2025 AMC 8 Problems/Problem 9
Contents
[hide]Problem
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?
Solution 1
Notice that this is simply the sum of the numbers on the clock face divided by . Why? This is because for a given number, it will be divided by
due to its averaging with its counterpart on the other side of the clock face, and then it will be divided by
when we average out all the smaller averages. Since the sum of the first
positive integers is
, our answer is
. ~cxsmi
Solution 2
The pairs for the opposite numbers on the clock are ,
,
,
,
, and
. The averages of each of these pairs are
and
respectively. The averages of
and
are
~Bepin999
Video Solution 1 by SpreadTheMathLove
https://www.youtube.com/watch?v=jTTcscvcQmI
Video Solution by Thinking Feet
See Also
2025 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.