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(4!)^n is a factor of 12!, but (4!)^(n+1) is not factor of 1

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by Max@Math Revolution » Sun Mar 13, 2016 9:21 pm
(4!)^n is a factor of 12!, but (4!)^(n+1) is not factor of 12!. What is the value of n?

A. 1
B. 2
C. 3
D. 4
E. 5


* A solution will be posted in two days.
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by Max@Math Revolution » Wed Mar 16, 2016 5:22 pm
(4!)^n is a factor of 12!, but (4!)^(n+1) is not factor of 12!. What is the value of n?

A. 1
B. 2
C. 3
D. 4
E. 5


-> 12!=210(integers) is derived. (4!)n=(23n)(3n) and in order to satisfy (4!)n+1=(23n+3)(3n+1), n should be 3.
Thus, the answer is C.
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