If \(n\) is an integer, which of the following must be even?
(A) \(n + 1\)
(B) \(n + 2\)
(D) \(2n + 1\)
I’m not going to spend too much time on this one. I suspect many students would be temped to use process of elimination with numbers (one odd and one even) or the properties of odds and evens. Both of those would work, but knowing the canonical form of odds and evens will lead you directly to the answer with little or no thought.
Canonical forms are expressions that mathematicians use to talk about entire groups of numbers algebraically without resorting to specific examples. In general the GMAT doesn’t require you to do that kind of thinking – specific example work great on multiple choice questions. However, there are cases where a little extra math can go a long way. This is one of those cases.
- All even integers can be expressed as \(2k\) where \(k\) is an integer.
- All odd integers can be expressed as \(2k + 1\) where \(k\) is an integer.
The correct answer is C.