Question

An n-digit number is a positive number with exactly n digits. Nine hundred distinct n-digit 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. 6
• B. 7
• C. 8
• D. 9

Answer 1

Answer: (B)

7

Answer 2

Distinct n-digit numbers which can be formed using digits 2,5 and 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 the least value of n is 7