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

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

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New post 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.

Kudos [?]: 28 [0], given: 4

Senior Manager
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Joined: 16 Jan 2009
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Kudos [?]: 232 [0], given: 16

Concentration: Technology, Marketing
GMAT 1: 700 Q50 V34
GPA: 3
WE: Sales (Telecommunications)
Re: DS - Inequality [#permalink]

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New post 01 Jun 2009, 15:35
Could you please post the link to the graphical solution?
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Lahoosaher

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Re: DS - Inequality [#permalink]

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New post 01 Jun 2009, 18:33

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Re: DS - Inequality [#permalink]

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New post 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, \(A\).
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Hades

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Re: DS - Inequality   [#permalink] 02 Jun 2009, 00:02
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If X/Y > 2 . Is 3X + 2Y < 18 ? 1. X-Y < 2 2. Y-X

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