It is currently 15 Dec 2017, 08:17

Decision(s) Day!:

CHAT Rooms | Olin (St. Louis) R1 | Tuck R1 | Ross R1 | Fuqua R1


Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The decimal d is formed by writing in succession all the pos

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

3 KUDOS received
Intern
Intern
avatar
Joined: 24 Jan 2012
Posts: 9

Kudos [?]: 211 [3], given: 3

The decimal d is formed by writing in succession all the pos [#permalink]

Show Tags

New post 24 Sep 2013, 07:35
3
This post received
KUDOS
24
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

69% (01:04) correct 31% (00:59) wrong based on 483 sessions

HideShow timer Statistics

The decimal d is formed by writing in succession all the positive integers in increasing order after the decimal point; that is d = 0.123456789101112

What is the 100th digit of d to the right of decimal point ?

a) 0
b) 1
c) 5
d) 8
e) 9


I got the answer of this question after writing the 100th term in the series - although it was correct but it was time consuming. Not able to figure out the pattern. Can someone please help ?
[Reveal] Spoiler: OA

Last edited by Narenn on 24 Sep 2013, 10:30, edited 1 time in total.
Pls use the question stem to name the topic

Kudos [?]: 211 [3], given: 3

Expert Post
23 KUDOS received
MBA Section Director
User avatar
P
Status: Back to work...
Affiliations: GMAT Club
Joined: 21 Feb 2012
Posts: 4842

Kudos [?]: 3857 [23], given: 2464

Location: India
City: Pune
GMAT 1: 680 Q49 V34
GPA: 3.4
WE: Business Development (Manufacturing)
GMAT ToolKit User Premium Member
Re: 100th digit in series [#permalink]

Show Tags

New post 24 Sep 2013, 07:47
23
This post received
KUDOS
Expert's post
7
This post was
BOOKMARKED
Here is comparatively simpler way....

The number is 0.123456789101112.........

After Decimal digit
1 - 9 -------------------- 9 Digits
10 - 19 ----------------- 20 digits
20 - 29 ----------------- 20 digits
30 - 39 ----------------- 20 digits
40 - 49 ----------------- 20 digits
50 - 54 ----------------- 10 digit

5 and 4 are the 98th and 99th digits respectively hence 100th will be 5

Alternate Approach

Assume there are 100 blank spaces to fill.
First 9 places will be filled by first 9 single digit numbers i.e. 1 to 9.

We are now left with 91 places which will be filled by 2 digit numbers starting from 10.

TO fill 91 places we would need 91/2 = 45 numbers starting from 10. which will end on the number 54. Next number, for filling out 91th place, will be 5 from (55).

Hope that helps! :-D

Narenn
_________________

100+ Interview Debriefs from GMAT Club members

Must Read Forum Topics Before You Kick Off Your MBA Application

New GMAT Club Decision Tracker - Real Time Decision Updates

Kudos [?]: 3857 [23], given: 2464

2 KUDOS received
Current Student
User avatar
Joined: 06 Sep 2013
Posts: 1965

Kudos [?]: 759 [2], given: 355

Concentration: Finance
GMAT ToolKit User
Re: The decimal d is formed by writing in succession all the pos [#permalink]

Show Tags

New post 24 Feb 2014, 13:32
2
This post received
KUDOS
3
This post was
BOOKMARKED
violetsplash wrote:
The decimal d is formed by writing in succession all the positive integers in increasing order after the decimal point; that is d = 0.123456789101112

What is the 100th digit of d to the right of decimal point ?

a) 0
b) 1
c) 5
d) 8
e) 9


I got the answer of this question after writing the 100th term in the series - although it was correct but it was time consuming. Not able to figure out the pattern. Can someone please help ?


Good problem + 1

Now, let's see first we have those single digit numbers that occupy 9 spaces

Then the next integers from 10 to 19 will be 10 of them that will occupy 2 places each hence 20
The next ones will be from 20 to 29, 10 of them again, 2 places each hence 20 and so on
...
Until we get to 50-59 which will be 10 integers again, 2 places each hence 20 digits.

Now the 100th digit will be in the 50-59 range taking into consideration the first 9 single digit integers.

We also know that the tenth digits is always in an even place while the units digit is in the odd place. Therefore, the 100th digit will be the tenth digit of the given range (50-59) thus 5

Answer is C

Hope its clear
Cheers
J

Kudos [?]: 759 [2], given: 355

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1849

Kudos [?]: 2790 [0], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: The decimal d is formed by writing in succession all the pos [#permalink]

Show Tags

New post 04 Mar 2014, 21:33
0.123456789101112.........
We require to find the 100th digit from decimal
Looking at the series carefully, 10 th digit is 1, 12th digit is 1 & so on...... means 100th digit (even) will be in the tenth place of that number......

We require to find Tenth place of the two digit number; 100th term would be the digit near to 5 ... Answer = C
_________________

Kindly press "+1 Kudos" to appreciate :)

Kudos [?]: 2790 [0], given: 193

Intern
Intern
User avatar
Joined: 17 May 2012
Posts: 45

Kudos [?]: 12 [0], given: 126

Re: The decimal d is formed by writing in succession all the pos [#permalink]

Show Tags

New post 19 Nov 2014, 22:49
Hi,

The question stem sounds way too difficult for me to comprehend. Can someone kindly explain what the question asking us to find?

Thanks

Kudos [?]: 12 [0], given: 126

1 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1849

Kudos [?]: 2790 [1], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: The decimal d is formed by writing in succession all the pos [#permalink]

Show Tags

New post 20 Nov 2014, 00:05
1
This post received
KUDOS
1
This post was
BOOKMARKED
aj0809 wrote:
Hi,

The question stem sounds way too difficult for me to comprehend. Can someone kindly explain what the question asking us to find?

Thanks


d = 0.123456789101112 .........

The above series goes on .......... infinite

We require to find "100th digit" of d to the right of decimal point
_________________

Kindly press "+1 Kudos" to appreciate :)

Kudos [?]: 2790 [1], given: 193

4 KUDOS received
Current Student
avatar
Joined: 08 Feb 2014
Posts: 206

Kudos [?]: 84 [4], given: 145

Location: United States
Concentration: Finance
GMAT 1: 650 Q39 V41
WE: Analyst (Commercial Banking)
Premium Member
Re: The decimal d is formed by writing in succession all the pos [#permalink]

Show Tags

New post 03 Dec 2014, 16:53
4
This post received
KUDOS
1
This post was
BOOKMARKED
They ask for the 100th term. Clearly they don't expect us to write out the next 100 terms, thus there must be a shortcut.

first write out the first ten terms (careful, not the first ten complete numbers):

1 2 3 4 5 6 7 8 9 1

next, write out the next ten numbers, and so on:

1 2 3 4 5 6 7 8 9 1
0 1 1 1 2 1 3 1 4 1
5 1 6 1 7 1 8 1 9 2
0 2 1 2 2 2 3 2 4 2
5 2 6 2 7 2 8 2 9 3...

The 100th term will be divisible by ten, and thus will be in the farthest column to the right. Notice that this column seems to repeat each digit once, before increasing by 1 (we have a 1, followed by a 1, then a 2, which is followed by a 2, then a 3...)

The 100th term will be the tenth term in the last column, so with the pattern above in mind, write out the the first ten digits: 1122334455. Thus the answer is 5.

Kudos [?]: 84 [4], given: 145

Expert Post
8 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7800

Kudos [?]: 18136 [8], given: 236

Location: Pune, India
Re: The decimal d is formed by writing in succession all the pos [#permalink]

Show Tags

New post 03 Dec 2014, 19:17
8
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
aj0809 wrote:
Hi,

The question stem sounds way too difficult for me to comprehend. Can someone kindly explain what the question asking us to find?

Thanks


Look at the question one sentence at a time:

"The decimal d is formed by writing in succession all the positive integers in increasing order after the decimal point; "

This is how decimal d is formed - write all positive integers (i.e. 1, 2, 3, etc) in increasing order

"that is d = 0.123456789101112"

Here they have shown what they mean
d = 0.123456789101112... and so on goes the decimal

"What is the 100th digit of d to the right of decimal point ?"

If you continue putting down positive integers in increasing order, you will get a decimal with infinite digits to the right of decimal. What will be the 100th digit?
d = 0.1234567891011121314...
first digit after decimal is 1
second digit is 2
third digit is 3
10th digit is 1
What will be 100th digit?
First 9 digit will be 1 to 9.
Next 90 digits will come from the next 45 two digit numbers. The next 45 two digit numbers are 10 - 54.
We have accounted for 99 digits. The 100th digit will be the 5 of 55.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 18136 [8], given: 236

Expert Post
1 KUDOS received
SVP
SVP
User avatar
G
Joined: 11 Sep 2015
Posts: 1911

