What is the average of all numbers between 9 and 90 which are divisibl...
To find the average of all numbers between 9 and 90 that are divisible by 8, we need to first determine the count of such numbers and then calculate their sum. Finally, we can divide the sum by the count to find the average.
1. Count of numbers divisible by 8 between 9 and 90:
- The smallest number divisible by 8 in this range is 16.
- The largest number divisible by 8 in this range is 88.
- We can find the count by subtracting the two values and dividing by 8, and then adding 1 to include both ends of the range.
- Count = (88 - 16) / 8 + 1 = 11
2. Sum of numbers divisible by 8 between 9 and 90:
- To find the sum, we can use the formula for the sum of an arithmetic series: Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term.
- In this case, a = 16, l = 88, and n = 11.
- Sum = (11/2)(16 + 88) = 11 * 104 = 1144
3. Average:
- To find the average, we divide the sum by the count.
- Average = 1144 / 11 = 104.3636...
Since the question asks for the average as an integer, we need to round down to the nearest whole number. The largest whole number less than 104.3636 is 104. Therefore, the average of all numbers between 9 and 90 that are divisible by 8 is 104.
Therefore, the correct answer is option B) 52.