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Question

For positive integer n, 3n<n! when

A
n6
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B
n>7
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C
n7
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D
n7
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Solution

The correct option is C n7
For positive integer n,
3n<n!
Let n=1
31<1!
=3<1 which is not possible.
Let n=2
32<2!
=9<2 which is not possible.
Let n=6
36<6!
=729<720 which is not possible.
Let n=7
37<7!
=2187<5040 which is possible.
For positive integer n, 3n<n! when n7

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