Arithmetic & Commercial Maths› Averages
There are nine 2-digit consecutive odd numbers. If 59 is the mean of the first five such numbers, then what is the mean of all the nine numbers ?
Answer b.
The answer is (b) 63. The mean of the first five terms is the 3rd term (59), and the mean of all nine is the 5th term, two steps of 2 higher. Consecutive odd numbers differ by 2, so they form an arithmetic progression. The mean of any odd count of evenly spaced terms is the middle term. For the first five terms the middle is the 3rd term, so the 3rd term is 59. The terms are then 55, 57, 59, 61, 63, 65, 67, 69, 71 (all two-digit odd numbers). Check: the first five (55 to 63) sum to 295, and 295 / 5 = 59. For all nine terms the middle one is the 5th term, which is 63. Check by sum: 55 + 57 + 59 + 61 + 63 + 65 + 67 + 69 + 71 = 567, and 567 / 9 = 63. Shortcut: the 5th term is two steps of 2 above the 3rd, so 59 + 4 = 63.
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