alltimeacheiver 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

First factor 1 + x + y + xy = 15. You get (1 + x)(1 + y) = 15.
Because it is stated that x and y are both positive integers, the only possible values could be [(1,15) , (3,5)]
if (x,y) = (1,15) or (15,1) then x + y = 14. However, this means that either one of x or y will have to take the value of 0 which is not acceptable based on the conditions stated in the question. So, that leaves us only with the possibility of (x,y) = (3,5) or (5,3) then x + y = 6. So the answer is C.

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Anurag@Gurome wrote:1 + x + y + xy = 15
1 + x + y(1 + x) = 15
(1 + x)(1 + y) = 15

It is given that x and y are positive integers and 15 can be expressed as a multiple of 2 integers: (1, 15) and (3, 5).
If (1 + x)(1 + y) = 1 * 15 implies 1 + x = 1 and 1 + y = 15 or x = 0 and y = 14
So, x + y = 14
If (1 + x)(1 + y) = 3 * 5 implies 1 + x = 3 and 1 + y = 5 or x = 2 and y = 4
So, x + y = 6
From the above two values of x + y, 6 is the only choice.

[spoiler]The correct answer is C.[/spoiler]