Difference between revisions of "2016 AMC 8 Problems/Problem 8"
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==Solution== | ==Solution== | ||
− | {{ | + | We can group each subtracting pair together: |
+ | <cmath>(100-98)+(96-94)+(92-90)+ \ldots +(8-6)+(4-2).</cmath> | ||
+ | After subtracting, we have: | ||
+ | <cmath>2+2+2+\ldots+2+2=2(1+1+1+\ldots+1+1).</cmath> | ||
+ | There are 50 even numbers, therefore there are <math>50/2=25</math> even pairs. Therefore the sum is <math>2 \cdot 25=\boxed{\textbf{(C) }50}</math> |
Revision as of 08:45, 23 November 2016
Find the value of the expression
Solution
We can group each subtracting pair together: After subtracting, we have: There are 50 even numbers, therefore there are even pairs. Therefore the sum is