Find the average of all the numbers between 21 and 70 which are divisible by 3 and leave the remainder 2.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 45.5.
A number that gives remainder 2 when divided by 3 can = 3k + 2
The first and last such numbers in range (k) = 7 → 3×7 + 2 = 23 and k = 22 → 3×22 + 2 = 68
So numbers in this form = 23, 26, 29, ..., 68
First term a = 23, Last term l = 68 and Common difference d = 3
⇒ n = ((l - a) / d) + 1
⇒ n = ((68 - 23) / 3) + 1 = (45 / 3) + 1 = 15 + 1 = 16 terms
Average = (First term + Last term) / 2
Average = (23 + 68) / 2 = 91 / 2 = 45.5