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# For the positive integers a and b, represents the number of zeros bet

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For the positive integers a and b, represents the number of zeros bet  [#permalink]

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11 Aug 2019, 04:16
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Difficulty:

85% (hard)

Question Stats:

32% (02:30) correct 68% (02:40) wrong based on 25 sessions

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For the positive integers $$a$$ and $$b$$, $$k'$$ represents the number of zeros between the decimal point and the first nonzero digit to the right of the decimal point in the reciprocal of the product of $$a$$ and $$b$$, when that reciprocal is expressed as a terminating decimal. What is the value of $$k' (6^5, 5^6)$$ ?

A. 7

B. 8

C. 9

D. 10

E. 11

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For the positive integers a and b, represents the number of zeros bet  [#permalink]

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Updated on: 25 Aug 2019, 06:57
1/ab = 1/(6^5*5^6) = 1/(3^5*10^5*5)
= 1/1215 * 10^-5 = (1/1.215)*10^-8
(1/1.215) is a number less than 1 but greater than 0.1 of the form '0.xyz' where x,y,z are single digit numbers with x <> 0
This will give 8 zeros between decimal point and first non-zero digit right of the decimal point.

Sent from my iPhone using GMAT Club Forum

Originally posted by karthik1488 on 11 Aug 2019, 05:07.
Last edited by karthik1488 on 25 Aug 2019, 06:57, edited 1 time in total.
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Re: For the positive integers a and b, represents the number of zeros bet  [#permalink]

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24 Aug 2019, 15:45
2^5·3^5·5^6
Combine the 2s and 5s to get terminating 0s.
10^5·3^5·5=121,500,000

It is the reciprocal so 1/121,500,000

And I said 9 as there are nine digits. Calculator tells me 8. Don't know why. Expert please respond
Re: For the positive integers a and b, represents the number of zeros bet   [#permalink] 24 Aug 2019, 15:45