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
Please help explain this futher! I get to this point: (1 + x) (1 + y) =15 but what do i do further to get the answer 6?
1 + x + y + xy = 15
1 + x + y(1 + x) =15
(1+x)(1+ y)=15
now what?? thank you!
If x and y are positive integers and 1 + x + y + xy = 15 ...
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 124
- Joined: Wed May 19, 2010 10:20 pm
- Thanked: 3 times
- GMAT Score:1100
-
- Legendary Member
- Posts: 576
- Joined: Sat Mar 13, 2010 8:31 pm
- Thanked: 97 times
- Followed by:1 members
1 + x + y + xy = 15
or (1+x)(1+y)=15
15 can be expressed as multiple of two integers as (1,15)and (3,5)
if (1+x)(1+y)=1*15..1+x=1 or x=0 and y=14..so x+y=14
if (1+x)(1+y)=3*5..1+x=3 or x=2 and y=4..so x+y=6
only C is in ans choice
ans option C
or (1+x)(1+y)=15
15 can be expressed as multiple of two integers as (1,15)and (3,5)
if (1+x)(1+y)=1*15..1+x=1 or x=0 and y=14..so x+y=14
if (1+x)(1+y)=3*5..1+x=3 or x=2 and y=4..so x+y=6
only C is in ans choice
ans option C
Last edited by liferocks on Thu May 20, 2010 2:42 am, edited 1 time in total.
"If you don't know where you are going, any road will get you there."
Lewis Carroll
Lewis Carroll
- sanju09
- GMAT Instructor
- Posts: 3650
- Joined: Wed Jan 21, 2009 4:27 am
- Location: India
- Thanked: 267 times
- Followed by:80 members
- GMAT Score:760
[spoiler]You need to get rid of this...good to see that you have edited while I was quoting your work, and why did you use the spoiler function above?[/spoiler]liferocks wrote:1 + x + y + xy = 15
or (1+x)(1+y)=15
15 can be expressed as multiple (or the product?) of two integers as (1,15)and (3,5)
if (1+x)(1+y)=1*15..1+x=1 or x=0 and y=14..so x+y=14.............not applicable
if (1+x)(1+y)=3*5..1+x=3 or x=2 and y=4..so x+y=6....now edited
only C is in ans choice
ans option C
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
-
- Legendary Member
- Posts: 576
- Joined: Sat Mar 13, 2010 8:31 pm
- Thanked: 97 times
- Followed by:1 members
Now used the spoiler in both placessanju09 wrote:[spoiler]You need to get rid of this...good to see that you have edited while I was quoting your work, and why did you use the spoiler function above?[/spoiler]liferocks wrote:1 + x + y + xy = 15
or (1+x)(1+y)=15
15 can be expressed as multiple (or the product?) of two integers as (1,15)and (3,5)
if (1+x)(1+y)=1*15..1+x=1 or x=0 and y=14..so x+y=14.............not applicable
if (1+x)(1+y)=3*5..1+x=3 or x=2 and y=4..so x+y=6....now edited
only C is in ans choice
ans option C
"If you don't know where you are going, any road will get you there."
Lewis Carroll
Lewis Carroll
- sanju09
- GMAT Instructor
- Posts: 3650
- Joined: Wed Jan 21, 2009 4:27 am
- Location: India
- Thanked: 267 times
- Followed by:80 members
- GMAT Score:760
...and what should be the correct wordings in this case?
this: 15 can be expressed as multiple of two integers
or that: 15 can be expressed as the product of two integers
multiple and the product are two different words with different meanings in mathematics
this: 15 can be expressed as multiple of two integers
or that: 15 can be expressed as the product of two integers
multiple and the product are two different words with different meanings in mathematics
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
-
- Legendary Member
- Posts: 576
- Joined: Sat Mar 13, 2010 8:31 pm
- Thanked: 97 times
- Followed by:1 members
Hmm..second one is definitely right and conveys the meaning correctly..but technically first one is also correct if we take a multiplicity factor as 1sanju09 wrote:...and what should be the correct wordings in this case?
this: 15 can be expressed as multiple of two integers
or that: 15 can be expressed as the product of two integers
"If you don't know where you are going, any road will get you there."
Lewis Carroll
Lewis Carroll
- sanju09
- GMAT Instructor
- Posts: 3650
- Joined: Wed Jan 21, 2009 4:27 am
- Location: India
- Thanked: 267 times
- Followed by:80 members
- GMAT Score:760
postmortem is not carried out on living beingsliferocks wrote:Hmm..second one is definitely right and conveys the meaning correctly..but technically first one is also correct if we take a multiplicity factor as 1sanju09 wrote:...and what should be the correct wordings in this case?
this: 15 can be expressed as multiple of two integers
or that: 15 can be expressed as the product of two integers
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
-
- Legendary Member
- Posts: 610
- Joined: Fri Jan 15, 2010 12:33 am
- Thanked: 47 times
- Followed by:2 members
if (1+x)(1+y) = 15
and x any y are +ve integers
then (1+x) (1+y) = 5*3 and not 15*1
cos 1+x or 1+y = 1 implies x or y = 0
if 1+x = 5
1+y = 3
it is not necessary to find the values of x and y seperately
adding the two (1+x)+(1+y) = 8
x+y = 6
and x any y are +ve integers
then (1+x) (1+y) = 5*3 and not 15*1
cos 1+x or 1+y = 1 implies x or y = 0
if 1+x = 5
1+y = 3
it is not necessary to find the values of x and y seperately
adding the two (1+x)+(1+y) = 8
x+y = 6
- sanju09
- GMAT Instructor
- Posts: 3650
- Joined: Wed Jan 21, 2009 4:27 am
- Location: India
- Thanked: 267 times
- Followed by:80 members
- GMAT Score:760
your name was missing in the hit list of my Quant Commandoskstv wrote:if (1+x)(1+y) = 15
and x any y are +ve integers
then (1+x) (1+y) = 5*3 and not 15*1
cos 1+x or 1+y = 1 implies x or y = 0
if 1+x = 5
1+y = 3
it is not necessary to find the values of x and y seperately
adding the two (1+x)+(1+y) = 8
x+y = 6
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com