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Circumference and Diameter Ratio

XAT 2022 · Quantitative Ability & Data Interpretation · Medium · Numbers

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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…3.141614161416\dots (repeating endlessly).

What is A−BA - B?

  1. A.

    21414

  2. B.

    7138

  3. C.

    21417

  4. D.

    21413

  5. E.

    15

Answer

B

Explanation

Let x=3.14161416⋯=3+14169999=3+4723333=104713333x = 3.14161416\dots = 3 + \frac{1416}{9999} = 3 + \frac{472}{3333} = \frac{10471}{3333}. Since AA and BB are coprime, A=10471A = 10471 and B=3333B = 3333. A−B=10471−3333=7138A - B = 10471 - 3333 = 7138.

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