November 14, 2018 November 14, 2018 07:00 PM PST 08:00 PM PST Join the webinar and learn timemanagement tactics that will guarantee you answer all questions, in all sections, on time. Save your spot today! Nov. 14th at 7 PM PST November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
Author 
Message 
CEO
Joined: 21 Jan 2007
Posts: 2632
Location: New York City

X and Y are positive integers. If 1/x + 1/y < 2, which of
[#permalink]
Show Tags
22 Nov 2007, 04:34
X and Y are positive integers. If 1/x + 1/y 4
B. XY>1
C. X/Y + Y/X 0
E. none
how can i solve this quickly? not even sure how to start the approach == Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.



VP
Joined: 21 Jul 2006
Posts: 1401

this is what I think:
when looking at 1/x + 1/y < 2, i know for a fact that both X and Y can't be 1. because if they are, then 1/1 + 1/1 = 2 which doesn't agree with the question. The only way that the 2 fractions can be smaller is to have either one of the variables bigger than 1 or both variables bigger than 1. Therefore, for sure at least that XY must be greater than 1, therefore my answer is B.
what's the OA?



Manager
Joined: 08 Nov 2007
Posts: 93

tarek99 wrote: this is what I think:
when looking at 1/x + 1/y < 2, i know for a fact that both X and Y can't be 1. because if they are, then 1/1 + 1/1 = 2 which doesn't agree with the question. The only way that the 2 fractions can be smaller is to have either one of the variables bigger than 1 or both variables bigger than 1. Therefore, for sure at least that XY must be greater than 1, therefore my answer is B.
what's the OA?
Couldnt you have one as 1 and the other as or even 0.5?



VP
Joined: 21 Jul 2006
Posts: 1401

no because the question clearly says that X and Y are positive integers



Retired Moderator
Joined: 05 Jul 2006
Posts: 1726

X and Y are positive integers. If 1/x + 1/y < 2, which of the following must be true?
A. X+Y>4
B. XY>1
C. X/Y + Y/X < 1
D. (xy)^2 > 0
E. none
NO NEED TO SOLVE , (XY)^2 IS ALWAYS +VE IE > 0 .
MY ANSWER IS D



Intern
Joined: 06 Sep 2007
Posts: 8

If x and y are same int
is D right?



Manager
Joined: 26 Sep 2007
Posts: 63

Answer is B (XY>1)
1/x + 1/y <2>1



Manager
Joined: 26 Sep 2007
Posts: 63

Answer is B (XY>1)
Both x and y are positive integers, so minimum positive value for one of the variable can be 1 and minimum value for other variable will be greater than 1 in order to satisfy the equation.
So, XY>1



Intern
Joined: 11 Nov 2007
Posts: 3

B is the answer. 1/x + 1/y <2> (x+y) / 2
(x+y)/2 >= 1
so xy > 1



Director
Joined: 09 Aug 2006
Posts: 733

Re: 11.35 positive integers
[#permalink]
Show Tags
22 Nov 2007, 21:54
bmwhype2 wrote: X and Y are positive integers. If 1/x + 1/y <2>4 B. XY>1 C. X/Y + Y/X <1> 0 E. none
how can i solve this quickly? not even sure how to start the approach
Getting B.
1/x + 1/y < 2 = (x + y)/xy < 2
Since x and y are +ve integers (given), x & y cannot both be equal to 1. Since one of them has to be greater than 1 (lets say y), then the product of xy has to be greater than 1 as well.



SVP
Joined: 29 Aug 2007
Posts: 2379

bmwhype2 wrote: X and Y are positive integers. If 1/x + 1/y < 2, which of the following must be true?
A. X+Y>4 B. XY>1 C. X/Y + Y/X < 1 D. (xy)^2 > 0 E. none
seems the question is poorly structures: both B and D are correct since x and y are +ve integers.



Intern
Joined: 28 Aug 2007
Posts: 19
Location: London, United Kingdom

D isn't always true. x could be 2 and y could be 2
Then D would = 0.
B is only option that is always true.



SVP
Joined: 29 Aug 2007
Posts: 2379

mantymooney wrote: D isn't always true. x could be 2 and y could be 2
Then D would = 0.
B is only option that is always true.
agree. you are correct.



NonHuman User
Joined: 09 Sep 2013
Posts: 8759

Re: X and Y are positive integers. If 1/x + 1/y < 2, which of
[#permalink]
Show Tags
25 Oct 2018, 07:19
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). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: X and Y are positive integers. If 1/x + 1/y < 2, which of &nbs
[#permalink]
25 Oct 2018, 07:19






