NEW HERE? LEARN MORE
closeclose
Last visit was: 03 May 2024, 22:11 It is currently 03 May 2024, 22:11
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

A number N is formed by placing first 100 integers in order

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
B
enak
Intern
Intern
Joined: 06 Aug 2017
Posts: 3
Own Kudos [?]: 26 [27]
Given Kudos: 48
Send PM
A number N is formed by placing first 100 integers in order [#permalink] New post   01 Aug 2018, 23:06
2
Kudos
25
Bookmarks
00:00
A
B
C
D
E

Difficulty:

75% (hard)

Question Stats:

54% (02:04) correct 46% (02:01) wrong based on 227 sessions
Hide Show timer Statistics
A number N is formed by placing integers in order (N= 1234567891011121314.......). If N is a 150 digit number, what is the remainder when N is divided by 10?

(A) 1
(B) 3
(C) 7
(D) 8
(E) 9
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14869
Own Kudos [?]: 65078 [5]
Given Kudos: 431
Location: Pune, India
Send PM
Re: A number N is formed by placing first 100 integers in order [#permalink] New post   02 Aug 2018, 03:08
3
Kudos
2
Bookmarks
Expert Reply
enak wrote:
A number N is formed by placing first 100 integers in order (N= 1234567891011121314.......). If N is a 150 digit number, what is the remainder when N is divided by 10?

(A) 1
(B) 3
(C) 7
(D) 8
(E) 9


N is obtained by placing integers in order (it shouldn't say first 100 because that defines the number of digits as 192)

N has 150 digits -
The first 9 digits will be 1 - 9. Now we need to figure out the next 141 digits.
Each subsequent number will be a 2 digit number. So we get 140 digits using the next 70 numbers. So these will be integers from 10 to 79. These will give us 140 digits.
The last digit will be the next digit of 80 i.e. it will be 8.

N = 123456789101112....767778798

When divided by 10, the remainder will be the same as the units digit of N i.e. 8.

Answer (D)
General Discussion
User avatar
L
pushpitkc
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 2873
Own Kudos [?]: 5208 [4]
Given Kudos: 47
Location: India
GPA: 3.12
Send PM
Re: A number N is formed by placing first 100 integers in order [#permalink] New post   02 Aug 2018, 00:25
2
Kudos
2
Bookmarks
enak wrote:
A number N is formed by placing first 100 integers in order (N= 1234567891011121314.......). If N is a 150 digit number, what is the remainder when N is divided by 10?

(A) 1
(B) 3
(C) 7
(D) 8
(E) 9


What we need is to figure out is the 150th digit of the integer N!

So, if 9 digits(1-9) are consumed by one-digit numbers,
every set of 10 numbers(eg 10-19) will consume 20 more places in N.
Positions 10-29 will be occupied by 10-19
Positions 30-49 will be occupied by 20-29
Positions 50-69 will be occupied by 30-39
Positions 70-89 will be occupied by 40-49
Positions 90-109 will be occupied by 50-59
Positions 110-129 will be occupied by 60-69
Positions 130-149 will be occupied by 70-79

Therefore, the 150th digit is 8(Option D), which is also the remainder when N is divided by 10
avatar
B
Gayluk
Intern
Intern
Joined: 15 Jul 2018
Posts: 7
Own Kudos [?]: 5 [2]
Given Kudos: 73
GMAT 1: 700 Q47 V39
Send PM
Re: A number N is formed by placing first 100 integers in order [#permalink] New post   02 Aug 2018, 02:07
2
Kudos
My approach is as follows:

We have 150 digits, but 100 numbers, and we know that the first 9 numbers take 9 digits, hence 150 - 9 = 141 digits, are left for the remaining two-digit numbers, which start from 10. Since we cannot divide 141 by 2, lets divide 140 by 2 which gives us 70. That means that starting from 10 we will have totally 70 two-digit numbers, hence 150 digit will start with 8 ( remember we stated from 10 => 10 + 70 = 80).

Hope it helps :) !
User avatar
B
jnitish25
Intern
Intern
Joined: 20 Jul 2016
Posts: 7
Own Kudos [?]: 12 [2]
Given Kudos: 18
Send PM
Re: A number N is formed by placing first 100 integers in order [#permalink] New post   02 Aug 2018, 02:40
2
Kudos
The pattern is quite simple if closely observed. Every 10th digit repeats itself and then gets incremented by 1.
1 1 2 2 3 3 4 4 5 5 6 6... .
Last digit of number formed from first 10 digits is 1
Last digit of number formed from first 30 digits is 2
...
Hence last digit of number formed from first 150 digits is 8.

Posted from my mobile device
User avatar
B
EvanSamPhuong
Intern
Intern
Joined: 24 Jul 2018
Posts: 4
Own Kudos [?]: 0 [0]
Given Kudos: 15
Send PM
Re: A number N is formed by placing first 100 integers in order [#permalink] New post   02 Aug 2018, 03:20
enak wrote:
A number N is formed by placing first 100 integers in order (N= 1234567891011121314.......). If N is a 150 digit number, what is the remainder when N is divided by 10?

(A) 1
(B) 3
(C) 7
(D) 8
(E) 9


Ans: D

150-9=141

We have 141 digits formed by placing consecutive 2-digit numbers starting from 10.

141/2 = 70.5
=> N ends after placing 70.5 2-digit numbers starting from 10

Placing 70 2-digit numbers starting from 10, we'll have:

123456789101112...777879

(Or 9+70=79)

Placing 0.5 2-digit starting after 79 => placing the first digit of 80 => 8

Posted from my mobile device
User avatar
L
CAMANISHPARMAR
VP
VP
Joined: 12 Feb 2015
Posts: 1064
Own Kudos [?]: 2109 [0]
Given Kudos: 77
Send PM
Re: A number N is formed by placing first 100 integers in order [#permalink] New post   06 Aug 2018, 06:57
We can answer this question if we know the units digit. To find the units digit of a 150 digits number we follow the following quick strategy:-

First 9 digits + next 140 digits (next 70 two digit integers but the 70th number is 79)

Therefore the 150th digit is 8. Hence the reminder when N is divided by 10 is 8.

Option D is the correct answer.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32804
Own Kudos [?]: 825 [0]
Given Kudos: 0
Send PM
Re: A number N is formed by placing first 100 integers in order [#permalink] New post   20 Apr 2024, 05:31
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.
GMAT Club Bot
gmatclubot
Re: A number N is formed by placing first 100 integers in order [#permalink]
20 Apr 2024, 05:31
Moderators:
Bunuel
Math Expert
93025 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions