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

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

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New post 13 Nov 2008, 23:27
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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
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Re: DS: Hard one [#permalink]

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New post 14 Nov 2008, 00:46
A.
from (1), \(x>2\)y and \(x<y+2.\)

so \(2y<x<y+2\) ==>\(y<2\).

now \(3x+2y=3(x-y)+5y\)
\(=(<6) + (<10)\)
\(=<18\)-- sufficient.

from (ii), \(x>2y\)and \(x>y-2\) --insuff

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Re: DS: Hard one [#permalink]

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New post 14 Nov 2008, 01:52
1st statement is easy. I didn't understand how second statement is insufficient /sufficient.
Can anybody explain statement 2 ?
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Re: DS: Hard one [#permalink]

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New post 14 Nov 2008, 02:39
Hi prasun84..

you can't say x>2y by just seeing the (x/y)>2.
coz you never know y is +ve or -ve.

Let see how to solve this,

Given Data

(x/y)>2 ----------- 1and
1) x-y < 2

So, x <y+2
substitute in 1) we get,

y+2/y > 2
then 1+ 2/y >2,
2/y>1

Reciprocate, y/2 <1
so y<2 ------------------- 2

from 1) x-y < 2, we also know x-2 <y
sub this,

x/x-2 >2
reciprocate,
(x-2)/x <2, ... 1-2/x <2 ... -2/x < 1
Recipricate,
-x/2 >1.. -x>2 or x < -2 --------- 3) So SUFF

since x <-2 and y<2 both shud be negative to make (x/y)>2.
if both are negative then 3x+2y<18.

2) y-x < 2

y < 2+x

x/(x+2) >2
reiprocate,
1+2/x <2
2/x < 1
reciprocate,
x/2 >1
x>2 ----------------------- 1)

also, x > y-2
so 1-2/y >2
-2/y > 1
reciprocate, -y<2.. y>-2 -------- 2)

So insuff..
since to satisfy x/y > 2 both should be positive and since they are postitive we cant say 3x+2y<18..


So A....

Any comments...
Note: i have substituted the values directly even if it is less or greater.. just for approx.

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Re: DS: Hard one [#permalink]

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New post 14 Nov 2008, 03:57
Bidisha, whats the QA for this one ?

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Re: DS: Hard one   [#permalink] 14 Nov 2008, 03:57
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If (x/y)>2, is 3x+2y<18? (1) x-y is less than 2 (2)

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