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This problem trains for: SAT-I, AMC-8, GMAT.

For any integer value n, how many values can the expression below have?

n is an integer, therefore it is either even::

or it is odd:

Therefore, for n odd the expression is equal to:

and for n even the expression is:

One can see that the expression is built in such a way as to have the same value,

regardless of the value of n.

The correct answer is A.