Bunuel wrote:
Does the integer k have at least four different prime factors?
(1) k/14 is an integer
(2) k/30 is an integer
Is k = a*b*c*d*n ?
Where a,b,c,d are different prime factors.
1) k = 14n
14 = 2*7
=> if k = 14, then it's prime factors are 2 and 7 => No.
=> if k = 14*15, then it's prime factors are 2,3,5 and 7 => Yes.
2 different answers. Insufficient.
2) k = 30m
30 = 2*3*5
=> if k = 30, then it's prime factors are 2,3 and 5 => No.
=> if k = 210, then it's prime factors are 2,3,5 and 7 => Yes.
2 different answers. Insufficient.
1+2)
k is divisible by 14 and 30 => k's prime factors are 2,3,5 and 7 at least.
Sufficient. Answer is C.
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