Math Relationship / Translating

[linpeng06]

I don't understand the following question:

If j and k are even integers and j< k, which of the following equals the number of even integers that are greater than j and less than k ?
a. (k-j-2)/2
b. (k-j-1)/2
c.(k-j)/2
d.(k-j

The explanation says since j and k are even integers, it follows that k = j + 2n . Where did this come from? I don't see how they got k = j+2n; having trouble translating it.

[tommywallach]

k = j+2n

Just think about it logically. If j is (for example) 4, what could k be?

It could be 6, 8, 10, 12, 14, 16.

In other words, k is always j + SOME MULTIPLE OF 2. The way we express SOME MULTIPLE OF 2 algebraically is with a new variable (in this case, they use "n").

Hope that helps!

-t