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

It is currently 24 Oct 2014, 07:36

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

m25#02

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
1 KUDOS received
Manager
Manager
User avatar
Joined: 21 Feb 2008
Posts: 87
Schools: UCLA Anderson '12
Followers: 4

Kudos [?]: 17 [1] , given: 2

m25#02 [#permalink] New post 17 Oct 2008, 13:28
1
This post received
KUDOS
2
This post was
BOOKMARKED
How many integers are divisible by 3 between 10! and 10! + 20 inclusive?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

[Reveal] Spoiler: OA
B

Source: GMAT Club Tests - hardest GMAT questions

Last edited by duuuma on 23 Oct 2008, 08:14, edited 1 time in total.
Kaplan Promo CodeKnewton GMAT Discount CodesManhattan GMAT Discount Codes
Manager
Manager
avatar
Joined: 15 Oct 2008
Posts: 112
Followers: 1

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

Re: m25 #2 [#permalink] New post 28 Oct 2008, 08:39
bigfernhead wrote:
Can someone show me the quick and easy way to do this?

How many integers divisible by 3 are there between 10! and 10! + 20 inclusive?

6
7
8
9
10


IMO: 7
10!, 10!+3, 10!+6, 10!+9, 10!+12, 10!+15, 10!+18.
Current Student
avatar
Joined: 28 Dec 2004
Posts: 3403
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 164 [0], given: 2

Re: m25 #2 [#permalink] New post 28 Oct 2008, 11:42
i get 8... because when you divide (10!+9) you are still left with one more 3..from 9
Manager
Manager
avatar
Joined: 15 Oct 2008
Posts: 112
Followers: 1

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

Re: m25 #2 [#permalink] New post 28 Oct 2008, 11:48
fresinha12 wrote:
i get 8... because when you divide (10!+9) you are still left with one more 3..from 9


if that is the case, then should you also consider 10!+18?
I will still stay with 7, though.
2 KUDOS received
SVP
SVP
User avatar
Joined: 30 Apr 2008
Posts: 1893
Location: Oklahoma City
Schools: Hard Knocks
Followers: 30

Kudos [?]: 440 [2] , given: 32

Re: m25 #2 [#permalink] New post 28 Oct 2008, 12:18
2
This post received
KUDOS
How can you have more than 7 when you're only talking about 21 numbers? 10! is the first, and 10!+20 is the 21st number. If the very first number is divisible by 3, then that means there are 7 numbers between 10! and 10!+20 that are divisible by 3.

10! is divisble by 3
10!+3 is too
10!+6 is too
10!+9 is too
10!+12 is too
10!+15 is too
10!+18 is too

that's 7

It's the same as saying "How many integers are divisible by 3 between 1! and 1!+20.

This question focuses more on the span between 10! and 10!+20 than the actual divisibility issue.

There will always be 7 when you have 21 consecutive numbers and determine how many are divisble by 3 because 21 is divisible by 3 seven times.
_________________

------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Get the best GMAT Prep Resources with GMAT Club Premium Membership

CEO
CEO
User avatar
Joined: 29 Aug 2007
Posts: 2500
Followers: 54

Kudos [?]: 512 [0], given: 19

Re: m25 #2 [#permalink] New post 28 Oct 2008, 12:38
jallenmorris wrote:
How can you have more than 7 when you're only talking about 21 numbers? 10! is the first, and 10!+20 is the 21st number. If the very first number is divisible by 3, then that means there are 7 numbers between 10! and 10!+20 that are divisible by 3.

10! is divisble by 3
10!+3 is too
10!+6 is too
10!+9 is too
10!+12 is too
10!+15 is too
10!+18 is too

that's 7

It's the same as saying "How many integers are divisible by 3 between 1! and 1!+20.
This question focuses more on the span between 10! and 10!+20 than the actual divisibility issue.

There will always be 7 when you have 21 consecutive numbers and determine how many are divisble by 3 because 21 is divisible by 3 seven times.


jallenmorris, are you sure with the statement above marked red?

