2025 AMC 8 Problems/Problem 9
Contents
[hide]Problem
Ningli looks at the 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
numbers?
Solution 1
Our answer is
~Sigmacuber
Solution 2
The averages of all of 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
Solution 3 (most efficient)
The problem is asking for the average of all numbers. To find the average of all
numbers, you find the sum of all the integers from
to
which is
, and divide it by
because there are 12 terms. Therefore, the answer is
.
~JacQueen2024
Video Solution 1 by SpreadTheMathLove
https://www.youtube.com/watch?v=jTTcscvcQmI
Video Solution 2
Video Solution 3 by Thinking Feet
Video Solution 4 by Cool Math Problems
https://youtu.be/BRnILzqVwHk?si=Akl6WBBA3yIJYI4X&t=399
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.