Problem:
The average of the numbers 1,2,3,…,98,99, and x is 100x. What is x?
Answer Choices:
A. 10149​
B. 10150​
C. 21​
D. 10151​
E. 9950​
Solution:
The average of the numbers is
1001+2+⋯+99+x​=100299⋅100​+x​=10099⋅50+x​=100x
This equation is equivalent to 9999x=(99⋅101)x=99⋅50, so x=(B)10150​​.
The problems on this page are the property of the MAA's American Mathematics Competitions