# 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) 2
*n* - (D) 3
*n*+ 1 - (E)
**4**CORRECT ANSWER*n*+ 1

##### 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, 4*n* is even, making 4*n* +1 an odd integer. The answer to this problem is (E). Note that 3*n* + 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)