Question

$(35{)}_n,(37{)}_n,\left(45{)}_{n}and\right(51{)}_n$ all are written in base n then the value of n, such that all the four numbers when written in decimal system, they must be the consecutive prime numbers :

• A. n = 8
• B. n = 2
• C. n = 12
• D. n = 6

Answer 1

The correct option is A n = 8

Going throught option (b) is the invalid option.
Option (d) is also wrong since $(53{)}_6$ = 33 which is not a prime number and option (c) is also wrong since $(53{)}_{12}$ = 60 + 3 = 63 which is not a prime number.
Hence option (a) is the correct. You can verify by assuming the value of n.