Problem:
What is the value of the following expression?
1+2−3+4+5−6+7+8−9+10+11−12
Answer Choices:
A. 18
B. 21
C. 24
D. 27
E. 30
Solution:
A helpful way to evaluate the expression is to notice the repeating pattern of signs: (+,+,−), (+,+,−), (+,+,−), (+,+,−). So we group the terms in threes: (1+2−3)+(4+5−6)+(7+8−9)+(10+11−12). Evaluating each group gives 0+3+6+9=(A) 18.
The problems on this page are the property of the MAA's American Mathematics Competitions