Math Multiple Choice
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
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)