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Senior DS Moderator V
Joined: 27 Oct 2017
Posts: 1219
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
What is the 21st digit of the decimal [  [#permalink]

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7 00:00

Difficulty:   75% (hard)

Question Stats: 48% (02:24) correct 52% (02:25) wrong based on 54 sessions

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Weekly Quant Quiz Question - 5

What is the 21st digit of the decimal $$\frac{1}{111} + \frac{1}{37} + \frac{1}{27} + \frac{1}{9} + \frac{1}{3}$$ ?
a) 5
b) 6
c) 7
d) 8
e) 9

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Senior DS Moderator V
Joined: 27 Oct 2017
Posts: 1219
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
What is the 21st digit of the decimal [  [#permalink]

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1

Official Solution:

$$\frac{1}{111} + \frac{1}{37} + \frac{1}{27} + \frac{1}{9} + \frac{1}{3}$$
= $$\frac{9}{999} + \frac{27}{999} + \frac{37}{999} + \frac{111}{999} + \frac{333}{3999}$$
= $$\frac{517}{999}$$
= 0.517517517...
It is clear that 7 at places 3rd, 6th, 9th... multiple of 3.
Hence 21st digit is 7

Method to convert fraction (with only 9 as digits in denominator) to decimal

• If the fraction is abc/999, decimal will be 0.abcabcabc...
We need to just repeat the numerator indefinitely after the decimal.
• if the fraction is ABC/99999, decimal will be 0.00ABC00ABC
We need to add zeros after zero at the start of numerator and repeat it indefinitely.

gmatbusters wrote:

Weekly Quant Quiz Question - 5

What is the 21st digit of the decimal $$\frac{1}{111} + \frac{1}{37} + \frac{1}{27} + \frac{1}{9} + \frac{1}{3}$$ ?
a) 5
b) 6
c) 7
d) 8
e) 9

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##### General Discussion
RC Moderator D
Joined: 24 Aug 2016
Posts: 744
Concentration: Entrepreneurship, Operations
GMAT 1: 630 Q48 V28 GMAT 2: 540 Q49 V16 Re: What is the 21st digit of the decimal [  [#permalink]

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1/111+1/37+1/27+1/9+1/3= .009 + .027+.037+.111+.333 = 0.xx7 as the 3rd is 7 the 21st is also 7 ==> Ans C
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Director  P
Joined: 31 Jul 2017
Posts: 516
Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33 GPA: 3.95
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Re: What is the 21st digit of the decimal [  [#permalink]

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2
This can be written as -

13/27 + 4/111 = 0.0360360360... + 0.481481.. = 0.517517

Hence, 7
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Manager  G
Joined: 23 Aug 2016
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GMAT 1: 660 Q49 V31 GPA: 2.84
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Re: What is the 21st digit of the decimal [  [#permalink]

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1
1/111+1/37=4/111=21st and 22nd digit=6,0
1/27+1/9+1/3=21st and 22nd digit 1,4
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Intern  B
Joined: 18 Oct 2017
Posts: 21
Location: India
Schools: IIM, Ryerson
Re: What is the 21st digit of the decimal [  [#permalink]

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3
1/3 = 0.3333(non- terminating)

Thus, 21st digit is 3

1/9 = 0.11111(non-terminating)

Thus, 21st digit is 1

1/27 = 0. 037037

Thus number repeats in sequence of 3 digits - 037, thus 21st digit number is 7

1/37 = 0.027. Thus, same as above, 21st digit is 7

1/111 = 0.009, thus, for same reason as above, 21st digit is 9

Adding above, 3+1+7+7+9 = 7

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Manager  S
Joined: 27 Aug 2014
Posts: 138
Concentration: Finance, Strategy
GPA: 3.9
WE: Analyst (Energy and Utilities)
Re: What is the 21st digit of the decimal [  [#permalink]

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1
Expressing each of the fractions in the decimal form:

1/3 = 0.333333333333.... --> 21st digit is 3
1/9 = 0.111111111111... --> 21st digit is 1
1/27 = 0.037037037037...--> 21st digit is 7
1/37 = 0.027027027027.. --> 21st digit is 7
1/111= 0.009009009...... --> 21st digit is 9

9+7+7+1+3 = 27, 7 is the 21st digit and 2 is carried over for sum in 20th digit.

C Re: What is the 21st digit of the decimal [   [#permalink] 29 Sep 2018, 15:11
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# What is the 21st digit of the decimal [

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