Re: Which of the following is divisible by an odd number of diff
[#permalink]
26 Sep 2024, 02:38
OE
The right answer(s) for this question must have an odd number of factors in order to be divisible by an odd number of different positive integers. First, eliminate any prime numbers since they are divisible only by themselves and 1. (B) 17 is a prime number. Now check the remaining choices. The factors of 9 are 1, 3, and 9, so (A) is a correct choice. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24 for a total of 8, so eliminate (C). The distinct factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36 for a total of 9, so (D) is a correct choice. Finally, the factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. Since there are 8 factors, (E) is incorrect. The correct choices are (A) and (D).