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

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

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13 May 2008, 00:48
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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
Joined: 17 May 2007
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13 May 2008, 01:02
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.
Current Student
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13 May 2008, 11:35
yeah..B too for me..

(y+x)/(xy)<2

y+x<2xy

if XY>1..then the above is true always..
VP
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13 May 2008, 12:34
I can't negate D...
Someone help...
Current Student
Joined: 28 Dec 2004
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13 May 2008, 12:39
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
VP
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13 May 2008, 13:17
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
Current Student
Joined: 28 Dec 2004
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13 May 2008, 13:22
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..
Manager
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13 May 2008, 15:36
it is not 2 because if x =-1 and y = 1, then 2 would not hold true.

Am i wrong here?
Manager
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13 May 2008, 15:49
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.
Manager
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14 May 2008, 17:40
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, 01:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: x, y are positive integers, if 1/x + 1/y <2, which of the   [#permalink] 08 Sep 2015, 01:42
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