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# In the decimal expansion of 23912/33333

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BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2606
GRE 1: 323 Q169 V154
In the decimal expansion of 23912/33333 [#permalink]

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07 Nov 2016, 12:16
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Difficulty:

95% (hard)

Question Stats:

33% (01:45) correct 67% (01:53) wrong based on 69 sessions

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In the decimal expansion of 23912/33333 ,what is the 98th digit to the right of the decimal.
A) 1
B) 2
C) 3
4) 6
5) 7

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Re: In the decimal expansion of 23912/33333 [#permalink]

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07 Nov 2016, 13:18
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stonecold wrote:
In the decimal expansion of 23912/33333 ,what is the 98th digit to the right of the decimal.
A) 1
B) 2
C) 3
4) 6
5) 7

$$\frac{23912}{33333}$$ = 0.71736

There is a pattern , the set of 5 digits keeps repeating , so we have a cyclic order....

98/5 = 19 complete cycles and 3 remainder...

3rd digit from the right will be 7

Hence, the correct answer will be (E) 7

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BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2606
GRE 1: 323 Q169 V154
In the decimal expansion of 23912/33333 [#permalink]

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07 Nov 2016, 13:29
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Abhishek009 wrote:
stonecold wrote:
In the decimal expansion of 23912/33333 ,what is the 98th digit to the right of the decimal.
A) 1
B) 2
C) 3
4) 6
5) 7

$$\frac{23912}{33333}$$ = 0.71736

There is a pattern , the set of 5 digits keeps repeating , so we have a cyclic order....

98/5 = 19 complete cycles and 3 remainder...

3rd digit from the right will be 7

Hence, the correct answer will be (E) 7

Hi.
Did you perform the long division ?
Actually we don't need to perform the division.

Any number of the form P/Q where P and Q are positive integers with the same number of digits and Q=10n-1 will have the same repeating pattern as the numerator.

E.G=>
3/9= 0.33333...
83/99= 0.83838383...
356/999=0.356356356...
1234/9999=0.123412341234...
34569/99999=0.345693456934569...

Hence
23912/33333 = 71736/9999=> 0.71736717367173671736.....
Clearly the pattern repeats after every 5 digits
So the 98th digit is 7

Regards
Stone Cold
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BSchool Forum Moderator
Joined: 12 Aug 2015
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GRE 1: 323 Q169 V154
Re: In the decimal expansion of 23912/33333 [#permalink]

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16 Feb 2018, 22:36
VP
Joined: 28 Mar 2017
Posts: 1002
Location: India
Concentration: Finance, Technology
GMAT 1: 730 Q49 V41
GPA: 4
Re: In the decimal expansion of 23912/33333 [#permalink]

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17 Feb 2018, 01:49
stonecold wrote:
In the decimal expansion of 23912/33333 ,what is the 98th digit to the right of the decimal.
A) 1
B) 2
C) 3
4) 6
5) 7

Multiply and divide by 3 :

=> 71736/99999

Thus, it is 0.71736..... repetitive decimal.

98/5= remainder=3 ..... so answer=7 ..."E"
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Re: In the decimal expansion of 23912/33333   [#permalink] 17 Feb 2018, 01:49
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