Problem:
Which terms must be removed from the sum
21+41+61+81+101+121
if the sum of the remaining terms is to equal 1?
Answer Choices:
A. 41 and 81
B. 41 and 121
C. 81 and 121
D. 61 and 101
E. 81 and 101
Solution:
21+41+61+81+101+121=12060+12030+12020+12015+12012+12010
Since 60+30+20+10=120, it is clear that one may remove 12015=81 and 12012=101. Furthermore, one sees easily from the right hand side above that no other terms sum to 12027. Thus one must remove 81 and 101.