Question

$n-digit$ numbers are formed using only three digits $2,5$ and $7$. The smallest value of $n$ for which $900$ such distinct numbers can be formed, is

• A. $6$
• B. $8$
• C. $9$
• D. $7$

Answer 1

The correct option is D $7$

Clearly the number of such $n$ digit numbers is $3^n$ as each place in the number can be filled by a non-zero digit $2,5,7$.

So we find the least $n$ such that $3^n>900$. Clearly $n=7$.

So the correct answer is option D.