EvenQ[expr] gives True if expr is an even integer, and False otherwise.
EvenQ[expr] returns False unless expr is manifestly an even integer (i.e., has head Integer, and is even).
You can use EvenQ[x] ^= True to override the normal operation of EvenQ, and effectively define x to be an even integer.
See The Mathematica Book: Section 2.3.5 and Section 3.1.1.
See also: IntegerQ, OddQ, TrueQ.