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If X and Y are positive, is X/Y + Y/X > 2? 1. x does not

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If X and Y are positive, is X/Y + Y/X > 2? 1. x does not [#permalink] New post 21 Nov 2007, 06:00
If X and Y are positive, is X/Y + Y/X > 2?

1. x does not equal y
2. x and y are integers which do not have common divisors EXCEPT 1

Last edited by bmwhype2 on 21 Nov 2007, 06:58, edited 1 time in total.
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Re: 12.16 Number Prop & Algebra [#permalink] New post 21 Nov 2007, 06:26
bmwhype2 wrote:
If X and Y are positive, is X/Y + Y/X > 2?

1. x does not equal y
2. x and y are integers which do not have common divisors


Can I take it no common divisors means more than one? Clearly as an integer all will have 1 as a divisor?

If I am right - I take the answer to be E

Statement 1 - x does not equal y:

take 5 and 4 - 5/4 + 4/5 = 2 - answer NO
take 1 and 2 - 2/1 + 1/2 = 2.5 - answer YES

Thus Insufficient


Statement 2 - They are integers without common divisors:

Again take 4 and 5 - answer NO
Take 1 and 2 - answer Yes...

I feel like I am missing something however.
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 [#permalink] New post 21 Nov 2007, 06:34
Expert's post
D

X/Y + Y/X>2
(X^2+Y^2)/XY>2
X^2+Y^2>2XY
X^2-2XY+Y^2>0
(X-Y)^2>0

1. X<>Y ==> (X-Y)^2>0 suff

2. X<>Y (x=y ==> x-common divisor) ==> (X-Y)^2>0 suff

----------------------
"take 5 and 4 - 5/4 + 4/5 = 2 - answer NO" - incorrect
(25+16)/20=41/20>2
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 [#permalink] New post 21 Nov 2007, 07:04
walker wrote:
D

X/Y + Y/X>2
(X^2+Y^2)/XY>2
X^2+Y^2>2XY
X^2-2XY+Y^2>0
(X-Y)^2>0

1. X<Y> (X-Y)^2>0 suff

2. X<Y> x-common divisor) ==> (X-Y)^2>0 suff

----------------------
"take 5 and 4 - 5/4 + 4/5 = 2 - answer NO" - incorrect
(25+16)/20=41/20>2


Wow... bad math on my part - thanks.
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 [#permalink] New post 23 Nov 2007, 10:07
OA is A.

Anyone want to try to explain?
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 [#permalink] New post 23 Nov 2007, 11:07
bmwhype2 wrote:
OA is A.

Anyone want to try to explain?


we simplified the stem down to
(x-y)^2 > 0

1. it is given that both numbers are positive. it does not matter which one is bigger because when we square the difference it becomes a positive number. any positive number is bigger than 0.

SUFF

2. if x=y and they are both 1, then 0^2 is not bigger than 0

insuff
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 [#permalink] New post 23 Nov 2007, 12:21
Expert's post
I've likely omitted " EXCEPT 1" :(
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 [#permalink] New post 23 Nov 2007, 13:32
What is the value of x=0.9 and Y=0.1 (X,Y can be a decimal since they is not specified as integers).Value will be less than 2
Also X=2,Y=1 will be greater than 2

So, A alone cannot solve this.
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--gregspirited

  [#permalink] 23 Nov 2007, 13:32
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If X and Y are positive, is X/Y + Y/X > 2? 1. x does not

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