There are 17 consecutive odd numbers. If the average of first 11 numbers is X. then what is the average of last 6 numbers?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. X + 17.
Let the 17 consecutive odd numbers be:
⇒ a, a+2, a+4, ......... , a+32
(a) is the first odd number.
The first 11 numbers are:
⇒ a, a+2, a+4, ...... , a+20
The sum of an arithmetic sequence is given by:
⇒ S = (n) / (2) × (first term) + (last term)
For the first 11 numbers, the sum is:
⇒ S = (11) / (2) × (a + (a+20)) = (11) / (2) × (2a + 20) = 11(a + 10)
The average of the first 11 numbers is:
⇒ (S) / (11) = (11(a+10)) / (11) = a + 10
this average is (X):
⇒ a + 10 = X
⇒ a = X - 10
Average of the Last 6 Numbers
⇒ a+22, a+24, a+26, a+28, a+30, a+32
⇒ S6 = (a+22) + (a+24) + (a+26) + (a+28) + (a+30) + (a+32)
⇒ S6 = 6a + (22 + 24 + 26 + 28 + 30 + 32) = 6a + 162
The average of the last 6 numbers is:
⇒ (S6) / (6) = (6a + 162) / (6) = a + 27
(a = X - 10), the average of the last 6 numbers is:
⇒ a + 27 = (X - 10) + 27 = X + 17