Bunuel wrote:

What is the sum of all consecutive integers from 10 to 100, inclusive?

A. 4550

B. 4950

C. 5005

D. 5500

E. 5555

We know that the general average formula is average = sum/quantity. This formula can be rearranged to isolate the sum of the values in the set: sum = average x quantity. This tells us that the sum of any set of numbers is equal to the number of terms in the set multiplied by the average of the numbers in the set.

Let’s start by determining how many terms are in the set.

quantity = 100 - 10 + 1 = 91

Next we can determine the average of the numbers from 10 to 100, inclusive. Since we are dealing with consecutive integers, which form an evenly spaced set of numbers, we can use the following formula to determine the average:

average = (1st number + last number)/2

average = (10 + 100)/2 = 110/2 = 55

Now, the sum can be calculated by means of the rearranged formula:

sum = 55 x 91 = 5,005

Answer: C

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