Problem:
101+102+103+104+105+106+107+108+109+1055=
Answer Choices:
A. 421
B. 6.4
C. 9
D. 10
E. 11
Solution:
The sum of all the numerators is 100. Consequently, the sum of all the fractions is 100/10=10.
OR
Regroup the fractions before adding:
(101+109)+(102+108)+(103+107)+(104+106)+(105+1055)=1+1+1+1+6=10.
Answer: D.
The problems on this page are the property of the MAA's American Mathematics Competitions