GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 05:39

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# X and Y are positive integers. If 1/x + 1/y < 2, which of

Author Message
SVP
Joined: 21 Jan 2007
Posts: 2254
Location: New York City
X and Y are positive integers. If 1/x + 1/y < 2, which of  [#permalink]

### Show Tags

22 Nov 2007, 05:34
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 re-post 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: 1151

### Show Tags

22 Nov 2007, 08:00
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: 77

### Show Tags

22 Nov 2007, 08:16
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: 1151

### Show Tags

22 Nov 2007, 09:11
no because the question clearly says that X and Y are positive integers
Retired Moderator
Joined: 05 Jul 2006
Posts: 1417

### Show Tags

22 Nov 2007, 11:42
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. (x-y)^2 > 0
E. none

NO NEED TO SOLVE , (X-Y)^2 IS ALWAYS +VE IE > 0 .

Intern
Joined: 06 Sep 2007
Posts: 7

### Show Tags

22 Nov 2007, 21:22
1
If x and y are same int

is D right?
Intern
Joined: 26 Sep 2007
Posts: 49

### Show Tags

22 Nov 2007, 21:59

1/x + 1/y <2>1
Intern
Joined: 26 Sep 2007
Posts: 49

### Show Tags

22 Nov 2007, 22:00

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: 2

### Show Tags

22 Nov 2007, 22:07
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: 598

### Show Tags

22 Nov 2007, 22:54
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: 1939

### Show Tags

23 Nov 2007, 01:34
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. (x-y)^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: 17
Location: London, United Kingdom

### Show Tags

23 Nov 2007, 06:53
2
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: 1939

### Show Tags

23 Nov 2007, 16:00
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.
Non-Human User
Joined: 09 Sep 2013
Posts: 13271
Re: X and Y are positive integers. If 1/x + 1/y < 2, which of  [#permalink]

### Show Tags

25 Oct 2018, 08:19
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.
_________________
Re: X and Y are positive integers. If 1/x + 1/y < 2, which of   [#permalink] 25 Oct 2018, 08:19
Display posts from previous: Sort by