Question from GMAT Prep

[bikash123]

Is |x-Y| >|X|-|Y| ?

I y<x
II xy<0


OA later

[outreach]

D

1)
x=2,y=1
equal

x=-1,y=-2
satisfies

x=0,y=-1
satisfies

suff

2)
x=-1,y=2
satisfies

x=1,y=-2
satisfies

suff

[4GMAT_Mumbai]

Hi,

Beg to differ on this ....

Is |x-Y| >|X|-|Y| ?

I y<x
II xy<0

Statement 1:

Y < X implies X > Y

When both X and Y are positive;

|x-Y| = X - Y
|X|-|Y| = X - Y

Here, |X-Y| = |X|-|Y|.

When both X and Y are -ve

|x-Y| = distance between X and Y
|X|-|Y| = negative value of the distance between X and Y.

Here, |X-Y| > |X|-|Y|.

As we get conflicting answers, stmt 1 is insufficient.

Statement 2:

The statement says that between X and Y; one is +ve and the other is -ve

|X-Y| = sum of the distances of each of X and Y from the origin
|X| - |Y| = difference between the distances of X and Y from the origin.

Here, I am using the interpretation that |A| = distance of A from the origin.

Since sum of two +ve numbers will always be greater than the difference b/w the two +ve numbers; we can deduce that |X-Y| will always be greater than |X|-|Y|.

Hence, stmt 2 is sufficient.

My choice would be B.

This is a classic trap case - The use of 'proving by examples' failing with an interesting mix of inequalities and modulus.

Hope this helps. Thanks.

[bikash123]

B
i solved this problem by plugging the numbers.

[ashish2104]

IMO B.

1) y<x, consider two cases: y=1 & x=3 then |x-y| = |x|-|y|
when y=-3 and x=-2 then |x-y| > |x|-|y|
hence not sufficient

2)xy<0 implies either x is -ve and y is +ve or x is +ve and y is -ve
with this in mind, we will again consider two cases:
x=-2 and y=3, then |x-y| > |x|-|y|
x=4 and y =-2, then |x-y| > |x|-|y|
hence sufficient.

[san2009]

answer should be B

when i look at the original question .... i rephrased to the following:
do x and y have opposite signs?
the reason being:
if x and y have the same sign, then there will be no difference between abs(x-y) and abs(x) - abs (y)
try numbers and see for yourself
on absolute equations such as this, this is generally my first strategy -- it usually works b/c gmat doesnt have too many complicated equations
anyways, with the rephrasing, the statements are kinda easy to interpret.