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jaspreetsra
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jaspreetsra
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Is |x| + |y| = 0?
|x| + |y| = 0, only possible when x=y=0. and if x=y=0, then I & II both follows. I don't know what will be the option.
|x| + |y| = 0, only possible when x=y=0. and if x=y=0, then I & II both follows. I don't know what will be the option.
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.
This seems like serious overkill.
Here's an easier proof:
x + 2|y| = 0
x = -2|y|
Then
y + 2|x| = 0
y + 2|-2|y|| = 0
y + 4|y| = 0
Hence y = 0.* Plugging this back into x + 2|y| = 0, we find that x also = 0, so we're done.
* If this step doesn't make sense, think of it this way. 4|y| = -y says that y is four times as far from 0 as is -y. But y and -y are the SAME distance from 0! So this won't work for any value of y other than 0 itself.
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
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
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GMATGuruNY
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Does |x| + |y| = 0?[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
Statement 1: x + 2|y| = 0
Statement 1 is satisfied by x=-2 and y=1, since -2 + 2|1| = 0.
If x=-2 and y=1, does |x| + |y| = 0?
NO.
Statement 1 is also satisfied by x=0 and y=0, since 0 + 2|0| = 0.
If x=0 and y=0, does |x| + |y| = 0?
YES.
Since the answer is NO in the first case but YES in the second case, INSUFFICIENT.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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I like the idea, and x = y = 0 is one solution ... but it isn't the ONLY solution, so we can't reduce the question simply to that. (For an intuitive example, consider the question "Am I in Africa?" If I say, "I'm in Egypt", then the answer to the question is yes, but that doesn't CHANGE the question to "Am I in Egypt?")[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
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deepak4mba
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