Question

Shireen draws a circle in her courtyard. She then measures the circle's circumference and its diameter with her measuring tape and records them as two integers, A and B respectively. She finds that A and B are co-primes, that is, their greatest common divisor is 1. She also finds their ratio, A:B, to be: $3.141614161416\dots$ (repeating endlessly).

What is $A - B$ ?

Accepted Answer

B. Let $x = 3.14161416\dots = 3 + \frac{1416}{9999} = 3 + \frac{472}{3333} = \frac{10471}{3333}$. Since $A$ and $B$ are coprime, $A = 10471$ and $B = 3333$. $A - B = 10471 - 3333 = 7138$.

Circumference and Diameter Ratio

Explanation

Practise this under exam conditions