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If n  is an odd integer, which of the following must be an odd integer?

• (A) n - 1
• (B) n + 1
• (C) 2n
• (D) 3n + 1
• (E) 4n + 1    CORRECT ANSWER

Explanation:

If n is an odd integer, both one more and one less than n  will be even integers, eliminating choices (A) and (B). Any even multiple of n  will be an even integer, eliminating choice (C). However, 4n  is even, making 4n +1 an odd integer. The answer to this problem is (E). Note that 3n  + 1 is even if n  is odd and it is odd if n  is even. Since the question asks, "Which of the following MUST be an odd integer," (D) cannot be the correct answer.

(from the October 20, 1998 test)