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# What is sum of the eighty-third and eighty-fourth digits to the right

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What is sum of the eighty-third and eighty-fourth digits to the right  [#permalink]

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10 Jun 2016, 04:03
4
00:00

Difficulty:

45% (medium)

Question Stats:

71% (02:38) correct 29% (02:28) wrong based on 135 sessions

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What is sum of the eighty-third and eighty-fourth digits to the right of the decimal point when the fraction $$\frac{7}{27}$$ is written as a repeating decimal?

(A) 16

(B) 14

(C) 12

(D) 7

(E) 5

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Md. Abdur Rakib

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Re: What is sum of the eighty-third and eighty-fourth digits to the right  [#permalink]

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10 Jun 2016, 07:25

Not sure of any shortcut, but divided 7/27 for first 5 decimals, since 27 is 9*3 and both are repeating decimals and 27 is less than 100.So it seems 259 is repeating.so 84 is a factor of 3, so the 83rd and 84th will be 5,9. So answer is 14.
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Re: What is sum of the eighty-third and eighty-fourth digits to the right  [#permalink]

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10 Jun 2016, 07:36
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Bring the denominator to the form of 999

(7 * 37)/(27 * 37) = 259/999

259 will repeat successively --> 83rd and 84th digits are 5 and 9 --> 5 + 9 = 14

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Re: What is sum of the eighty-third and eighty-fourth digits to the right  [#permalink]

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10 Jun 2016, 07:49
AbdurRakib wrote:
What is sum of the eighty-third and eighty-fourth digits to the right of the decimal point when the fraction $$\frac{7}{27}$$ is written as a repeating decimal?

(A) 16

(B) 14

(C) 12

(D) 7

(E) 5

7/27= .259.... and the digits repeat themselves.

84 is a factor of three, after every three digits the digits are repeating.

So 84th digit will be= 9

and 83rd digit will be= 5

9+5=14
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Re: What is sum of the eighty-third and eighty-fourth digits to the right  [#permalink]

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10 Jun 2016, 07:59
7/27 = 0,259259...

So, the 84th term, which is a multiple of 3, is equal to 9, and the 83rd term is equal to 5
9+5 = 14
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Re: What is sum of the eighty-third and eighty-fourth digits to the right  [#permalink]

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30 Sep 2017, 06:41
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Re: What is sum of the eighty-third and eighty-fourth digits to the right &nbs [#permalink] 30 Sep 2017, 06:41
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