Question
Quantitative Aptitude Question on Number Systems
Consider the expression (xxx)b = (62)b , where b is the base and x is any digit in base b. Find the value of (b + x).
A
5
B
12
C
10
D
7
Answer
7
Explanation
Solution
(xxx)b = x(b2 + b1 + b0)10
x(b2 + b1 + b0)10 = (62)10
x(b2 + b1 + b0)10 = (62)10
x = 2 or 31
But x is a digit. So, it cannot be 31; x must be 2.
(b2 + b1 + b0)10 = (31)10 = (52 + 51 + 1)10 = (52 + 51 + 50)10
b = 5
So, (b + x) = (5 + 2) = 7
So, the correct option is (D) : 7.