Gate Exam Numerical Ability Number System

The numeral 123 is in some base other than 10. When you change it to base 10, you get 66 base 10. In what base was the numeral 123 written?
Option
(a) 7
(b) 8
(c) 12
(d) 9

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Gate Other Question

Suppose we design a number system in which every number is represented by a different symbol, with no two of the symbols having anything in common. Which of the following would be disadvantages of the system?

I. This system could not have any symbol for zero.
II This system could not have the unique representation property.
III It would be hard to learn all of the different symbols.

(a) II and III only
(b) III only
(c) I and II
(d) II only
For the same amount of work carpenter A takes 6 hours less than carpenter B, if together they complete the work in 13 hrs 20 min; in how much time will carpenter B alone complete the work?