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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.