If a positive odd integer N has p positive factors, how many positive

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 of 4

Now check the answer choices:
A) p = 2 No good. We want an output of 4. ELIMINATE
B) 2p = (2)(2) = 4. PERFECT! KEEP B
C) P+1 = 2 + 1 = 3 No good. We want an output of 4. ELIMINATE
D) 2p+1 = (2)(2) + 1 = 5 No good. We want an output of 4. 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 of 4

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 of 6

Now check the REMAINING answer choices:
B) 2p = (2)(3) = 6. PERFECT! KEEP B
E) Cannot be determined. POSSIBLE. KEEP E

At this point, it SEEMS LIKELY that the correct answer is B
NOTE: This strategy of testing values, while not perfect, can still help you eliminate answer choices to give yourself a better chance of correctly guessing the right answer.

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