Quote:
11. Is |x+y|>|x-y|?
(1) |x| > |y|
(2) |x-y| < |x|
Question Stem : Is the distance between X and -Y greater than the distance between X and Y?
Note : Using number line approach.
St. (1) : |x| > |y|
OR, The distance between X and the origin is greater than the distance between Y and the origin.
Now we can have two cases :
(a) When X is positive : In this case, X > Y for the above condition to be true.
_________|_________|_________|_________|_________|__________
_________________-Y______Origin______Y........ Region of X.........
Thus we can see that the distance between X and - Y will always be greater than the distance between X and Y. Hence question stem is true.
(b) When X is negative : In this case, X < -Y for the statement to be true.
_________|_________|_________|_________|_________|__________
.... Region of X.....-Y_____Origin_______Y___________
Thus we can see that the distance between X and -Y will always be less than the distance between X and Y. Hence, question stem becomes false.
Due to conflicting statements, St (1) becomes Insufficient.
St. (2) : |x-y| < |x|
OR, the distance between X and Y is less than the distance between X and the origin.
Now again let us consider the different cases :
(a) When X is positive : For the statement to be true and for X to be positive, X must be greater than Y/2. For any value of X less than Y/2 the statement will become false. The statement will be true for any value greater than Y/2.
Thus we see that only one case comes into the picture. Now let us see how it relates to the question stem.
_________|_________|____;____|_________|________
________-Y____Origin__y/2...Y...... Region of X....
Thus we can see that the distance between X and - Y will be greater than the distance between X and Y for all values of X > Y/2. Thus question stem is true.
St. (2) is sufficient.
Answer : B
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Click below to check out some great tips and tricks to help you deal with problems on Remainders!
http://gmatclub.com/forum/compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942
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