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

Since at any place, any of the digits 2, 5 and 7 can be used total number of such positive n-digit numbers are $3^{n}$. Since we have to form 900 distinct numbers, hence$3^{n} \geq 900 \Rightarrow n = 7$