xy = 1 or x = 0 --> insufficient (2) yxy = y --> xy = 1 or y = 0 --> insufficient

(1)+(2) --> xy = 1 or x=y=0 --> insufficient.

hardworker_indian: In your approach, you should take the combination of the 2 statements rather than the interception.

I have a fundamental difficulty accepting E here. I could've sworn that Kaplan teaches you to look for interception -- hence my thought-flow was same as hardworking indian's.

alright, I finally realized why answer is E here
x and y could both be zeros in both equations (thus eliminating the possibility that xy=1), and both equations would still equal 0.

the lesson learned here is that interception method does not apply when alternative solutions exist