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:

When two groups of the same size overlap almost completely, like first 8 and 2nd to 9th here, which differ only by one term leaving and one term entering, the difference between their two sums directly gives the difference between the leaving and entering terms, without needing every individual value.

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).