Why do you add +1 in counting test questions? Here's an example question from the SAT question of the day:

On the last day of a one-week sale, customers numbered 149 through 201 were waited on. How many customers were waited on that day?
  Possible answers: 51, 52, 53, 152, 153.

The correct answer here is 53, which is the result of (201-149) + 1 = 53.
What's the reasoning in adding the +1?

Let $C_n$ be the customer numbered $n$. List the customers in question: 
$$C_{149},C_{150},C_{151},\ldots,C_{200},C_{201}\;.$$
Now write their numbers in the form $148+\text{something}$:
$$C_{148+\underline1},C_{148+\underline2},C_{148+\underline3},\ldots,C_{148+\underline{52}},C_{148+\underline{53}}\;.$$
In this form it’s clear that if you ignore the $148$, you’re just counting from $1$ through $53$, so there are $53$ customers. Now think back to see where the $53$ came from: it was what had to be added to the base-point $148$ to get $201$, the last customer number, so it was $201-148$.
A little thought will show you that the same idea works in general, and that the base-point number will always be that of the last customer not being counted, so it will be one less than the number of the first customer that you want to count. If you’re counting the customers from $C_{\text{first}}$ through $C_{\text{last}}$, your base-point number will be $\text{base}=\text{first}-1$, and your counted customers will be
$$C_{\text{base}+1},C_{\text{base}+2},C_{\text{base}+3},\ldots,C_{\text{base}+?}\;,$$
where $\text{base}+?=\text{last}$. Thus, the question mark must be
$$?=\text{last}-\text{base}=\text{last}-(\text{first}-1)=\text{last}-\text{first}+1\;.$$
