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# If x/y >2, is 3x+2y<18? 1. x-y is less than 2 2. y-x

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VP
Joined: 22 Nov 2007
Posts: 1079
If x/y >2, is 3x+2y<18? 1. x-y is less than 2 2. y-x [#permalink]

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22 Jan 2008, 22:54
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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
Manager
Joined: 04 Jan 2008
Posts: 83

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24 Jan 2008, 11:59
A
we are given x/y >2, so x is more than double y
S1 gives, x-y < 2 , consider some values 2,4 or 4,8 or 5, 10 or 50,100
only values lesser than 2,4 will satisfy S1.
when we substitute any of those values in given eqn, it will be less than 18.
S2, gives y-x<2 or x-y>2, this gives many values for x and y which may or may not exceed 18

So, A
Re: another inequality   [#permalink] 24 Jan 2008, 11:59
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