Probably you want to say "How many integers are divisible by 3 between 0 and 20 (or 1!+20)?
_________________

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

SVP
SVP
User avatar
Joined: 30 Apr 2008
Posts: 1893
Location: Oklahoma City
Schools: Hard Knocks
Followers: 30

Kudos [?]: 440 [0], given: 32

Re: m25 #2 [#permalink] New post 28 Oct 2008, 12:40
Isn't 1! = 1? and then 1! + 20 = 21?

So how many integers are divisble between 1! and 1!+20 inclusive? (I didn't say inclusive before).

The point of my statement is that the question does not mater that it's 10!, the key to the question is how many consecutive numbers there are in a row. Since there are 21 consecutive numbers, there will always be 7 integers in that set of 21 numbers that are divisible by 3.

GMAT TIGER wrote:
jallenmorris wrote:
How can you have more than 7 when you're only talking about 21 numbers? 10! is the first, and 10!+20 is the 21st number. If the very first number is divisible by 3, then that means there are 7 numbers between 10! and 10!+20 that are divisible by 3.

10! is divisble by 3
10!+3 is too
10!+6 is too
10!+9 is too
10!+12 is too
10!+15 is too
10!+18 is too

that's 7

It's the same as saying "How many integers are divisible by 3 between 1! and 1!+20.
This question focuses more on the span between 10! and 10!+20 than the actual divisibility issue.

There will always be 7 when you have 21 consecutive numbers and determine how many are divisble by 3 because 21 is divisible by 3 seven times.


jallenmorris, are you sure with the statement above marked red?

Probably you want to say "How many integers are divisible by 3 between 0 and 20 (or 1!+20)?

_________________

------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 03 Apr 2010
Posts: 3
Followers: 0

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

Re: m25 #2 [#permalink] New post 10 May 2010, 16:20
okay, what I really want to know is if there's a quicker way to figure out this problem. Afaik, you're not allowed to use a calculator on the official exam. So how did you figure out what 10! equals to in such a short time? Do you really have to literally write that all out on paper to figure out that number?

Do all this 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 on the paper? thats really time consuming and could easily make a mistake. I mean, yea sure, as soon as I can figure out what 10! equals to. I can definitely figure out whether it's divisible by 3 then on to the final step. But, figuring out what is 10! is really an issue here on a time-constraint basis
2 KUDOS received
CIO
CIO
avatar
Joined: 02 Oct 2007
Posts: 1218
Followers: 87

Kudos [?]: 691 [2] , given: 334

GMAT ToolKit User
Re: m25 #2 [#permalink] New post 12 May 2010, 00:26
2
This post received
KUDOS
I'm not sure why you need to calculate the exact number of 10!. As far as this question is concerned, you just need to understand that 10! is divisible by 3. Please make sure you read through all posts of this thread carefully.

If you know what a factorial is, you know that 10! is surely divisible by all numbers less than and equal to 10. Use it as a fact. You don't have to calculate the exact 10!

I hope this makes sense. Sorry if I misunderstood your question.
Norlan wrote:
okay, what I really want to know is if there's a quicker way to figure out this problem. Afaik, you're not allowed to use a calculator on the official exam. So how did you figure out what 10! equals to in such a short time? Do you really have to literally write that all out on paper to figure out that number?

Do all this 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 on the paper? thats really time consuming and could easily make a mistake. I mean, yea sure, as soon as I can figure out what 10! equals to. I can definitely figure out whether it's divisible by 3 then on to the final step. But, figuring out what is 10! is really an issue here on a time-constraint basis

_________________

Welcome to GMAT Club! :)
Facebook TwitterGoogle+LinkedIn
Want to solve GMAT questions on the go? GMAT Club iPhone app will help.
Please read this before posting in GMAT Club Tests forum
Result correlation between real GMAT and GMAT Club Tests
Are GMAT Club Test sets ordered in any way?

Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
User avatar
Joined: 01 Nov 2010
Posts: 196
Location: India
Concentration: Technology, Marketing
GMAT Date: 08-27-2012
GPA: 3.8
WE: Marketing (Manufacturing)
Followers: 6

Kudos [?]: 20 [0], given: 30

Re: m25#02 [#permalink] New post 29 Nov 2010, 07:01
my Ans is 7.
the Nos which are divisible by 3 between 10! and 10!+20 is
10!
10!+3
10!+6
10!+9
10!+12
10!+15
10!+18.
thats all.
_________________

kudos me if you like my post.

