It is currently 22 Jun 2017, 14:07

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# X and Y are positive integers. If \frac{1}{X} + \frac{1}{Y}

Author Message
Senior Manager
Joined: 20 Dec 2004
Posts: 251
X and Y are positive integers. If \frac{1}{X} + \frac{1}{Y} [#permalink]

### Show Tags

02 Apr 2008, 15:48
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

$$X$$ and $$Y$$ are positive integers. If $$\frac{1}{X} + \frac{1}{Y} \lt 2$$ , which of the following must be true?

* $$X + Y \gt 4$$

* $$XY \gt 1$$

* $$\frac{X}{Y} + \frac{Y}{X} \lt 1$$

* $$(X - Y)^2 \gt 0$$

* none of the above
_________________

Stay Hungry, Stay Foolish

Current Student
Joined: 31 Aug 2007
Posts: 369

### Show Tags

02 Apr 2008, 19:28
I would say II...can explain if correct...OA?
Manager
Joined: 03 Jan 2008
Posts: 106

### Show Tags

02 Apr 2008, 19:32
neelesh wrote:
$$X$$ and $$Y$$ are positive integers. If $$\frac{1}{X} + \frac{1}{Y} \lt 2$$ , which of the following must be true?

* $$X + Y \gt 4$$

* $$XY \gt 1$$

* $$\frac{X}{Y} + \frac{Y}{X} \lt 1$$

* $$(X - Y)^2 \gt 0$$

* none of the above

1/x +1/y < 2 <--> (x+y)/xy <2
Since x>0. y> 0 --> x+y <2xy ---> xy>(x+y)/2
x, y are intergers--> x,y>=1 --> x+y >=2 --> (x+y)/2 >=1

---> xy>1--> B
Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12

### Show Tags

02 Apr 2008, 20:52
i get B as well..remember x and y are positive integers
Intern
Joined: 24 Feb 2008
Posts: 41

### Show Tags

02 Apr 2008, 21:13
this can be illustarted well with an example

1/x+1/y<2 resolves to x+y/xy < 2

x y x+y xy
1 1 2 1 -> equation doesnt hold true
1 2 3 2 -> equation holds true
2 2 4 4 -> equation holds true
2 3 5 6 -> equation holds true
and so on...

for all the values other than first, the equation holds true. Hence the answer is xy > 1. (B)
Director
Joined: 14 Jan 2007
Posts: 774

### Show Tags

05 Apr 2008, 00:28
neelesh wrote:
$$X$$ and $$Y$$ are positive integers. If $$\frac{1}{X} + \frac{1}{Y} \lt 2$$ , which of the following must be true?

* $$X + Y \gt 4$$

* $$XY \gt 1$$

* $$\frac{X}{Y} + \frac{Y}{X} \lt 1$$

* $$(X - Y)^2 \gt 0$$

* none of the above

for 1/x + 1/y to be 2, x=1 and y =1
for 1/x + 1/y less than 2, at least one of x and y should be greater than 1.
so xy will always be greater than 1
hence 'B'

Last edited by vshaunak@gmail.com on 05 Apr 2008, 17:27, edited 1 time in total.
CEO
Joined: 17 Nov 2007
Posts: 3583
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

### Show Tags

05 Apr 2008, 14:40
pmenon wrote:
why would d be incorrect ?

for example, x=2 and y=2 --> (2-2)^2>0 - is not true but must be true.
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Re: PS: Inequality   [#permalink] 05 Apr 2008, 14:40
Display posts from previous: Sort by