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# x, y are positive integers, if 1/x + 1/y <2, which of the

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SVP
Joined: 04 May 2006
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x, y are positive integers, if 1/x + 1/y <2, which of the [#permalink]

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12 May 2008, 23:48
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x, y are positive integers, if 1/x + 1/y <2, which of the following must be true?

1. x+y > 4
2. xy>1
3. x/y + y/x <1
4.(x-y)^2 >0
5. none of the above
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CEO
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13 May 2008, 00:02
B

$$1/x + 1/y < 2 ==> x+y < 2xy$$
Now x and y are positive integers, however $$if x = 1 and y = 1 then x+y = 2xy = 2$$

Therefore x and y cant both be 1 or xy > 1.

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Current Student
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13 May 2008, 10:35
yeah..B too for me..

(y+x)/(xy)<2

y+x<2xy

if XY>1..then the above is true always..

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VP
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13 May 2008, 11:34
I can't negate D...
Someone help...

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Current Student
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13 May 2008, 11:39
bkk145 wrote:
I can't negate D...
Someone help...

hmm..(x-y)^2>0

suppose x=2 y=2..

1/x=1/2+1/2=1<2

however (2-2)=0

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VP
Joined: 10 Jun 2007
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13 May 2008, 12:17
fresinha12 wrote:
bkk145 wrote:
I can't negate D...
Someone help...

hmm..(x-y)^2>0

suppose x=2 y=2..

1/x=1/2+1/2=1<2

however (2-2)=0

But (2-2)^2 is not >0
it equals to 0

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Current Student
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13 May 2008, 12:22
bkk145 wrote:
fresinha12 wrote:
bkk145 wrote:
I can't negate D...
Someone help...

hmm..(x-y)^2>0

suppose x=2 y=2..

1/x=1/2+1/2=1<2

however (2-2)=0

But (2-2)^2 is not >0
it equals to 0

exactly..it doesnt have to be true..the question is asking which of these answer choices HAS to be true..

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Manager
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13 May 2008, 14:36
it is not 2 because if x =-1 and y = 1, then 2 would not hold true.

Am i wrong here?

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Manager
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13 May 2008, 14:49
jingy77 wrote:
it is not 2 because if x =-1 and y = 1, then 2 would not hold true.

Am i wrong here?

both x and y are positive numbers. I had the same thought as you but then figure out that x cannot be -1.

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Manager
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14 May 2008, 16:40
man, there i go again, missing the small details!

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Re: x, y are positive integers, if 1/x + 1/y <2, which of the [#permalink]

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08 Sep 2015, 00:42
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Re: x, y are positive integers, if 1/x + 1/y <2, which of the   [#permalink] 08 Sep 2015, 00:42
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# x, y are positive integers, if 1/x + 1/y <2, which of the

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