Question

An $n$ digit number is a positive number with exactly $n$ digit. Nine hundred distinct $n$ digits numbers are to be formed using only the three digits $2,5$ and $7.$ The smallest value of $n$ for which this is possible is

• A. $5$
• B. $8$
• C. $6$
• D. $7$

Answer 1

The correct option is D $7$

Distinct n digit numbers which can be formed using digits $2,5,7$ are $3^n$.

We have to find n so that $3^n\ge 900$

$\Rightarrow 3^{n-2}\ge 100$

$\Rightarrow n-2\ge 5$

$\Rightarrow n\ge 7$

So least value of $n$ is $7$.