May 24 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day! May 27 10:00 PM PDT  11:00 PM PDT Special savings are here for Magoosh GMAT Prep! Even better  save 20% on the plan of your choice, now through midnight on Tuesday, 5/27 May 30 10:00 PM PDT  11:00 PM PDT Application deadlines are just around the corner, so now’s the time to start studying for the GMAT! Start today and save 25% on your GMAT prep. Valid until May 30th. Jun 01 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 17 May 2008
Posts: 12

If x and y are positive integers and 1 + x + y + xy = 15,
[#permalink]
Show Tags
12 Jun 2008, 04:45
Question Stats:
78% (01:59) correct 22% (02:09) wrong based on 300 sessions
HideShow timer Statistics
If x and y are positive integers and 1 + x + y + xy = 15, what is the value of x + y? A. 3 B. 5 C. 6 D. 8 E. 9
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Math Expert
Joined: 02 Sep 2009
Posts: 55271

Re: Arithmatic Problem
[#permalink]
Show Tags
12 Sep 2010, 09:11
udaymathapati wrote: What's the approach to solve following example. If x and y are positive integers and 1 + x + y + xy = 15, what is the value of x + y? A. 3 B. 5 C. 6 D. 8 E. 9 \(1+x+y+xy=15\) > \((x+1)(y+1)=15=3*5\); As \(x\) and \(y\) are positive integers then \(x+1=3\) and \(y+1=5\), or viseversa (x+1=1 and y+=15 or viseversa is not possible as in this case one of the unknowns becomes zero and we are told that both unknowns are positive). So \(x+1=3\) and \(y+1=5\), or viseversa > no need to solve for \(x\) and \(y\), just add them > \(x+1+y+1=3+5\) > \(x+y=6\). Answer: C.
_________________




Manager
Joined: 29 Aug 2005
Posts: 239

Re: If x and y are positive integers and 1 + x + y + xy = 15,
[#permalink]
Show Tags
13 Jun 2008, 03:23
mrwaxy wrote: If x and y are positive integers and 1 + x + y + xy = 15, what is the value of x + y? A. 3 B. 5 C. 6 D. 8 E. 9 1+x+y+xy=15 1+x + y(x+1)=15 (1+x)(1+y)=15 (1+x)(1+y)=3*5 this implies x=2 and y = 4 therefore x+y = 2 + 4 = 6 hence C is the answer
_________________
The world is continuous, but the mind is discrete




Manager
Joined: 21 Mar 2008
Posts: 75

Re: If x and y are positive integers and 1 + x + y + xy = 15,
[#permalink]
Show Tags
12 Jun 2008, 07:49
mrwaxy wrote: If x and y are positive integers and 1 + x + y + xy = 15, what is the value of x + y? A. 3 B. 5 C. 6 D. 8 E. 9 Try each answer choices. For A: 1 + 3 + xy = 15; xy = 11 (impossible, 11 prime number. 1 + 11 doesn't equal 3) For B: 1 + 5 + xy = 15; xy = 9 (no combination of xy = 9 and x + y = 5) For C: 1 + 6 + xy = 15; xy = 8 (x + y = 6; x = 2, y = 4 or x = 4, y = 2) For D: 1 + 8 + xy = 15; xy = 6 (no combination of xy = 6 and x + y = 8) For E: 1 + 9 + xy = 15; xy = 5 (impossible, 5 prime number. 1 + 5 doesn't equal 9) Therefore, answer C.



Manager
Joined: 10 Mar 2008
Posts: 65

Re: If x and y are positive integers and 1 + x + y + xy = 15,
[#permalink]
Show Tags
13 Jun 2008, 01:25
mrwaxy wrote: If x and y are positive integers and 1 + x + y + xy = 15, what is the value of x + y? A. 3 B. 5 C. 6 D. 8 E. 9 1 + x + y + xy = 15 1 + x + y (1+ x) = 15 (1 + x) (1+ y) = 3*5 x+y=(31)+(51) =2+4=6 C. 6



Intern
Joined: 15 Aug 2010
Posts: 8
Concentration: Healthcare, Marketing
WE: Other (Health Care)

Re: Arithmatic Problem
[#permalink]
Show Tags
12 Sep 2010, 07:58
I think this is how it is calculated;
Factors of 15 are 1,3,5,and 15.
So 1 + x + y +xy = (1+x)(1+y) = 15. Basically find product of two numbers that is equal to 15. This can be factorized as follows
1 + x = 3 and 1 + y = 5 (as product of 3x5 = 15) > x = 2 and y = 4
OR
1 + x = 15 and 1 + y = 1 (as product of 15x1 = 15) > x=14 and y=0
However problem indicates that x,y>0, so value of x = 2 and y = 4.
Value of x+y = 2+4 = 6
Ans C



