# How do you find the two greatest consecutive even integers whose sum is less than 217?

Oct 29, 2016

The two greatest consecutive even integers are $106 \mathmr{and} 108$

#### Explanation:

Let the two consecutive even integers are $2 n \mathmr{and} 2 n + 2$

Their sum is $2 n + 2 n + 2 = 4 n + 2 < 217 \mathmr{and} 4 n < 215 \mathmr{and} 2 n < 107.5$

So the even number before $107.5$ is $2 n = 106 \mathmr{and} 2 n + 2 = 106 + 2 = 108$

The two greatest consecutive even integers are $106 \mathmr{and} 108$ [Ans]