Sara is an avid lottery player. In the certain game she plays, she must pick one number between 30 and 39, inclusive, one number between 40 and 49, inclusive, and one number between 50 and 59, inclusive. She believes that she will have the best chance of winning if her three numbers, as a set, have the greatest number of distinct prime factors possible. According to Sara’s theory, which of the following sets of three numbers should she use?	Choose the correct option.
A) 32−48−52 B) 33−42−56 C) 39−40−54 D) 38−49−51 E) 36−42−56
A: 32 (2 as the only PF), 48 (2 and 3 as PF), 52 ( 2 and 13 and PF) - Distinct Prime Factors as a set = 3 (2, 3, and 13).   B: 33 (11 and 3 as PF), 42 (2,3, and 7 as PF), 56 (2 and 7 as PF) - Distinct Prime Factors as a set = 4 (11, 3, 2, and 7).   C: 39 (3 and 13 as PF), 40 (2 and 5 as PF) and 54 (3 and 2 as PF) - Distinct Prime Factors as a set = 4 (3, 13, 2, and 5)   D: 38 (2 and 19 as PF), 49 (7 only) and 51 (17 and 3 as PF) - Distinct Prime Factors as a set = 5 (2, 19, 7, 3, and 17).   E: 36 (2 and 3 as PF), 42 (2, 3, and 7) and 56 ( 2 and 7 as PF) - 38−49−51istinct Prime Factors as a set = 3 (2, 3, 7)   Answer 38−49−51.
<result>D</result>
Sara is an avid lottery player. In the certain game she plays, she must pick one number between 30 and 39, inclusive, one number between 40 and 49, inclusive, and one number between 50 and 59, inclusive. She believes that she will have the best chance of winning if her three numbers, as a set, have the greatest number of distinct prime factors possible. According to Sara’s theory, which of the following sets of three numbers should she use?