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]

21 Nov 2007, 07:00

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, 07:58, edited 1 time in total.

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Re: 12.16 Number Prop & Algebra [#permalink]

21 Nov 2007, 07:26

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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21 Nov 2007, 07:34

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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21 Nov 2007, 08:04

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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23 Nov 2007, 11:07

OA is A.

Anyone want to try to explain?

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23 Nov 2007, 12:07

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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23 Nov 2007, 13:21

I've likely omitted " EXCEPT 1"

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23 Nov 2007, 14:32

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.
_________________

--gregspirited

[#permalink] 23 Nov 2007, 14:32

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

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

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