jcnasia wrote:Here's a fun proof to show that if x + 2|y| = 0 and y + 2|x| = 0 then |x| + |y| = 0.

x + 2|y| = 0 and y + 2|x| = 0
=> x + y + 2|x| + 2|y| = 0 //add the two equations to each other
=> -1/2(x + y) = |x| + |y| //rearrange the equation

-1/2(x + y) <= |-1/2(x + y)| //since absolute value of a number is never less than the number
=> -1/2(x + y) <= 1/2(|x + y|) //rearrange inequality

1/2(|x + y|) <= 1/2(|x| + |y|) //since |x + y| is always less than or equal to |x| + |y| (see below for proof of this)
1/2(|x| + |y|) <= |x| + |y| //since 1/2 of a non-negative number is always less than the whole number

By combining all these inequalities, we get...
-1/2(x + y) <= 1/2(|x + y|) <= 1/2(|x| + |y|) <= |x| + |y|

1/2(|x| + |y|) = |x| + |y| //since -1/2(x + y) = |x| + |y| and 1/2(|x| + |y|) is between these two values
=> 0 = 1/2(|x| + |y|) //rearrange the equation
Therefore: 0 = |x| + |y| //rearrange the equation

Well, to me, it's a fun proof, but you should probably use one of the previous solutions on the actual gmat so you don't waste time.

[email protected] wrote:Can't we rephrase the question as is X and Y equal to zero.
By which we can say from A) we can say x=-2 and y+/-1.so definitely x and y both are not equal to zero so is it not option D. Please correct me if I m missing some logic

[email protected] wrote:Can't we rephrase the question as is X and Y equal to zero.
By which we can say from A) we can say x=-2 and y+/-1.so definitely x and y both are not equal to zero so is it not option D. Please correct me if I m missing some logic