# 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 09:45, 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