Carcass wrote:
In N is a positive integer less than 200, and 14N60 is an integer, then N has how many different positive prime factors?
A. 2
B. 3
C. 5
D. 6
E. 8
Let's choose a
nice value of N that satisfies the given information.
GIVEN: 14N/60 is an integer
Prime factorize the numerator and denominator to get: (7)(2)(N)/(2)(2)(3)(5) is an integer
Simplify: (7)(N)/(2)(3)(5) is an integer
Notice that, when
N = 30 (aka the product of 2, 3, and 5), then (7)(
N)/(2)(3)(5) = (7)
(2)(3)(5)/(2)(3)(5) = 7, which IS an integer
So, N =
30 satisfies the given information.
N has how many different positive prime factors?30 = (2)(3)(5)
So, N has 3 different positive prime factors (2, 3 and 5)
Answer: B