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Let D be a recurring decimal of the form D=0.a1 a2 a1 a2.... [#permalink]
16 Dec 2007, 01:28

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Let D be a recurring decimal of the form D=0.a1 a2 a1 a2...., where digits a1 and a2 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?

Let D be a recurring decimal of the form D=0.a1 a2 a1 a2...., where digits a1 and a2 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?

a) 18 b) 108 c) 198 d) 288 e) 158

Please explain your answer

Walker u r ridiculous! so good at these.

Anyway, i remembered that 90/99=.90909090909090....

so one of the integers must be divisble by 9 and 11.

I, too, would be very curious in knowning the source of this question.
Does someone has idea if the real GMAT could give questions of a similar difficulty?
It seemes VERY STRANGE to me that GMAT would want you to remember that formula of the summatory.

Let D be a recurring decimal of the form D=0.a1 a2 a1 a2...., where digits a1 and a2 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?

a) 18 b) 108 c) 198 d) 288 e) 158

Please explain your answer

For those who dont want to be troubled by the Geometric Series and its formula, here is a short-cut to remember:
any recurring decimal with 'n' recurring digits can be written as: A/B
A = the n recurring digits
B = 10^n - 1

I, too, would be very curious in knowning the source of this question. Does someone has idea if the real GMAT could give questions of a similar difficulty? It seemes VERY STRANGE to me that GMAT would want you to remember that formula of the summatory.

Re: Let D be a recurring decimal of the form D=0.a1 a2 a1 a2.... [#permalink]
17 Aug 2013, 10:29

tarek99 wrote:

Let D be a recurring decimal of the form D=0.a1 a2 a1 a2...., where digits a1 and a2 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?

a) 18 b) 108 c) 198 d) 288 e) 158

0.123412341234.................... = 1234/9999

0.34343434........................... = 34/99

0.543543543543..................... = 543/999

so, 0.a1a2a1a2a1a2a1a2................ = a1a2/99 and 198 is a multiple of 99 . so Answer is (C) _________________

Re: Let D be a recurring decimal of the form D=0.a1 a2 a1 a2.... [#permalink]
21 Aug 2014, 12:01

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