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 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 3ⁿ. We have to find n so that 3ⁿ ≥ 900 ⇒ 3^{n - 2} ≥ 100.

⇒ n - 2 ≥ 5 ⇒ n ≥ 7

So the least value of n is 7.