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

It is currently 20 Aug 2014, 08:48

Flash Sale:

The Economist GMAT Tutor - 15% Off All Courses


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

How many different positive integers d are there such that

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
GMAT Instructor
avatar
Joined: 04 Jul 2006
Posts: 1270
Location: Madrid
Followers: 23

Kudos [?]: 119 [0], given: 0

How many different positive integers d are there such that [#permalink] New post 16 Apr 2008, 12:52
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (00:00) correct 0% (00:00) wrong based on 0 sessions
How many different positive integers d are there such that 48 divided by d yields a remainder of d - 4?

Two
Three
Four
Five
Six

Last edited by kevincan on 16 Apr 2008, 13:01, edited 2 times in total.
spelling
Current Student
User avatar
Joined: 27 Mar 2008
Posts: 416
Schools: Kellogg Class of 2011
Followers: 1

Kudos [?]: 38 [0], given: 1

GMAT Tests User
Re: PS. Remainders [#permalink] New post 16 Apr 2008, 13:10
Answer is B - Three

4 is fairly obvious. 48/4 gives remainder of 0 and d-4 = 0

26 is also fairly obvious since we need a number d such that
d+d-4 = 48 which gives d = 26

Since 26 and 48 both have a common factor (2), there is another number, 13 which should satisfy the condition as 13 does.
Current Student
avatar
Joined: 28 Dec 2004
Posts: 3405
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 158 [0], given: 2

GMAT Tests User
Re: PS. Remainders [#permalink] New post 16 Apr 2008, 13:22
the way i did this..

48=DN+r where r=d-4

48=D*N+D-4

52=D(N+1)

i quickly look for prime factors of 52..they are 13*2^2...

number of possible ways of writting 52..13*4, 26*2, 52*1 i.e 3 ...

Last edited by FN on 16 Apr 2008, 13:32, edited 1 time in total.
CEO
CEO
User avatar
Joined: 21 Jan 2007
Posts: 2770
Location: New York City
Followers: 6

Kudos [?]: 211 [0], given: 4

GMAT Tests User
Re: PS. Remainders [#permalink] New post 16 Apr 2008, 13:32
fresinha12 wrote:
the way i did this..

48=DN+r where r=d-4

48=D*N+D-4

52=D(N+1)

i quickly look for prime factors of 52..they are 13*2^2...

number of possible divisors of 52..13*4, 26*2, 52*1 i.e 3 ...


can you explain why u prime factorized?
_________________

You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

Current Student
avatar
Joined: 28 Dec 2004
Posts: 3405
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 158 [0], given: 2

GMAT Tests User
Re: PS. Remainders [#permalink] New post 16 Apr 2008, 13:33
i shouldnt use the word divisors..i meant how many ways can your get 52 using integers? 3 ways
VP
VP
avatar
Joined: 10 Jun 2007
Posts: 1467
Followers: 5

Kudos [?]: 97 [0], given: 0

GMAT Tests User
Re: PS. Remainders [#permalink] New post 16 Apr 2008, 14:53
kevincan wrote:
How many different positive integers d are there such that 48 divided by d yields a remainder of d - 4?

Two
Three
Four
Five
Six


Three.

48 = d*n + (d-4)
52 = d*(n+1)
We know that
52 = 2*2*13 = 2^2 * 13^1, which yields 3*2 = 6 factors.
The 6 factors are: 1, 2, 4, 13, 26, 52
This means d can only equal to these 6 numbers

List them out
(d, remainder of 48/d, d-4)
(1, 0, -3) <-No
(2, 0, -2) <-No
(4, 0, 0) <-Yes
(13, 9, 9) <-Yes
(26, 22, 22) <-Yes
52 cannot yield remainder.

d can be 4, 13, 26
Current Student
avatar
Joined: 28 Dec 2004
Posts: 3405
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 158 [0], given: 2

GMAT Tests User
Re: PS. Remainders [#permalink] New post 16 Apr 2008, 15:00
what if i changed the question and asked how many integers are there such that when 48 divided by d gives remainder d-3?
VP
VP
avatar
Joined: 10 Jun 2007
Posts: 1467
Followers: 5

Kudos [?]: 97 [0], given: 0

GMAT Tests User
Re: PS. Remainders [#permalink] New post 16 Apr 2008, 15:06
fresinha12 wrote:
what if i changed the question and asked how many integers are there such that when 48 divided by d gives remainder d-3?


51 = d*(n+1)

3*17 = 51
There are 4 factors: 1, 3, 17, 51
Same way
(d, remainder, d-3)
(1, 0, -2)
(3, 0, 0)
(17, 14, 14)
51 won't give it.

Two I got.
Current Student
avatar
Joined: 28 Dec 2004
Posts: 3405
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 158 [0], given: 2

GMAT Tests User
Re: PS. Remainders [#permalink] New post 16 Apr 2008, 15:21
exactly..ways to write 51, is 13*7 and 51*1, i.e 2 ways.. there are 2 such numbers..



bkk145 wrote:
fresinha12 wrote:
what if i changed the question and asked how many integers are there such that when 48 divided by d gives remainder d-3?


