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

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Senior RC Moderator
Joined: 02 Nov 2016
Posts: 3454
GPA: 3.39
For the positive integers a and b, represents the number of zeros bet  [#permalink]

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11 Aug 2019, 05:16
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40% (02:44) correct 60% (02:41) wrong based on 8 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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Joined: 05 Nov 2017
Posts: 9
For the positive integers a and b, represents the number of zeros bet  [#permalink]

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11 Aug 2019, 06:07
1/ab = 1/(6^5*5^6) = 1/(3^5*10^5*5)
= 1/1215 * 10^-5
1/1215 has three zeros between decimal point and first non zero digit.
10^-5 has four zeros between decimal point and first non zero digit.
So k' = 3 + 4 = 7

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For the positive integers a and b, represents the number of zeros bet   [#permalink] 11 Aug 2019, 06:07
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