If x and y are positive integers and 1 + x + y +xy = 21 : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 24 Jan 2017, 09:37

### 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

# If x and y are positive integers and 1 + x + y +xy = 21

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 13 May 2011
Posts: 317
WE 1: IT 1 Yr
WE 2: Supply Chain 5 Yrs
Followers: 21

Kudos [?]: 252 [1] , given: 11

If x and y are positive integers and 1 + x + y +xy = 21 [#permalink]

### Show Tags

11 Jun 2012, 07:20
1
KUDOS
4
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

64% (02:16) correct 36% (01:05) wrong based on 125 sessions

### HideShow timer Statistics

If x and y are positive integers and 1 + x + y +xy = 21, what is the value of x?

(1) y>3
(2) y=6

[Searched, but couldn't find]
[Reveal] Spoiler: OA
Joined: 28 Mar 2012
Posts: 314
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 29

Kudos [?]: 399 [0], given: 23

Re: If x and y are positive integers and 1 + x + y +xy = 21 [#permalink]

### Show Tags

11 Jun 2012, 07:29
1
This post was
BOOKMARKED
Hi,

We have, 1 + x + y +xy = 21 (where x & y are natural numbers/positive integers)
or x(1+y) = 20 -y
or x = (20-y)/(1+y)

Using (1)
y > 3, i.e., y = 4, 5, 6...
when y=4, x = (20-4)/5 = 16/5 (not a natural number)
when y=5, x = (20-5)/6 = 15/6 (not a natural number)
when y=6, x = (20-6)/7 = 14/7 = 2
when y=7, x = (20-7)/8 = 13/8 (not a natural number), and for remaining values of y, there would be no positive integral value of x.
so, (x,y) = (2,6). Sufficient

Using (2)
y = 6, => x = (20-6)/(1+6) = 2
so, (x,y) = (2,6). Sufficient.

Regards,
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93648 [5] , given: 10583

Re: If x and y are positive integers and 1 + x + y +xy = 21 [#permalink]

### Show Tags

11 Jun 2012, 07:40
5
KUDOS
Expert's post
2
This post was
BOOKMARKED
Good question. +1.

If x and y are positive integers and 1 + x + y +xy = 21, what is the value of x?

$$1 + x + y +xy = 21$$ --> $$(x+1)(y+1)=21$$ --> either $$x+1=3$$ and $$y+1=7$$ OR $$x+1=7$$ and $$y+1=3$$. Notice that $$x+1=1$$ and $$y+1=21$$ OR $$x+1=21$$ and $$y+1=1$$ is not possible since in this case either $$x$$ or $$y$$ equals zero and we are told that $$x$$ and $$y$$ are positive integers.

Now, from $$x+1=3$$ and $$y+1=7$$ --> $$x=2$$ and $$y=6$$ AND from $$x+1=7$$ and $$y+1=3$$ --> $$x=6$$ and $$y=2$$.

(1) y>3 --> $$y=6$$, so $$x=2$$. Sufficient.
(2) y=6 --> $$x=2$$. Sufficient.

Hope it's clear.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13543
Followers: 578

Kudos [?]: 163 [0], given: 0

Re: If x and y are positive integers and 1 + x + y +xy = 21 [#permalink]

### Show Tags

13 Mar 2015, 12:27
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 Club Legend
Joined: 09 Sep 2013
Posts: 13543
Followers: 578

Kudos [?]: 163 [0], given: 0

Re: If x and y are positive integers and 1 + x + y +xy = 21 [#permalink]

### Show Tags

20 Oct 2016, 22:12
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: If x and y are positive integers and 1 + x + y +xy = 21   [#permalink] 20 Oct 2016, 22:12
Similar topics Replies Last post
Similar
Topics:
1 If x and y are positive integers, is x/y > 1? 2 22 Apr 2016, 05:37
1 If x and y are positive integers, is x/y an integer? 3 20 Dec 2015, 04:29
22 x and y are positive integers, is x=y ? 18 17 Aug 2015, 01:37
2 If x and y are positive integers, is x - y > (x+y)/2 ? (1) y < x (2) 7 24 Mar 2015, 03:40
6 If x is a positive integer and x^y=1, what is the value of x? 5 29 Dec 2014, 03:59
Display posts from previous: Sort by