If x and y are two numbers on the number line, is x + y = 0 ?

Question

If x and y represent number on the number line, is x + y = 0?

(1) Distance between x and 0 is the same as distance between y and 0.
(2) |x-y| = |x| +|y|

GMATbuster's Collection

Chethan92 · Accepted Answer

From S1:

Distance between x and 0 is the same as the distance between y and 0.
Let say x = 4 and y = -4. The distance between x and 0 and y and 0 are same, i.e, 4.
and x+y = 0
Let say x = 4 and y = 4. The distance between x and 0 and y and 0 are same, i.e, 4.
But, x+y = 8.
INSUFFICIENT.

From S2:

|x-y| = |x| +|y|
X and Y arre of different signs.
But what are the values of X and Y? No info.
INSUFFICIENT.

Combining both:
X and Y are of opposite signs and the distance are same.
Hence x+y = 0
SUFFICIENT.

C is the answer.

nick1816 · Answer

Statement 1-
|x|=|y|
If x and y have same signs then x+y is not 0
If x and y have opposite signs then x+y is 0

Statement 2

|x-y|=|x|+|y|
which implies that x and y have opposite signs.

If |x|=|y|, then x+y is 0.
If |x|≠|y|, then x+y≠0

Combining both statements 
x and y are equal in magnitude, and have opposite signs.
Hence x+y=0
Sufficient

GMATBusters · Answer

Hi

The inference from Statement 2 is not entirely correct.
St 2: |x-y| = |x| +|y|

Correct inference:  X and Y are of opposite sign or either X or Y or both = 0

gvij2017 · Answer

If x and y are two numbers on the number line, is x + y = 0 ?

Let's talk about the language of the question stem.

x and y are two numbers on the number line. Now "two numbers" may be same or distinct. In this case, if two number lies on the same side of 0, they are not two numbers, but one number. I think that the term "two numbers" itself indicates that both numbers are different.

Is it necessary to explicitly mention identical or distinct for such questions? Or should I assume numbers different than each other?

Please clarify this. I have done numerous question wrong because of this confusion.

Chethan92 · Answer

Hi  gvij2017 , If you see the statement 1. X and Y can be the same or different numbers.
If it is not explicitly mentioned then X and Y can be same or different.

RichaSingha · Answer

hi,
Is the following not a valid inference to draw from statement 2?
|x-y| = distance between x and y
|x| = distance of x from origin
|y| = distance of y from origin
hence, from st 2: distance between x and y is equal to distance of x from origin + distance of y from origin.
This should mean x and y are either of opposite signs and equal magnitude or both 0. In both the cases x+y is equal to 0.
If true, B should be the answer.

Chethan92 · Answer

Hi,  RichaSingha ,

Given, |x-y| = |x|+|y|
From this, yes x and y are of different signs or 0, but not necessarily equal. What if x = 4 and y = -3
|x-y| = |x|+|y| = 7 = 7. Satisifes. and x+y = 4-3 = 1. not equal to zero.
What if x = 3 and y = -3
|x-y| = |x|+|y| = 6 = 6. Satisifes. and x+y = 0.
Both Yes and No are possible. Hence B is not sufficient.

Hope this helps.

VeritasPrepErika · Answer

So you're right all the way up until the last three sentences. We DO know that if x and y don't both equal 0, they must have opposite signs. However,  we DON'T know that they must be of equal magnitude.

Let's take x = 5 and y = -4 as an example. Testing this with Statement 2, we get |5 - (-4)| = |5| + |- 4| --> |9| = 5 + 4 --> 9 = 9. So this works with Statement 2! However, it gives x + y = 1.

On the other hand, if x and y do have equal magnitude as well as opposite signs (as in x = 5 and y = -5), we will get x + y = 0.

So given Statement 2, we can get a YES or a NO, making it insufficient.

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If x and y are two numbers on the number line, is x + y = 0 ?

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