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

It is currently 23 Apr 2019, 15:07

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

Let N=123456789101112.....4344 be the 79-digit number that is formed

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

Hide Tags

 
Manager
Manager
avatar
G
Status: Manager
Joined: 02 Nov 2018
Posts: 180
Location: Bangladesh
GMAT ToolKit User CAT Tests
Let N=123456789101112.....4344 be the 79-digit number that is formed  [#permalink]

Show Tags

New post Updated on: 18 Mar 2019, 21:52
1
1
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

63% (02:29) correct 38% (02:35) wrong based on 8 sessions

HideShow timer Statistics

Let N=123456789101112.....4344 be the 79-digit number that is formed by writing the integers from 1 to 44 in order, one after the other. What is the remainder when N is divided by 45?


A. 1

B 4

C. 9

D. 18

E. 44

_________________
Give a kudos if u find my post helpful. kudos motivates active discussions :)


Originally posted by Noshad on 18 Mar 2019, 05:12.
Last edited by Noshad on 18 Mar 2019, 21:52, edited 1 time in total.
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7579
Re: Let N=123456789101112.....4344 be the 79-digit number that is formed  [#permalink]

Show Tags

New post 18 Mar 2019, 06:53
1
Noshad wrote:
Let N=123456789101112.....4344 be the 79-digit number that is formed by writing the integers from 1 to 44 in order, one after the other. What is the remainder when N is divided by 45?


A. 1

B 4

C. 9

D. 18

E. 44



A LOGIC, which can get your probability of scoring high..
We are looking for division by 45, so any multiple of 45 will have 0 or 5 as units digit, and hence the units digit of remainder will be 4-0=4 or x4-5=9..
Thus possible answers will be 4 , 9 and 44..

Now let us solve it..
so let us find the remainder when N is divided by 9 as 45=5*9..
Sum of digits of 1234...4344
(1+2+3..9)+(10+11+12+13+..18+19)+(20+..29)+(30+..39)+(40+41+..44)=(1+2+3..9)+(1*10+1+2+3+..9)+(2*10+1+2+3+..9)+(3*10+1+2+3+..9)+(4*5+1+2+3+4)
=45+(10+45)+(20+45)+(30+45)+(20+10)=45*4+90, so the number N is divisible by 9....

Any number that we get as N-9x will also be divisible by 9..
But for N-9x to be divisible by 45, it has to be divisible by 5 too, so the units digit will be 0 or 5...

N has a 4 in units digit, so when subtract 9 from it, the units digit will be 5. Thus 12345....4335 will be divisible by 45 and the remainder will be 9.

C
_________________
GMAT Club Bot
Re: Let N=123456789101112.....4344 be the 79-digit number that is formed   [#permalink] 18 Mar 2019, 06:53
Display posts from previous: Sort by

Let N=123456789101112.....4344 be the 79-digit number that is formed

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.