51 = d*(n+1)

3*17 = 51
There are 4 factors: 1, 3, 17, 51
Same way
(d, remainder, d-3)
(1, 0, -2)
(3, 0, 0)
(17, 14, 14)
51 won't give it.

Two I got.
Director
Director
avatar
Joined: 01 May 2007
Posts: 795
Followers: 1

Kudos [?]: 57 [0], given: 0

GMAT Tests User
Re: PS. Remainders [#permalink] New post 16 Apr 2008, 15:48
I'm thinking FOUR...3,17,1,51
SVP
SVP
avatar
Joined: 04 May 2006
Posts: 1941
Schools: CBS, Kellogg
Followers: 15

Kudos [?]: 269 [0], given: 1

Premium Member CAT Tests
Re: PS. Remainders [#permalink] New post 16 Apr 2008, 20:34
fresinha12 wrote:
the way i did this..

48=DN+r where r=d-4

48=D*N+D-4

52=D(N+1)



And my reasoning:
D is different possitive interger, factor of 52
52=2^2 *13. So D = (2+1)*(1+1)=6

E
_________________

Get the best GMAT Prep Resources with GMAT Club Premium Membership

CEO
CEO
User avatar
Joined: 29 Aug 2007
Posts: 2501
Followers: 53

Kudos [?]: 500 [0], given: 19

GMAT Tests User
Re: PS. Remainders [#permalink] New post 16 Apr 2008, 20:57
bkk145 wrote:
kevincan wrote:
How many different positive integers d are there such that 48 divided by d yields a remainder of d - 4?

Two
Three
Four
Five
Six


Three.

48 = d*n + (d-4)
52 = d*(n+1)
We know that
52 = 2*2*13 = 2^2 * 13^1, which yields 3*2 = 6 factors.
The 6 factors are: 1, 2, 4, 13, 26, 52
This means d can only equal to these 6 numbers

List them out
(d, remainder of 48/d, d-4)
(1, 0, -3) <-No
(2, 0, -2) <-No
(4, 0, 0) <-Yes
(13, 9, 9) <-Yes
(26, 22, 22) <-Yes
52 cannot yield remainder.

d can be 4, 13, 26


beautiful work but, imo, we can add 52 as well.
48 divided by 52 has a reminder of 48 which is equal to 52 - 4.

so possible values for d = 4, 13, 26 and 52.
_________________

Verbal: new-to-the-verbal-forum-please-read-this-first-77546.html
Math: new-to-the-math-forum-please-read-this-first-77764.html
Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT

Senior Manager
Senior Manager
avatar
Joined: 29 Jan 2007
Posts: 451
Location: Earth
Followers: 2

Kudos [?]: 38 [0], given: 0

GMAT Tests User
Re: PS. Remainders [#permalink] New post 16 Apr 2008, 22:41
Ans 4.

Did it just like fresinha

plus added 4 as fourth integer.

So numbers are 4,13,26,52.

Lilke your questions Kevincan. Makes me think.
VP
VP
avatar
Joined: 10 Jun 2007
Posts: 1467
Followers: 5

Kudos [?]: 97 [0], given: 0

GMAT Tests User
Re: PS. Remainders [#permalink] New post 17 Apr 2008, 05:27
Dreaming here again...agree with 52
Current Student
avatar
Joined: 28 Dec 2004
Posts: 3405
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 158 [0], given: 2

GMAT Tests User
Re: PS. Remainders [#permalink] New post 17 Apr 2008, 06:11
how do we quickly see that 48/52 will give us a remainder of 48?

i totally missed 52..
VP
VP
avatar
Joined: 10 Jun 2007
Posts: 1467
Followers: 5

Kudos [?]: 97 [0], given: 0

GMAT Tests User
Re: PS. Remainders [#permalink] New post 17 Apr 2008, 07:07
fresinha12 wrote:
how do we quickly see that 48/52 will give us a remainder of 48?

i totally missed 52..


This is from wiki:

"When dividing 3 by 10, 3 is the remainder as we always take the front number as the remainder when the second number is of higher value."

http://en.wikipedia.org/wiki/Remainder
Current Student
User avatar
Joined: 27 Mar 2008
Posts: 416
Schools: Kellogg Class of 2011
Followers: 1

Kudos [?]: 38 [0], given: 1

GMAT Tests User
Re: PS. Remainders [#permalink] New post 17 Apr 2008, 07:25
Yea.. Answer should be 4.

I didn't consider 52 myself.
Re: PS. Remainders   [#permalink] 17 Apr 2008, 07:25
    Similar topics Author Replies Last post
Similar
Topics:
8 Experts publish their posts in the topic How many different positive integers are factors of 441 sugu86 7 13 Apr 2012, 01:42
1 How many different positive integers are factors of 441? lumone 4 02 Mar 2008, 13:01
The positive integer x has how many different positive sharadGmat 3 12 Aug 2006, 16:57
The positive integer x has how many different positive bewakoof 6 21 Jan 2006, 13:32
X is prime and y is positive integer, How many different gamjatang 13 11 Dec 2005, 05:36
Display posts from previous: Sort by

How many different positive integers d are there such that

  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®.