Kudos [?]: 2754 [1], given: 364

Location: Canada
Re: the decimal d is formed by writing in succession all positive integers [#permalink]

Show Tags

New post 15 Feb 2016, 15:43
1
This post received
KUDOS
Expert's post
abhasjha wrote:
The decimal d is formed by writing in succession all the positive integers in increasing order after the decimal point; that is d = 0.123456789101112

What is the 100th digit of d to the right of decimal point ?

a) 0
b) 1
c) 5
d) 8
e) 9


One-digit numbers:
.123456789
9 digits down, 91 remaining

Two-digit numbers:
With 91 remaining, we can handle 45 TWO-DIGIT NUMBERS (which will accommodate 90 of the required digits)
That is 10, 11, 12, .....54 (55 is next)
So, the 98th digit is 5, the 99th digit is 4, which means the 100th digit will be 5

Answer: C

ASIDE: To determine that there are 45 digits from 10 to 54 inclusive, I used a nice rule that says: the number of integers from x to y inclusive equals y - x + 1


Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2754 [1], given: 364

DS Forum Moderator
avatar
S
Joined: 21 Aug 2013
Posts: 570

Kudos [?]: 185 [0], given: 289

Location: India
Premium Member CAT Tests
Re: The decimal d is formed by writing in succession all the pos [#permalink]

Show Tags

New post 22 May 2017, 10:11
d = 0.1234567891011121314151617...

from 1 to 9 = 9 digits.. remaining digits are 91
After that all numbers (10, 11, 12, 13, ...) are composed of 'sets of two each' , meaning they are all 2 digit numbers.
So to figure this out, we can divide 91 by 2 and write it in the form: Dividend = Divisor*Quotient + Remainder
(dividend is 91, divisor is 2)

Now, 91 = 2*45 + 1

This means we will have '45' sets of two-digit numbers.. and a remainder of '1' means that our required digit will be the 1st digit of the 46th number.

Once again, we need to figure out 1st digit of the 46th number After 9, i.e., once we start counting from 10 onwards.

46th number after 9 = 46+9 = 55
So our required digit is the 1st digit of 55, or 5.

Hence answer is C

Kudos [?]: 185 [0], given: 289

Intern
Intern
avatar
B
Joined: 03 May 2014
Posts: 14

Kudos [?]: [0], given: 3

CAT Tests
Re: The decimal d is formed by writing in succession all the pos [#permalink]

Show Tags

New post 20 Nov 2017, 07:17
VeritasPrepKarishma wrote:
aj0809 wrote:
Hi,

The question stem sounds way too difficult for me to comprehend. Can someone kindly explain what the question asking us to find?

Thanks


Look at the question one sentence at a time:

"The decimal d is formed by writing in succession all the positive integers in increasing order after the decimal point; "

This is how decimal d is formed - write all positive integers (i.e. 1, 2, 3, etc) in increasing order

"that is d = 0.123456789101112"

Here they have shown what they mean
d = 0.123456789101112... and so on goes the decimal

"What is the 100th digit of d to the right of decimal point ?"

If you continue putting down positive integers in increasing order, you will get a decimal with infinite digits to the right of decimal. What will be the 100th digit?
d = 0.1234567891011121314...
first digit after decimal is 1
second digit is 2
third digit is 3
10th digit is 1
What will be 100th digit?
First 9 digit will be 1 to 9.
Next 90 digits will come from the next 45 two digit numbers. The next 45 two digit numbers are 10 - 54.
We have accounted for 99 digits. The 100th digit will be the 5 of 55.


Using your reasoning above I just wanted to check if this would be the right approach if the question asked for the 200th digit to the right of the decimal.

First 9 digits is 1 to 9
The next 191 digits will come from a combination of two digit and three digit numbers because we do not have enough two digit integers to reach 200 digits.
So we have to find how many digits we need to get to the 99th two digit integer. From 10 - 99 is 90 two digit integers which is 180 digits therefore next 180 digits will come from the next 90 two digit numbers which are 10 - 99.
We now have 9 + 180 = 189 digits but we still need 11 to get to the 200th digit.
Because the next batch of numbers are 3 digit numbers we need to take the next 3 (11/3) three digit numbers with are 100, 101, 102 with a remainder of 2 1(0)3. Therefore 0 is the 200th digit.

Kudos [?]: [0], given: 3

Re: The decimal d is formed by writing in succession all the pos   [#permalink] 20 Nov 2017, 07:17
Display posts from previous: Sort by

The decimal d is formed by writing in succession all the pos

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.