Question

There are 6 consecutive integers and 5 consecutive integers. The average of the 6 integers is 2 less than the average of the 5 integers. The sum of the 5 integers is 4 more than the sum of the 6 integers. Find the average of the 6 integers.

• A. 6
• B. 5
• C. 4
• D. 3

Answer 1

Answer:

A. 6

Let the average of the 6 consecutive integers be (x).

Then the average of the 5 consecutive integers is:

x+2

Step 1: Find their sums

Sum of 6 integers:

6x

Sum of 5 integers:

5(x+2)=5x+10

Given that the sum of the 5 integers is 4 more than the sum of the 6 integers:

5x+10=6x+4
10-4=6x-5x
x=6

So, the average of the 6 integers is 6.