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

 It is currently 21 Oct 2019, 23:18

### 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 99th digit after the decimal point in the

Author Message
TAGS:

### Hide Tags

Board of Directors
Joined: 01 Sep 2010
Posts: 3405
What is the 99th digit after the decimal point in the  [#permalink]

### Show Tags

Updated on: 10 Mar 2012, 08:41
1
10
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:38) correct 25% (01:31) wrong based on 279 sessions

### HideShow timer Statistics

What is the 99th digit after the decimal point in the decimal expansion of 2/9 + 3/11?

A. 1
B. 2
C. 4
D. 7
E. 9

_________________

Originally posted by carcass on 10 Mar 2012, 08:23.
Last edited by Bunuel on 10 Mar 2012, 08:41, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 58398
Re: What is the 99th digit after the decimal point in the decim  [#permalink]

### Show Tags

10 Mar 2012, 08:37
carcass wrote:
What is the 99th digit after the decimal point in the decimal expansion of 2/9 + 3/11?

A. 1
B. 2
C. 4
D. 7
E. 9

$$\frac{2}{9} + \frac{3}{11}=\frac{22}{99} + \frac{27}{99}=\frac{49}{99}=0.494949...$$. So, 99th (odd placed after the decimal) digit will be 4.

For more on converting a recurring decimal to fraction check this: math-number-theory-88376.html

Hope it helps.
_________________
Board of Directors
Joined: 01 Sep 2010
Posts: 3405
Re: What is the 99th digit after the decimal point in the  [#permalink]

### Show Tags

10 Mar 2012, 09:54
I have not added OA because I hoped in a more long discussion.

Thanks
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1747
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: What is the 99th digit after the decimal point in the  [#permalink]

### Show Tags

02 Sep 2014, 23:02
2
$$\frac{2}{9} = 0.222222222...........2$$

$$\frac{3}{11}= 0.272727.............. 27$$

$$\frac{2}{9} + \frac{3}{11} = 0.4949494949....... 49$$

Odd's have 4

99th would have 4

_________________
Kindly press "+1 Kudos" to appreciate
Manager
Joined: 24 Aug 2016
Posts: 61
Location: India
WE: Information Technology (Computer Software)
Re: What is the 99th digit after the decimal point in the  [#permalink]

### Show Tags

18 Sep 2016, 02:04
$$\frac{2}{9}$$ = 0.22222.... ==> 99th digit is 2

$$\frac{3}{11}$$ = 0.27272727.... ==> Every odd digit is 2. So, 99th digit will be 2.

2 +2 = 4 ( Ans C)
_________________
"If we hit that bullseye, the rest of the dominos will fall like a house of cards. Checkmate."
Senior Manager
Joined: 24 Nov 2015
Posts: 490
Location: United States (LA)
What is the 99th digit after the decimal point in the  [#permalink]

### Show Tags

18 Sep 2016, 05:23
$$\frac{2}{9}$$ + $$\frac{3}{11}$$ = $$\frac{49}{99}$$

$$\frac{49}{99}$$ = 0.49494949..............

so the digits are getting repeated in order of two digits 49

so the 99 th digit is 4

Manager
Status: Single
Joined: 02 Jan 2016
Posts: 176
Location: India
Concentration: General Management, Accounting
GMAT 1: 730 Q49 V40
GPA: 4
WE: Law (Manufacturing)
Re: What is the 99th digit after the decimal point in the  [#permalink]

### Show Tags

25 Jan 2018, 22:55
Bunuel wrote:
carcass wrote:
What is the 99th digit after the decimal point in the decimal expansion of 2/9 + 3/11?

A. 1
B. 2
C. 4
D. 7
E. 9

$$\frac{2}{9} + \frac{3}{11}=\frac{22}{99} + \frac{27}{99}=\frac{49}{99}=0.494949...$$. So, 99th (odd placed after the decimal) digit will be 4.

For more on converting a recurring decimal to fraction check this: http://gmatclub.com/forum/math-number-theory-88376.html

Hope it helps.

HI what do you mean by 99th digit could you explain, I understand the theory of repeating no.'s but what do you mean by 99th Digit ?
Math Expert
Joined: 02 Sep 2009
Posts: 58398
Re: What is the 99th digit after the decimal point in the  [#permalink]

### Show Tags

25 Jan 2018, 23:00
hero_with_1000_faces wrote:
Bunuel wrote:
carcass wrote:
What is the 99th digit after the decimal point in the decimal expansion of 2/9 + 3/11?

A. 1
B. 2
C. 4
D. 7
E. 9

$$\frac{2}{9} + \frac{3}{11}=\frac{22}{99} + \frac{27}{99}=\frac{49}{99}=0.494949...$$. So, 99th (odd placed after the decimal) digit will be 4.

For more on converting a recurring decimal to fraction check this: http://gmatclub.com/forum/math-number-theory-88376.html

Hope it helps.

HI what do you mean by 99th digit could you explain, I understand the theory of repeating no.'s but what do you mean by 99th Digit ?

We need 99th digit after the decimal point of 0.494949...

The first digit is 4, the second digit is 9, the third digit is 4 again, the fourth digit is 9 again, ... 99th (odd placed after the decimal) digit will be 4.
_________________
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815
Re: What is the 99th digit after the decimal point in the  [#permalink]

### Show Tags

29 Jan 2018, 11:05
carcass wrote:
What is the 99th digit after the decimal point in the decimal expansion of 2/9 + 3/11?

A. 1
B. 2
C. 4
D. 7
E. 9

2/9 + 3/11 = 22/99 + 27/99 = 49/99 = 0.494949….

SInce each odd-positioned digit to the right of the decimal point has a value of 4, the 99th digit is 4.

Alternate Solution:

We see that 2/9 = 0.222… and 3/11 = 0.272727…

If we add the two decimal expressions, we see that we obtain 0.494949… Since all the odd-positioned digit to the right of the decimal point has a value of of 4, the 99th digit is 4.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
Joined: 09 Sep 2013
Posts: 13385
Re: What is the 99th digit after the decimal point in the  [#permalink]

### Show Tags

30 Sep 2019, 20:05
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: What is the 99th digit after the decimal point in the   [#permalink] 30 Sep 2019, 20:05
Display posts from previous: Sort by