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.
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Correct answer: A
Explanation
The correct answer is option 1 i.e. 6.
Let the 5 consecutive integers be: n, n + 1, n + 2, n + 3, n + 4
Sum = n + n + 1 + n + 2 + n + 3 + n + 4 = 5n + 10
Average = (5n + 10)/5 = n + 2
Let the 6 consecutive integers be: m, m + 1, m + 2, m + 3, m + 4, m + 5
Sum = m + m + 1 + m + 2 + m + 3 + m + 4 + m + 5 = 6m + 15
Average = (6m + 15)/6 = m + 2.5
So, m + 2.5 = n + 2 – 2
⇒ n = m + 2.5 .....(1)
5n + 10 = 6m + 15 + 4
⇒ 5n = 6m + 9 .....(2)
From (1): n = m + 2.5 ⇒ 5n = 5m + 12.5
Now, 5m + 12.5 = 6m + 9
⇒ m = 3.5
Average of 6 integers = m + 2.5 = 3.5 + 2.5 = 6