XAT 2022 Question Paper | Quantitative Aptitude and Data Interpretation

XAT Previous Year Paper | XAT QADI Questions | Question 12

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Question 12 : 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 coprimes, that is, their greatest common divisor is 1. She also finds their ratio, A:B, to be: 3.141614161416... (repeating endlessly).

What is A - B ?

  1. 21413
  2. 7138
  3. 21417
  4. 15
  5. 21414

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Explanatory Answer

It is given that \(\frac{A}{B}\) = 3.14161416 . . . .
\(\frac{A}{B}\) = \(\frac{31413}{9999}\)
These two are not co-primes. These two numbers have 3 also in common.
\(\frac{A}{B}\) = \(\frac{10471}{3333}\). Now, these two are co-primes.
Hence the difference of A - B = 10471 - 3333 = 7138.

The answer is '7138'

Choice B is the correct answer.

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