GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Mar 2019, 08:38

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# What is the 21st digit of the decimal [

Author Message
TAGS:

### Hide Tags

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

### Show Tags

29 Sep 2018, 10:19
7
00:00

Difficulty:

75% (hard)

Question Stats:

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

### HideShow timer Statistics

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

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

### Show Tags

29 Sep 2018, 22:53
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

_________________
##### General Discussion
RC Moderator
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]

### Show Tags

29 Sep 2018, 10:27
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
_________________

Please let me know if I am going in wrong direction.
Thanks in appreciation.

Director
Joined: 31 Jul 2017
Posts: 516
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: What is the 21st digit of the decimal [  [#permalink]

### Show Tags

29 Sep 2018, 10:34
2
This can be written as -

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

Hence, 7
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

Manager
Joined: 23 Aug 2016
Posts: 108
Location: India
Concentration: Finance, Strategy
GMAT 1: 660 Q49 V31
GPA: 2.84
WE: Other (Energy and Utilities)
Re: What is the 21st digit of the decimal [  [#permalink]

### Show Tags

29 Sep 2018, 10:35
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
_________________

Thanks and Regards,

Honneeey.

In former years,Used to run for "Likes", nowadays, craving for "Kudos". :D

Intern
Joined: 18 Oct 2017
Posts: 21
Location: India
Schools: IIM, Ryerson
Re: What is the 21st digit of the decimal [  [#permalink]

### Show Tags

29 Sep 2018, 12:11
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

Posted from my mobile device
Manager
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]

### Show Tags

29 Sep 2018, 15:11
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
Display posts from previous: Sort by