Number Base Systems Equation

XAT 2013 · QADI · Hard · Number Systems

All XAT 2013 questions More Number Systems questions All CAT QADI

Consider the expression $(xxx)_b = x^3$ , where b is the base, and x is any digit of base b. Find the value of b:

A.
5
B.
6
C.
7
D.
8
E.
None of the above

Answer

E

Explanation

$(xxx)_b = x \cdot b^2 + x \cdot b + x = x(b^2 + b + 1)$ . $x(b^2 + b + 1) = x^3 \implies b^2 + b + 1 = x^2$ . Since $x < b$ , $x^2 < b^2 < b^2 + b + 1$ , so $b^2 + b + 1 = x^2$ has no valid integer solution with $x < b$ . Thus, None of the above.

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace