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101st digit after the decimal point

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Director
Director
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Joined: 16 May 2014
Posts: 594
GRE 1: Q165 V161
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Kudos [?]: 439 [0], given: 64

101st digit after the decimal point [#permalink] New post 08 May 2016, 03:00
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Question Stats:

68% (02:19) correct 31% (00:24) wrong based on 19 sessions
x = 1/3 + 1/9 + 1/27 + 1/37

Column AColumn B
101st digit after the decimal point in the decimal representation of x5


A bit hard one. Truth be told chances of getting a question like this in actual GRE is quite slim. Still good to practise these.
Kudos to the answer with the best explanation.
[Reveal] Spoiler: OA

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Manager
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Posts: 144
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Kudos [?]: 71 [0], given: 17

Re: 101st digit after the decimal point [#permalink] New post 26 May 2016, 08:18
B
bcoz 101st digit will be zero
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Manager
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Re: 101st digit after the decimal point [#permalink] New post 26 May 2016, 19:42
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the value is 508/999; This is a repeating decimal .508508.....; Hence 99th digit will be 8, so 101th digit will be 0. Hence answer is B
Intern
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Kudos [?]: 2 [0], given: 5

Re: 101st digit after the decimal point [#permalink] New post 27 May 2016, 17:58
soumya1989 wrote:
x = 1/3 + 1/9 + 1/27 + 1/37

Column AColumn B
101st digit after the decimal point in the decimal representation of x5


A bit hard one. Truth be told chances of getting a question like this in actual GRE is quite slim. Still good to practise these.
Kudos to the answer with the best explanation.




LCM of 27 & 37 is 999. So whatever goes to numerator, will repeat itself in the decimal reprsentation. In this case it is 508.
Now, 101 leaves a remainder of 2 when it is divided by the cyclicity period of the representation. Here, the cyclicity period is 3.
Therefore the 2nd digit of 508 will be the 101th number.

Ans: B
Manager
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Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 77 [0], given: 99

Re: 101st digit after the decimal point [#permalink] New post 28 Apr 2018, 20:43
AkashDU wrote:
soumya1989 wrote:
x = 1/3 + 1/9 + 1/27 + 1/37

Column AColumn B
101st digit after the decimal point in the decimal representation of x5


A bit hard one. Truth be told chances of getting a question like this in actual GRE is quite slim. Still good to practise these.
Kudos to the answer with the best explanation.




LCM of 27 & 37 is 999. So whatever goes to numerator, will repeat itself in the decimal reprsentation. In this case it is 508.
Now, 101 leaves a remainder of 2 when it is divided by the cyclicity period of the representation. Here, the cyclicity period is 3.
Therefore the 2nd digit of 508 will be the 101th number.

Ans: B



How did you get 508 in numerator?
Re: 101st digit after the decimal point   [#permalink] 28 Apr 2018, 20:43
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