Question

The average of the first 7 numbers in a series is 60. When the 8th number is added, the average of the first 8 numbers becomes 63. The 9th number is 11 more than the 8th number. It is also given that the average of the 2nd to the 9th numbers is 66. Find the value of the 1st number in the series.

• A. 68
• B. 70
• C. 71
• D. 75

Hint:

In problems involving consecutive averages, the difference in sums directly gives the value of the newly added member. For example, Sum(8 numbers) - Sum(7 numbers) = 8th number.

Answer 1

The Correct Option is C

Step 1: Get every needed total: sum of first 8 \( = 8\times63=504 \); sum of 2nd-to-9th \( =8\times66=528 \); \( N_8 = 504-(7\times60)=84 \), so \( N_9=84+11=95 \).
Step 2: Total of all 9 numbers \( = (\text{first 8}) + N_9 = 504+95=599 \).
Step 3: The 2nd-to-9th sum is just this total with \( N_1 \) removed:
\[ N_1 = 599 - 528 = \boxed{71}. \]

Final answer: 71 (option C).