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

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

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New post 04 Oct 2008, 01:47
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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
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Re: DS - Inequality 2 [#permalink]

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New post 05 Oct 2008, 14:08
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.

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Re: DS - Inequality 2 [#permalink]

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New post 05 Oct 2008, 22:28
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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

So my answer is A

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Re: DS - Inequality 2 [#permalink]

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New post 05 Oct 2008, 22:37
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

So my answer is A


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.
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Re: DS - Inequality 2 [#permalink]

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New post 05 Oct 2008, 22:54
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

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Re: DS - Inequality 2 [#permalink]

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New post 05 Oct 2008, 23:03
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
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Re: DS - Inequality 2 [#permalink]

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New post 18 Oct 2008, 18:35
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?

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Re: DS - Inequality 2 [#permalink]

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New post 18 Oct 2008, 23:05
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

So my answer is A

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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Re: DS - Inequality 2   [#permalink] 18 Oct 2008, 23:05
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Ineqp) If (x/y)>2, is 3x+2y<18? (1) x-y is less than 2

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