L Let D be a recurring decimal of the form D=0. a1a2a1a2a1a2............; w

Question

L 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)

Options:

A . 18

B . 108

C . 198

D . 288

Answer: Option C
:
C
Ans: (c)

D = 0. a_{1} a_{2}; 100 D = a_{1} a_{2} . a_{1} a_{2}

(recurring); 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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