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
"No"
1001+2+⋯+99+x=100299⋅100+x=10099⋅50+x=100x
This equation is equivalent to 9999x=(99⋅101)x=99⋅50, so x=10150.
The problems on this page are the property of the MAA's American Mathematics Competitions