Problem:
What is the value of
1β(β2)β3β(β4)β5β(β6)?
Answer Choices:
A. β20
B. β3
C. 3
D. 5
E. 21
Solution:
We know that when we subtract negative numbers,
aβ(βb)=a+b
The equation becomes
1+2β3+4β5+6=(D)5β
OR
Like Solution 1, we know that when we subtract aβ(βb), that will equal a+b as the opposite/negative of a negative is a positive. Thus,
1β(β2)β3β(β4)β5β(β6)=1+2β3+4β5+6
We can group together a few terms to make our computation a bit simpler.
1+(2β3)+4+(β5+6)=1+(β1)+4+1=(D)5β
The problems on this page are the property of the MAA's American Mathematics Competitions