How many different prime numbers are factors of positive integer B?
1. 5 different prime numbers are factors of B^3 (Bcube).
Let
B = 6, # of different prime factors of B = 2 (2,3)
B^2 = 36 ((2^2)*(3^2)), # of different prime factors of B = 2 (2,3)
B^3 = 216 ((2^3)*(3^3)), # of different prime factors of B = 2 (2,3)
B^n = ((2^n)*(3^n)), # of different prime factors of B = 2 (2,3)
So, if B^n has X prime factors, then B has the same number of prime factors
Answer = 5 Sufficient
Sufficient!
2. 5 different prime numbers are factors of 3B.
Let B = 2*3*4*5*7, then 3B = 2*3*4*5*7*3
# of Prime factors of 3B = 5
# of Prime factors of B = 5
Let B = 2*4*5*7*11, then 3B = 2*4*5*7*11*3
# of Prime factors of 3B = 6
# of Prime factors of B = 5
Insufficient!
[spoiler]OA: A[/spoiler]
