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

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If x and y are positive integers and 1 + x + y + xy = 15, [#permalink]

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12 Jun 2008, 03:45
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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
[Reveal] Spoiler: OA

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Re: If x and y are positive integers and 1 + x + y + xy = 15, [#permalink]

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12 Jun 2008, 06:49
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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

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)

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Re: If x and y are positive integers and 1 + x + y + xy = 15, [#permalink]

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13 Jun 2008, 00:25
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=(3-1)+(5-1)
=2+4=6

C. 6
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Re: If x and y are positive integers and 1 + x + y + xy = 15, [#permalink]

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13 Jun 2008, 02:23
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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

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

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12 Sep 2010, 06:15
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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
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12 Sep 2010, 06:58
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
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12 Sep 2010, 08:11
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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 --> $$x+1+y+1=3+5$$ --> $$x+y=6$$.

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12 Sep 2010, 08:26
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
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Re: If x and y are positive integers and 1 + x + y + xy = 15, wh [#permalink]

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02 Jan 2015, 01:07
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Re: If x and y are positive integers and 1 + x + y + xy = 15, [#permalink]

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22 Jul 2015, 23:12
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Re: If x and y are positive integers and 1 + x + y + xy = 15, wh [#permalink]

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23 Jul 2015, 22:31
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 = 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

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Re: If x and y are positive integers and 1 + x + y + xy = 15, wh [#permalink]

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31 Aug 2016, 10:09
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Re: If x and y are positive integers and 1 + x + y + xy = 15, wh   [#permalink] 31 Aug 2016, 10:09
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