Is x = y ? (1) x - y = 6 (2) x + y = 0

Question

Is │x│=│y│?
(1) x - y = 6
(2) x + y = 0

GMAT TIGER · Answer

B.

(1) x - y = 6
x = y + 6

x = 0, y = -6
x = 5, y = -1

so insuff..
(2) x + y = 0
x = - y

so lxl = lyl
suff.

aim2010 · Answer

let's assume |x| = |y| => x = y or x = -y 
that is x - y = 0 OR x + y = 0

this, (2) is clearly sufficient.

now is it necessary that x - y = 6? let's see, not possible with x - y = 0 for sure. may be with x + y = 0, yes when x = 3 and y = -3 but these values are not required to make x + y = 0, are they, 4, -4 works too but doesn't make x - y = 6. thus insufficient.

Thus, B

elmagnifico · Answer

S2 is clearly sufficient. But lets examine S1. If x=y+6, that clearly states that X>Y, always. Doesnt this statement answer the question that x will not equal -y?
S1 should be sufficient as well, no?

leonidas · Answer

Thanks guys...... Here is what I got out of your posts:

To find wheather, x-y=0 or x+y=0 (Yes or No question)

Statement I is self-exlanatory, considering statement II,

The values (x,y) => (0,-6) and (5,-1) is not much useful to prove otherwise.

The values (3,-3) and say (9,3) will be useful.
Both the above x and y values meet the condition of x-y=6, but only (3,-3) meets the condition x+y=0 whereas (9,3) does not. Hence we get Yes and No.
There for insufficent.

Greenberg · Answer

Its best to solve absolute value problems as "distance on the number line" problems.

What you are being asked is "is the distance of x from 0 on the number line is equal to the distance of y from 0 on the same line".

This can only be true when x=-y or y=-x or x=y or

hence statement (1) is useless and statement (2) will give you the right answer (Yes)

leonidas · Answer

I agree. viewing it as a distance makes it always easier. I have a habit of complicating things

GMAT TIGER · Answer

if x = 3 and x = -3, x = y+6.

in this case lxl = lyl = 3

amitdgr · Answer

if statement one was x-y=0. Will that be sufficient ? as x = y and |x| = |y|

Is x = y ? (1) x - y = 6 (2) x + y = 0

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