Problem:
Which one of the following integers can be expressed as the sum of 100 consecutive positive integers?
Answer Choices:
A. 1,627,384,950
B. 2,345,678,910
C. 3,579,111,300
D. 4,692,581,470
E. 5,815,937,260
Solution:
Since
1+2+3+⋯+100=(100)(101)/2=5050
it follows that the sum of any sequence of 100 consecutive positive integers starting with a+1 is of the form
(a+1)+(a+2)+(a+3)+⋯+(a+100)​=100a+(1+2+3+⋯+100)=100a+5050.​
Consequently, such a sum has 50 as its rightmost two digits. Choice A is the sum of the 100 integers beginning with 16,273,800.