Ningli looks at the 6 pairs of numbers directly across from each other on a clock. She takes the average of each pair of numbers. What is the average of the resulting 6 numbers?

A. 5

B. 6.5

C. 8

D. 9.5

E. 12

1. 2025 AMC 8 官方解析

Answer (B): The pairs of opposite numbers and their averages are shown in the table below:

The average of these 6 numbers is
$\frac{4 + 5 + 6 + 7 + 8 + 9}{6} = \frac{39}{6} = \frac{13}{2} = 6.5.$

$\text{OR}$

The average of the 6 averages is
$\frac{\frac{1+7}{2} + \frac{2+8}{2} + \frac{3+9}{2} + \frac{4+10}{2} + \frac{5+11}{2} + \frac{6+12}{2}}{6} = \frac{1 + 2 + \dots + 12}{2 \cdot 6} = \frac{78}{12} = \frac{13}{2} = 6.5.$

Notice that this is the same as the average of the numbers on the clock.