Carcass wrote:
If x and y are integers greater than zero and x + y = 10, what is the least possible value of x - y?
(A) -12
(B) -11
(C) -10
(D) -9
(E) -8
Since x and y are
positive integers, there aren't that many solutions to the equation x + y = 10.
So let's start listing all possible solutions:
x = 1, y = 9 (in which case x - y = -8)
x = 2, y = 8 (in which case x - y = -6)
x = 3, y = 7 (in which case x - y = -4)
At this point, it's obvious that
-8 is the smallest possible value of x - y
Answer: E