Attitude determine everything.
all the best and God bless you.

5 KUDOS received
Manager
Manager
User avatar
Joined: 01 Nov 2010
Posts: 196
Location: India
Concentration: Technology, Marketing
GMAT Date: 08-27-2012
GPA: 3.8
WE: Marketing (Manufacturing)
Followers: 6

Kudos [?]: 20 [5] , given: 30

Re: m25 #2 [#permalink] New post 29 Nov 2010, 07:14
5
This post received
KUDOS
Norlan wrote:
okay, what I really want to know is if there's a quicker way to figure out this problem. Afaik, you're not allowed to use a calculator on the official exam. So how did you figure out what 10! equals to in such a short time? Do you really have to literally write that all out on paper to figure out that number?

Do all this 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 on the paper? thats really time consuming and could easily make a mistake. I mean, yea sure, as soon as I can figure out what 10! equals to. I can definitely figure out whether it's divisible by 3 then on to the final step. But, figuring out what is 10! is really an issue here on a time-constraint basis



Hey Norlan,

i hope i can suggest you a better quick and easy way.

since we all know that 10!=10x9x8x7x6x5x4x3x2x1
there has to be no doubt about divisibility of 10! by 3 as it has 3 as a factor.
so, numbers will be divisible by 3 if it contains 3 as factor.
starting from first no:
10! - it is divisible by 3(it has 3 as factor)
10!+1- not divisible ; as 10! is divisible by 3 but not 1.
10!+2
10!+3--10!+3x1
10!+4
10!+5
10!+6--10!+3x2
10!+7
10!+8
10!+9--10!+3x3
10!+10
10!+11
10!+12--10!+3x4
10!+13
10!+14
10!+15--10!+3x5
10!+16
10!+17
10!+18--10!+3x6
10!+19
10!+20

only above colored nos have 3 as a factor.
so, only these Nos will be divisible by 3
if you will count these no. it will be equal to 7.\\\

hope it will help you.
_________________

kudos me if you like my post.

Attitude determine everything.
all the best and God bless you.


Last edited by 321kumarsushant on 25 Apr 2012, 06:12, edited 3 times in total.
Joined: 31 Dec 1969
Location: United States
Concentration: Marketing, Other
GPA: 3.64
WE: Accounting (Accounting)
Followers: 0

Kudos [?]: 70 [0], given: 78681

CAT Tests
Re: m25#02 [#permalink] New post 30 Nov 2010, 00:28
Counting the number of integers within a range
=> substract the extremes and add one

Counting the multiples of x within a range:
=> find the nearest multiples of x (to the extremes)
=> substract them and divide by x
=> add one

Here:
(10!+18 -10!) / 3 = 6
6+1 = 7

Answer B
Manager
Manager
User avatar
Status: I rest, I rust.
Joined: 04 Oct 2010
Posts: 121
Schools: ISB - Co 2013
WE 1: IT Professional since 2006
Followers: 16

Kudos [?]: 101 [0], given: 8

Re: m25#02 [#permalink] New post 30 Nov 2010, 00:49
For me the approach was based on the fact that in consecutive numbers every third number will be divisible by 3...

so in any 21 consecutive numbers only 7 numbers can be divisible by 3, irerespective of from where the counting starts...so i simply ignored the 10! part....
_________________

Respect,
Vaibhav

PS: Correct me if I am wrong.

Retired Moderator
User avatar
Joined: 02 Sep 2010
Posts: 807
Location: London
Followers: 76

Kudos [?]: 507 [0], given: 25

GMAT ToolKit User Reviews Badge
Re: m25#02 [#permalink] New post 30 Nov 2010, 23:21
10! is divisible by 3.

