SBI PO – 2015 – 32

Question: The average of 7 consecutive odd numbers is 47. What is the greatest number among these seven numbers? [7 क्रमागत विषम संख्याओं का औसत 47 है. इन सात संख्याओं में सबसे बड़ी संख्या क्या है?] [Ans. (b) 53]

(a) 35      (b) 53     (c) 52     (d) 63     (e) None of these

Detailed explanation:

First Method: For any arithmetic series, middle term is the average of the series (if number of terms is odd).

For seven consecutive odd numbers, middle term, i. e., 4^th term is the average. Given that 47 is the average of the seven consecutive odd numbers, so 4^th term is 47.

Greatest number is 7^th term, which is 6 (2 × 3 = 6) more than 4^th term.

Therefore, greatest number is, 47 + 6 = 53. Ans.

Second Method: Let the seven consecutive odd numbers are (x - 6), (x - 4), (x - 2), x, (x + 2), (x + 4) and (x + 6)

Average of seven numbers is given 47; while no. of numbers is 7

Since, sum = average × number of item

So, (x - 6) + (x - 4) + (x - 2) + x + (x + 2) + (x + 4) + (x + 6) = 47 × 7

Or, 7x = 47 × 7, which implies that x = 47

Greatest of seven number = x + 6 = 47 + 6 = 53 Ans.