If a positive odd integer N has p positive factors, how many positive factors will 6N have ?
Choose the correct choice from the following:  A) p  B) 2p  C) P+1  D) 2p+1  E) Cannot be determined
I have added some extra text to make this question more GMAT-like:   Let's TEST some values of N   Try N = 3   The factors of 3 are {1, 3}. Here, p =2   So, 2N = (2)(3) = 6   The factors of 6 are {1, 2, 3, 6}. So, we have a total of4   Now check the answer choices:   A) p =2No good. We want an output of4. ELIMINATE   B) 2p = (2)(2) = 4. PERFECT! KEEP B   C) P+1 =2+ 1= 
<gadget id="calculator">2+ 1</gadget>
<output>3</output>
3 No good. We want an output of4. ELIMINATE   D) 2p+1= (2)(2) + 1 = 5 No good. We want an output of4. ELIMINATE   E) Cannot be determined. POSSIBLE. KEEP E   Let's TEST another value of N   Try N = 7   The factors of 7 are {1, 7}. Here, p =2   So, 2N = (2)(7) = 14   The factors of 14 are {1, 2, 7, 14}. So, we have a total of4   Now check the REMAINING answer choices:   B) 2p = (2)(2) =4. PERFECT! KEEP B   E) Cannot be determined. POSSIBLE. KEEP E   Let's TEST one more (non-prime) value of N   Try N = 9   The factors of 9 are {1, 3, 9}. Here, p =3   So, 2N = (2)(9) = 18   The factors of 18 are {1, 2, 3, 6, 9}. So, we have a total of6   Now check the REMAINING answer choices:   B) 2p = (2)(3) =6. PERFECT! KEEP B   E) Cannot be determined. POSSIBLE. KEEP E   pt this point, it SEEMS LIKELY that the correct answer is p
<result>A</result>
If a positive odd integer N has p positive factors, how many positive factors will 6N have ?