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

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VP
Joined: 30 Jun 2008
Posts: 1026
Ineqp) If (x/y)>2, is 3x+2y<18? (1) x-y is less than 2 [#permalink]

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04 Oct 2008, 00:47
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(Ineqp)

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

(1) x-y is less than 2
(2) y-x is less than 2
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

SVP
Joined: 17 Jun 2008
Posts: 1529
Re: DS - Inequality 2 [#permalink]

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05 Oct 2008, 13:08
D for me too.

From stmt1: x - y < 2 or x < y + 2

Now, x/y > 2 or, (y+2)/y > 2 or 1 + 2/y > 2 or 2/y > 1 that means, y is positive and less than 2....i.e. 0<y<2 and hence 0 < x < 4.

For maximum values of x = 4 and y = 2, 3x + 2y = 16 < 18. Hence, sufficient.

From stmt2: y-x < 2 or x > y-2.

Now, x/y > 2 or (1-2/y) > 2 or -2/y > 1 and this is possible only when 0>y>-2 and consequently, 0 > x > -4.

Again, 3x + 2y < 18 for any values of x and y. Hence, sufficient.
Manager
Joined: 30 Sep 2008
Posts: 111
Re: DS - Inequality 2 [#permalink]

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05 Oct 2008, 21:28
2
KUDOS
nice question

x/y > 2 then x,y must be both positive or both negative

if x,y are both negative, the inequation is always correct

so if x,y are both positive and the inequation is incorrect so the statement is insuff

x/y > 2 <=> x > 2y <=> 2y - x < 0 & x,y > 0

(1)
x - y < 2 (I)
2y - x < 0 (II)
(I) & (II) <=> y < 2 (III)
(I) & (III) <=> x < 4

so 3x+2y< 12 + 4 = 16 < 18

sufficient

(2)
we have x/y > 2 <=> x > 2y > y <=> y -x < 0
y - x < 2 (no new information)

so (2) insuff, we can check by giving it example

x = 32, y = 15 => 3x+2y > 18

VP
Joined: 30 Jun 2008
Posts: 1026
Re: DS - Inequality 2 [#permalink]

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05 Oct 2008, 21:37
lylya4 wrote:
nice question

x/y > 2 then x,y must be both positive or both negative

if x,y are both negative, the inequation is always correct

so if x,y are both positive and the inequation is incorrect so the statement is insuff

x/y > 2 <=> x > 2y <=> 2y - x < 0 & x,y > 0

(1)
x - y < 2 (I)
2y - x < 0 (II)
(I) & (II) <=> y < 2 (III)
(I) & (III) <=> x < 4

so 3x+2y< 12 + 4 = 16 < 18

sufficient

(2)
we have x/y > 2 <=> x > 2y > y <=> y -x < 0
y - x < 2 (no new information)

so (2) insuff, we can check by giving it example

x = 32, y = 15 => 3x+2y > 18

Wow ! Thanks. I get the statement 1 part from your post. Can you explain the statement 2 part, I don't seem to get it.
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Manager
Joined: 30 Sep 2008
Posts: 111
Re: DS - Inequality 2 [#permalink]

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05 Oct 2008, 21:54
yeah

x/y > 2 so x > 2y

(As y > 0, then 2y > y)
=> x > 2y > y
=> x > y
=> y - x < 0 < 2

=> y - x < 2

So (2) is obvious if x,y > 0 and x/y>2 which give no more information
VP
Joined: 30 Jun 2008
Posts: 1026
Re: DS - Inequality 2 [#permalink]

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05 Oct 2008, 22:03
So you proceeded the question by assuming that x and y are positive. Nice. I never thought of such approach. Thanks lyla. +1 for you
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Manager
Joined: 12 Feb 2008
Posts: 177
Re: DS - Inequality 2 [#permalink]

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18 Oct 2008, 17:35
amitdgr wrote:
So you proceeded the question by assuming that x and y are positive. Nice. I never thought of such approach. Thanks lyla. +1 for you

You cannot just assume that x is positive. Based on what you assume that?
VP
Joined: 17 Jun 2008
Posts: 1373
Re: DS - Inequality 2 [#permalink]

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18 Oct 2008, 22:05
lylya4 wrote:
nice question

x/y > 2 then x,y must be both positive or both negative

if x,y are both negative, the inequation is always correct

so if x,y are both positive and the inequation is incorrect so the statement is insuff

x/y > 2 <=> x > 2y <=> 2y - x < 0 & x,y > 0

(1)
x - y < 2 (I)
2y - x < 0 (II)
(I) & (II) <=> y < 2 (III)
(I) & (III) <=> x < 4

so 3x+2y< 12 + 4 = 16 < 18

sufficient

(2)
we have x/y > 2 <=> x > 2y > y <=> y -x < 0
y - x < 2 (no new information)

so (2) insuff, we can check by giving it example

x = 32, y = 15 => 3x+2y > 18

On of the toughest types of qustions in quant is inequalities !!you have realy given a very good tip to solve such !!!
Even I got A but with some confusion !!thanks for sharing the approach !!
+1 for u
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cheers
Its Now Or Never

Re: DS - Inequality 2   [#permalink] 18 Oct 2008, 22:05
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