Question

The number of positive $n$ in the range $12\le n\le 40$ such that the product $(n-1)(n-2).....3,2,1$, is not divisible by $n$ is

• A. $5$
• B. $7$
• C. $13$
• D. $14$

Answer 1

The correct option is B $7$

Product $(n-1)(n-2)...3\times 2\times 1$ is not divisible by $n$ if $n=4$ or a prime number.
We have to find the number of primes in
$12\le n\le 40$
$13,17,19,23,29,31,37$
$\therefore$ Number of positive integers in the range $=12\le n\le 40\Rightarrow 7$