Question

Let $N$ be least positive integer such that whenever a non-zero digit $c$ is written after the last digit of $N$, the resulting number is divisible by $c$. The sum of the digits of $N$ is

• A. $9$
• B. $18$
• C. $27$
• D. $36$

Answer 1

The correct option is A $9$

$N$ is least positive integer and when a digit $c$ is written after last digit of $N$, the resulting number is divisible by $c$.

$\Rightarrow$ So, $\frac{\left(N\right)c}{c}$

Least positive integer $\left(N\right)$ which is divisible by digit $c$ i.e. $(1-9)$

So possible number is

$\Rightarrow$ $\frac{(9\times 8\times 7\times 5)c}{c}$

Number, $9\times 8\times 7\times 5$ is divisible by all the digits from $1$ to $9$

$\Rightarrow$ So, Number is $72\times 35=2520=N$

$\Rightarrow$ Sum of the digits of number $N=2+5+2+0=9$