inequality

[demoskopico]

If x/y >2, is 3x+2y<18?

1. x-y is less than 2
2. y-x is less than 2

i solved this ds in this way:

if y>0 then x>2y
if y<0 then x<-2y

1. consider the case in which y>0

x<y+2
-x<-2y

thus y<2 and x<4 ans our inequality is true in all cases

case y<0:

x<-2y
x<2+y

3y<-2, thus y<-2/3 and x<4/3

thus 1. seems suff

2.let's try with y>0

we get x>-4 and y>-2 ...so we don't know if our ineq. is verified...insuff

OA is A.

I spend too much time in solving this way. is there any other quicker method?
thanks a lot

[kevin]

Realise that if x and y are both negative, 3x + 2y is obviously less than 18.