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

 It is currently 24 May 2019, 16:07 ### 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
Your Progress

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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # If x and y are positive integers and 1 + x + y + xy = 15, wh

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
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

1
11 00:00

Difficulty:   25% (medium)

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

_________________
Impossible is nothing...
##### Most Helpful Expert Reply
Math Expert V
Joined: 02 Sep 2009
Posts: 55271
Re: Arithmatic Problem  [#permalink]

### Show Tags

6
6
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 vise-versa (x+1=1 and y+=15 or vise-versa 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 vise-versa --> no need to solve for $$x$$ and $$y$$, just add them --> $$x+1+y+1=3+5$$ --> $$x+y=6$$.

Answer: C.
_________________
##### Most Helpful Community Reply
Manager  Joined: 29 Aug 2005
Posts: 239
Re: If x and y are positive integers and 1 + x + y + xy = 15,  [#permalink]

### Show Tags

3
2
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
##### General Discussion
Manager  Joined: 21 Mar 2008
Posts: 75
Re: If x and y are positive integers and 1 + x + y + xy = 15,  [#permalink]

### Show Tags

1
2
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

2
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=(3-1)+(5-1)
=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

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

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  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2933
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: If x and y are positive integers and 1 + x + y + xy = 15, wh  [#permalink]

### Show Tags

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 = 15

Values 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!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Target Test Prep Representative G
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

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
_________________

# Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com

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  B
Joined: 29 Jul 2017
Posts: 3
Re: If x and y are positive integers and 1 + x + y + xy = 15, wh  [#permalink]

### Show Tags

Can someone show me the details of this step?

1+x + y(x+1)=15

(1+x)(1+y)=15
Senior SC Moderator V
Joined: 22 May 2016
Posts: 2759
Re: If x and y are positive integers and 1 + x + y + xy = 15, wh  [#permalink]

### Show Tags

1
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.
Non-Human 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

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
Display posts from previous: Sort by

# If x and y are positive integers and 1 + x + y + xy = 15, wh

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

#### MBA Resources  