Find all School-related info fast with the new School-Specific MBA Forum

It is currently 01 Oct 2014, 06:37

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Find the smallest positive integer which will leave a

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 24 Jan 2005
Posts: 217
Location: Boston
Followers: 1

Kudos [?]: 4 [0], given: 0

Find the smallest positive integer which will leave a [#permalink] New post 24 Feb 2005, 17:31
Find the smallest positive integer which will leave a remainder of 1 when divided by2, a remainder of 2 when divided by 3, a remainder of 3 when divided by 4 and so on ...a remainder of 9 when divided by 10.
Manager
Manager
avatar
Joined: 24 Jan 2005
Posts: 217
Location: Boston
Followers: 1

Kudos [?]: 4 [0], given: 0

 [#permalink] New post 24 Feb 2005, 17:53
Just check your answer. 59 divided by 9 leaves a remainder of 6 and NOT 8.
Manager
Manager
avatar
Joined: 24 Jan 2005
Posts: 217
Location: Boston
Followers: 1

Kudos [?]: 4 [0], given: 0

 [#permalink] New post 24 Feb 2005, 17:55
Sorry 59 /9 leaves a remainder of 5 (not 6 or 8)
VP
VP
avatar
Joined: 18 Nov 2004
Posts: 1447
Followers: 2

Kudos [?]: 16 [0], given: 0

 [#permalink] New post 24 Feb 2005, 18:03
anirban16 wrote:
Just check your answer. 59 divided by 9 leaves a remainder of 6 and NOT 8.


Altho 59 divided by 9 leaves a remainder of 5, but u right my ans is wrong....I wud back solve it if there were ans choices. :-D
Manager
Manager
avatar
Joined: 24 Jan 2005
Posts: 217
Location: Boston
Followers: 1

Kudos [?]: 4 [0], given: 0

 [#permalink] New post 24 Feb 2005, 18:22
You are right.
Since it is a fundamental problem I didn't give any choices. Since it'd be too easy to back solve.
But if you solve it logically you end up learning a very basic concept in number theory
I'd explain after some more answers are posted
Manager
Manager
avatar
Joined: 24 Jan 2005
Posts: 217
Location: Boston
Followers: 1

Kudos [?]: 4 [0], given: 0

Yes 2519 it is [#permalink] New post 24 Feb 2005, 20:27
Yes 2519 it is.
The LCM of 1thru 10 is 2520 so 2520 will be divisible by by all the 10 numbers so 1 less than that will be the required number.
Manager
Manager
avatar
Joined: 01 Jan 2005
Posts: 168
Location: NJ
Followers: 1

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

 [#permalink] New post 25 Feb 2005, 03:42
It shud be some multiple of 59. 59 satisfies the requirement till 6.. but 7 onwards it doesn't.. I think it shud be some multiple of 59.
VP
VP
avatar
Joined: 18 Nov 2004
Posts: 1447
Followers: 2

Kudos [?]: 16 [0], given: 0

Re: Yes 2519 it is [#permalink] New post 25 Feb 2005, 06:23
anirban16 wrote:
Yes 2519 it is.
The LCM of 1thru 10 is 2520 so 2520 will be divisible by by all the 10 numbers so 1 less than that will be the required number.


Will remember this, good one.
Manager
Manager
avatar
Joined: 18 Nov 2004
Posts: 72
Followers: 1

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 25 Feb 2005, 07:44
thats a very good example. thanks for posting
Manager
Manager
avatar
Joined: 24 Jan 2005
Posts: 217
Location: Boston
Followers: 1

Kudos [?]: 4 [0], given: 0

 [#permalink] New post 25 Feb 2005, 12:08
My pleasure.
In between absurd problems I would put in reasonable ETS like questions.

I somehow feel that even if a question seems absurd and not possible be asked in GMAT but it can open some door in ur mind or clear some funda that might help you solving difficult ETS like questions.
SVP
SVP
User avatar
Joined: 03 Jan 2005
Posts: 2255
Followers: 12

Kudos [?]: 200 [0], given: 0

 [#permalink] New post 25 Feb 2005, 15:11
n=2k+1=3m+2=4s+3=...
n+1=2(k+1)=3(m+1)=4(s+1)=...

You can see n+1 is a product of 2, 3, 4, 5, 6 ...10
In other words, n+1=10!
n=10!-1
VP
VP
avatar
Joined: 18 Nov 2004
Posts: 1447
Followers: 2

Kudos [?]: 16 [0], given: 0

 [#permalink] New post 25 Feb 2005, 21:14
HongHu wrote:
n=2k+1=3m+2=4s+3=...
n+1=2(k+1)=3(m+1)=4(s+1)=...

You can see n+1 is a product of 2, 3, 4, 5, 6 ...10
In other words, n+1=10!
n=10!-1


Awesome ! u r the best. I always like algebraic approach.
SVP
SVP
User avatar
Joined: 03 Jan 2005
Posts: 2255
Followers: 12

Kudos [?]: 200 [0], given: 0

 [#permalink] New post 25 Feb 2005, 22:07
Actually, that's not right. :oops:
As we want the smallest number. We can see that we have 2, 3, 4=2*2, 5, 6=2*3, 7, 8=2*2*2, 9=3*3, 10=2*5
We really only need 5*7*8*9=2520
Then n=2520-1.
Sorry about that. :)
Manager
Manager
avatar
Joined: 27 Jan 2005
Posts: 100
Location: San Jose,USA- India
Followers: 1

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 27 Feb 2005, 01:19
Although these problems are generally backsolve-able,a DS can trick you or waste lot of your time. So it is better to know how to solve it.

Thanks for the discussion.
Manager
Manager
avatar
Joined: 24 Jan 2005
Posts: 217
Location: Boston
Followers: 1

Kudos [?]: 4 [0], given: 0

 [#permalink] New post 28 Feb 2005, 13:58
Yup that's same as finding the LCM of first 10 natural numbers.
Senior Manager
Senior Manager
avatar
Joined: 15 Feb 2005
Posts: 255
Location: Rockville
Followers: 1

Kudos [?]: 6 [0], given: 0

 [#permalink] New post 28 Feb 2005, 15:23
what is the LCM rule ?
Director
Director
avatar
Joined: 27 Dec 2004
Posts: 910
Followers: 1

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

 [#permalink] New post 28 Feb 2005, 17:38
what is the formular for finding the LCM of consecutive numbers?
Manager
Manager
avatar
Joined: 24 Jan 2005
Posts: 217
Location: Boston
Followers: 1

Kudos [?]: 4 [0], given: 0

 [#permalink] New post 04 Mar 2005, 12:06
Well there is no general formula for LCM. Just find the factors of all the consecutive numbers and multiply them. So LCM of 2, 4 and 8 will be 8 as 8 contains both the multiples 2 and 4.
LCM of 1,2,3,4,5,6,7,8,9,10 will be 9*8*7*5. (Since 1,2,3 hence also 6 and 10 are already contained in the product
  [#permalink] 04 Mar 2005, 12:06
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic What is the smallest positive integer x for which x^3 + 5x mikemcgarry 1 26 Dec 2013, 10:03
19 Experts publish their posts in the topic If x is the smallest positive integer that is not prime and manasishah 21 30 Jul 2013, 11:07
2 Experts publish their posts in the topic What is the smallest positive integer n for which 324 is a chintzzz 10 19 Jun 2010, 00:09
What is ths smallest positive integer n for which 324 is a positive soul 2 26 May 2006, 05:42
What is the smallest positive integer n for which 324 is a joemama142000 2 30 Nov 2005, 09:38
Display posts from previous: Sort by

Find the smallest positive integer which will leave a

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.