College

A list of consecutive integers begins with [tex] m [/tex] and ends with [tex] n [/tex]. If [tex] n - m = 66 [/tex], how many integers are in the list?

E. 2
F. 33
G. 66
H. 67

Answer :

To determine how many integers are in the list, we start with a few key points:

1. We have a list of consecutive integers starting with [tex]\( m \)[/tex] and ending with [tex]\( n \)[/tex].
2. The difference between the largest integer [tex]\( n \)[/tex] and the smallest integer [tex]\( m \)[/tex] is given as 66.

The number of integers in the list can be calculated as follows:

- When you have a list of consecutive integers from [tex]\( m \)[/tex] to [tex]\( n \)[/tex], the count is given by the expression [tex]\( (n - m) + 1 \)[/tex]. This is because you are including both the starting and ending numbers in your count.

Given that:
- [tex]\( n - m = 66 \)[/tex]

Now plug this into the formula:

[tex]\[
\text{Number of integers} = (n - m) + 1 = 66 + 1 = 67
\][/tex]

Therefore, there are 67 integers in the list.

The correct answer is H. 67.