If x-y > 10, is x-y > x+y ?

[alysekilleen]

If x-y > 10, is x-y > x+y ?

1) x = 8

2) y = -20

This is a data sufficiency question.

The correct answer is d.

An explanation from an instructor would be much appreciated.

Best,
Alyse

[gokul_nair1984]

Hi there.. I'm not an instructor but will try to explain this stuff..

If x-y > 10, is x-y > x+y ?

First of all rephrase the stem...x-y>x+y...=>-y>y..That means we just have to check if y is negative as only the negative of a negative number will be positive.

Case 1: x = 8(Given)

This means y>-2....Hence Sufficient

Case 2: y = -20...this again is Self Sufficient

Hence the option is D

[RonPurewal]

gokul, nice solution.

i guess we should probably elaborate on this:

Case 1: x = 8(Given)

This means y>-2....Hence Sufficient

this comes from plugging x = 8 back into the original inequality from the prompt (x - y > 10).
that gives
8 - y > 10
-y > 2
divide by -1 (don't forget to flip around the ">") to give
y < -2

therefore, y is negative.