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Quantitative Aptitude

Base Systems

Let D be a re...

Question

Let D be a recurring decimal of the form $D = 0. a_{1} a_{2} a_{1} a_{2} a_{1} a_{2} . . . . . . . . . . . .;$ where digits $a_{1}$ and $a_{2}$ lie between 0 and 9. Further, at most one of them is zero. Which of the following numbers necessarily produces an integer, when multiplied by D? (CAT 2000)

A

18

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B

108

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C

198

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D

288

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Solution

The correct option is C 198
$D = 0. a_{1} a_{2} (r e c u r r i n g); 100 D = a_{1} a_{2} . a_{1} a_{2} (r e c u r r i n g)$ . Thus, $99 D = a_{1} a_{2} \Rightarrow D = (\frac{a_{1} a_{2}}{99})$ .

Required number should thus be a multiple of 99. Hence 198 is the required number.

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