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# If X/Y > 2 . Is 3X + 2Y < 18 ? 1. X-Y < 2 2. Y-X

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Manager
Joined: 28 Jan 2004
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Location: India
If X/Y > 2 . Is 3X + 2Y < 18 ? 1. X-Y < 2 2. Y-X [#permalink]

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31 May 2009, 22:46
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If X/Y > 2 . Is 3X + 2Y < 18 ?

1. X-Y < 2
2. Y-X < 2

this is a demo. question by walker which he solved by using graphical technique. I tried to solve with graphical techniques but am not able to grasp it completely.

Can you guys solve it without using graphical approach.
Senior Manager
Joined: 16 Jan 2009
Posts: 349
Concentration: Technology, Marketing
GMAT 1: 700 Q50 V34
GPA: 3
WE: Sales (Telecommunications)

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01 Jun 2009, 15:35
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Lahoosaher

Manager
Joined: 08 Feb 2009
Posts: 141
Schools: Anderson

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01 Jun 2009, 18:33
Manager
Joined: 14 May 2009
Posts: 189

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02 Jun 2009, 00:02
mdfrahim wrote:
If X/Y > 2 . Is 3X + 2Y < 18 ?

1. X-Y < 2
2. Y-X < 2

this is a demo. question by walker which he solved by using graphical technique. I tried to solve with graphical techniques but am not able to grasp it completely.

Can you guys solve it without using graphical approach.

Solved via inequality manipulation

$$X/Y>2$$
==> $$X>2Y$$ if y>0
==> $$X<2Y$$ if y<0

Question:($$3X+2Y<18$$)?

(1) X-Y<2

X<Y+2

if y>0 $$2Y<X<Y+2$$
==> $$2Y<Y+2$$
==> $$Y<2$$
==> $$0<y<2$$ (from assumption that y>0)
and hence $$0<x<y<2$$
This gives us a YES answer

if y<0 $$X<2Y$$ and logically $$2Y<2*0=0$$
so $$x<2y<0$$
so X must be negative as well.
negative+negative <0
This gives us a YES answer

(1) is sufficient

(2) Y-X < 2
X>Y-2

==> $$X>2Y$$ if y>0
==> $$X<2Y$$ if y<0

if y<0 2y<0 x<2y<0
Both negative, YES

if y>0 2y>0 x>2y>0 x>0

also 0<y<2+x
so x>-2 but it can't be since x>0

But that's it I think. Let's pick numbers.

$$X=50, Y=2$$.
All inequalities satisfied, but 3X+2Y is NOT less than 18.

Final Answer, $$A$$.
_________________

Re: DS - Inequality   [#permalink] 02 Jun 2009, 00:02
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