Numerical System

Question

This was my interview question in the question paper. please help me in finding the answer .

" in a class of 100 students 24 of them are girls and 32 are not. Which numerical system base are we using here? ( Hint: Decimal system base is 10 and binary system base is 2) "

thanks in advance.

Answer 1

Hint: Assume that any person in the class is either a boy or a girl. Let $b$ be the base. Then we have $b^2=(2b+4)+(3b+2)$.

Answer 2

Hint: Since the last digit of the sum is $0$, we must have $4+2=10_b$, since the sum of two digits in any base is always less than $2b$.

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This assumes that the class contains no transgendered students who're counted as both girls and not-girls (or neither!)