Integers x and y are each odd, and x > y. Which of the following repre

To solve problems requiring us to calculate the number of values in a set, we need to know whether to include or exclude the extreme ends.

For example, say we want to find the number of values between 2 and 9.
1. Number of values between 2 and 9, inclusive (meaning that 2 and 9 are included):
(9-2)+1 = 8 (The numbers are 2,3,4,5,6,7,8,9)
2. Number of values between 2 and 9 (not including 2 and 9):
(9-2)-1 = 6 (The numbers are 3,4,5,6,7,8)
The takeaway is that we add 1 when we want to include the min and max and we subtract 1 when we want to exclude the min and max.

Same concept applies to finding the number of even or odd integers in a set. The key is to set both of your extreme ends as odd if finding the number of odd integers or to set both of your extreme ends as even if finding the number of even integers. In this problem, we know that x and y are both odd, that x is max and y is min, and that we're excluding x and y from the final result so:
\(\frac{x-y}{2}\) - 1 = \(\frac{x-y-2}{2}\)