CAT Exam Model Paper 4 with solutions for free online practice

We need to check for a base where 677 must have 5 digits if converted.
We also know that in Base 3, the decimal value of a 5-digit number must lie between 80 and 243 (as .‘81 signifies 10000' and ‘242 signifies 22222’ - the minimum and maximum possible 5-digit number in base 3).
So, the base cannot be 3.
Next we check for Base 4. The decimal value of a 5-digit number must lie between 255 and 1024. As 256 ≤ 677 ≤ 1023, this must be the minimum possible value of n.