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If x and y are positive integers and 1 + x + y + xy = 15 ...

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If x and y are positive integers and 1 + x + y + xy = 15 ...

by mitzwillrockgmat » Thu May 20, 2010 2:24 am
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! :)
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by liferocks » Thu May 20, 2010 2:32 am
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
Last edited by liferocks on Thu May 20, 2010 2:42 am, edited 1 time in total.
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by sanju09 » Thu May 20, 2010 2:37 am
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
[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]
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by liferocks » Thu May 20, 2010 2:42 am
sanju09 wrote:
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
[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]
Now used the spoiler in both places
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by sanju09 » Thu May 20, 2010 2:48 am
...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
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by liferocks » Thu May 20, 2010 2:51 am
sanju09 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
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 1 :D
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by sanju09 » Thu May 20, 2010 2:54 am
liferocks wrote:
sanju09 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
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 1 :D
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by kstv » Thu May 20, 2010 3:04 am
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
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by sanju09 » Thu May 20, 2010 3:10 am
kstv 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
your name was missing in the hit list of my Quant Commandos
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