Manager
Joined: 20 Jul 2010
Posts: 208

Re: Arithmatic Problem
[#permalink]
Show Tags
12 Sep 2010, 09:26
I went by answe choices. x+y+xy=14 (given) If x+y = 3 then x=1, y 2 = cannot satisfy 14. If x+y=5, x=4, y=1 cannot satisfy 14. x=2 and y=3 ..ruled out x+y=6 = I got the answer I liked the equation approach as its clean. Although I could solve it in less than a minute
_________________
If you like my post, consider giving me some KUDOS !!!!! Like you I need them



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2933
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: If x and y are positive integers and 1 + x + y + xy = 15, wh
[#permalink]
Show Tags
23 Jul 2015, 23:31
mrwaxy wrote: If x and y are positive integers and 1 + x + y + xy = 15, what is the value of x + y?
A. 3 B. 5 C. 6 D. 8 E. 9 Easiest way to solve this question seems substitution because the values can't be too big as the multiplication of those two Positive Integers x and y must be less than 15 as per the given expression 1 + x + y + xy = 15Values of x and y have to be less than 3 and 5 as 3*5=15 Let's try with 2 and 3 1+2+3+2*3 = 12 i.e. One of the numbers must be a little bigger Let's try with 2 and 4 1+2+4+2*4 = 15 BINGO!!!i.e. x+y = 2+4 = 6 Answer: option C
_________________
Prosper!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823

Re: If x and y are positive integers and 1 + x + y + xy = 15, wh
[#permalink]
Show Tags
08 Nov 2017, 17:41
mrwaxy wrote: If x and y are positive integers and 1 + x + y + xy = 15, what is the value of x + y?
A. 3 B. 5 C. 6 D. 8 E. 9 Note that the expression y + xy can be factored as y(1 + x). Let’s simplify the given equation: 1 + x + y(1 + x) = 15 (1 + x) + y(1 + x) = 15 The two terms on the left side of the equation have (1 + x) in common, so we can factor it out: (1 + x)(1 + y) = 15 Since x and y are positive integers, so are (1 + x) and (1 + y). We should investigate the different ways of writing 15 as a product of positive integers. Note that 15 can be expressed as a product of positive integers in two ways: 1 x 15 (scenario one) or 3 x 5 (scenario two). For scenario one, we have either 1 + x = 1 and 1 + y = 15 OR 1 + x = 15 and 1 + y = 1. Note that in either case, one of x or y equals 0; since x and y are given as positive, this scenario is ruled out. For scenario two, we have either 1 + x = 3 and 1 + y = 5, which means x = 2 and y = 4 OR 1 + x = 5 and 1 + y = 3, meaning x = 4 and y = 2. In either case, x + y = 6. Answer: C
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Intern
Joined: 29 Jul 2017
Posts: 3

Re: If x and y are positive integers and 1 + x + y + xy = 15, wh
[#permalink]
Show Tags
24 Dec 2017, 15:53
Can someone show me the details of this step?
1+x + y(x+1)=15
(1+x)(1+y)=15



Senior SC Moderator
Joined: 22 May 2016
Posts: 2759

Re: If x and y are positive integers and 1 + x + y + xy = 15, wh
[#permalink]
Show Tags
24 Dec 2017, 17:55
Quote: Can someone show me the details of this step?
1+x + y(x+1)=15
(1+x)(1+y)=15 xlgoh1992 , sure. 1) 1+x + y(x + 1) = 15 Factor out (1 + x) from the first two terms (because 1 + x is identical to x + 1 by which y is multiplied) 2) 1 (1 + x) + y(x+1) Notice that if you multiplied 1(1 + x) you would be back to: 1 + x 3) Note that (1 + x) has already been factored out in this term: y(x + 1)1 (1 + x) + y (x + 1)4) Combine what factoring out (1 + x) left: 1 and + y (1 + x) (1 + y) = 15 Hope that helps.
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.



NonHuman User
Joined: 09 Sep 2013
Posts: 11012

Re: If x and y are positive integers and 1 + x + y + xy = 15, wh
[#permalink]
Show Tags
11 Feb 2019, 09:42
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). 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 = 15, wh
[#permalink]
11 Feb 2019, 09:42






