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XAT 2022 — QA & DI Question 18

ProgressionsEasy
Passage / Data

Read the following scenario and answer the THREE questions that follow.
An examination had ten multiple choice questions; labelled Q1 to Q10 respectively. Each question had four answer options — A, B, C and D — of which one and only one was the correct answer. For each correct answer, the candidate obtained 1 mark. There were no negative marks for wrong answers. The answers chosen by six candidates named Om, Pavan, Qadir, Rakesh, Simranjeet and Tracey to each of the ten questions and the total marks obtained by each of them are shown in the table.

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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 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?

Answer & solution

  • A

    21414

  • 7138

  • C

    21417

  • D

    21413

  • E

    15

Solution

We have
3.1416141614161416......
= 3 + 0.1416 + 0.00001416 + 0.000000001416.....

= 3 + 1416104 + 1416108 + 14161012 + ....

Now excluding 3 we get a series with infinite Geometric progression such that first term is 1416104 and common ratio is 1104

Therefore we get sum as a1-r

= 14161041-1104

we get sum as 1416104-1

= 14169999

Now adding 3 we get value as :

314139999

Now adding 3 we get value A : B as :

104713333

So A - B will be = 7138

Hence, option (b).

XAT 2022 QA & DI Q18: Shireen draws a circle in her courtyard. She then measures the circle’s circumference and its diameter w — Solution | TheCATExam