So every third number after that will be as well. There are exactly 6 such numbers, 10!+3 ... 10!+18

So total numbers = 1+6 = 7
_________________

Math write-ups
1) Algebra-101 2) Sequences 3) Set combinatorics 4) 3-D geometry

My GMAT story

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Joined: 19 Oct 2010
Posts: 274
Location: India
GMAT 1: 560 Q36 V31
GPA: 3
Followers: 6

Kudos [?]: 38 [0], given: 27

Re: m25#02 [#permalink] New post 12 Jan 2011, 07:35
Damn! completely forgot to include 10! in my list. I guess that's the kinda booby trap they're setting.
_________________

petrifiedbutstanding

Intern
Intern
avatar
Joined: 21 May 2011
Posts: 48
Schools: Kellogg
Followers: 0

Kudos [?]: 2 [0], given: 7

Re: m25 [#permalink] New post 22 May 2011, 03:17
Hi Friends,

This is an amazing forum .. I am preparing for GMAT and planning to take it by June end..

I just took the M25 free sectional test and got 29 correct out of 37 ... 3 very silly mistakes :(

How do you all think I do ???

Cheers!
Thanks :)
_________________

I was born intelligent but education ruined me !

1 KUDOS received
CIO
CIO
avatar
Joined: 02 Oct 2007
Posts: 1218
Followers: 87

Kudos [?]: 691 [1] , given: 334

GMAT ToolKit User
Re: m25 [#permalink] New post 22 May 2011, 05:48
1
This post received
KUDOS
I think you're doing great! You must be very good at math :).

Welcome to the forum. You should be able to find a lot in here. Let me know if you need extra guidance with our resources. Here's a link to a study plan for beginners just in case:

gmat-study-plan-for-gmat-novices-start-your-gmat-journey-80727.html

BearBelly wrote:
Hi Friends,

This is an amazing forum .. I am preparing for GMAT and planning to take it by June end..

I just took the M25 free sectional test and got 29 correct out of 37 ... 3 very silly mistakes :(

How do you all think I do ???

Cheers!
Thanks :)

_________________

Welcome to GMAT Club! :)
Facebook TwitterGoogle+LinkedIn
Want to solve GMAT questions on the go? GMAT Club iPhone app will help.
Please read this before posting in GMAT Club Tests forum
Result correlation between real GMAT and GMAT Club Tests
Are GMAT Club Test sets ordered in any way?

Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 21 May 2011
Posts: 48
Schools: Kellogg
Followers: 0

Kudos [?]: 2 [0], given: 7

Re: m25 [#permalink] New post 22 May 2011, 07:16
Hey dzyubam,

Thanks for the encouragement :) My undergrad subject was Engg. ...

and you won't believe what I am about to write:

This is me:

WE1: IT ... 2.5 yrs

WE2: Market Research and Analytics: 1 year till now....

How nd why did you make the switch .. How do u plan to project it in ur essays ???


dzyubam wrote:
I think you're doing great! You must be very good at math :).

Welcome to the forum. You should be able to find a lot in here. Let me know if you need extra guidance with our resources. Here's a link to a study plan for beginners just in case:

BearBelly wrote:
Hi Friends,

This is an amazing forum .. I am preparing for GMAT and planning to take it by June end..

I just took the M25 free sectional test and got 29 correct out of 37 ... 3 very silly mistakes :(

How do you all think I do ???

Cheers!
Thanks :)

_________________

I was born intelligent but education ruined me !

CIO
CIO
avatar
Joined: 02 Oct 2007
Posts: 1218
Followers: 87

Kudos [?]: 691 [0], given: 334

GMAT ToolKit User
Re: m25 [#permalink] New post 22 May 2011, 23:50
Hehe :). Very funny. I'm not applying anywhere, I'm only helping out with this website.

Why I made the switch - I felt that Market Research was not my thing.

BearBelly wrote:
Hey dzyubam,

Thanks for the encouragement :) My undergrad subject was Engg. ...

and you won't believe what I am about to write:

This is me:

WE1: IT ... 2.5 yrs

WE2: Market Research and Analytics: 1 year till now....

How nd why did you make the switch .. How do u plan to project it in ur essays ???

_________________

Welcome to GMAT Club! :)
Facebook TwitterGoogle+LinkedIn
Want to solve GMAT questions on the go? GMAT Club iPhone app will help.
Please read this before posting in GMAT Club Tests forum
Result correlation between real GMAT and GMAT Club Tests
Are GMAT Club Test sets ordered in any way?

Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Director
Director
User avatar
Status: My Thread Master Bschool Threads-->Krannert(Purdue),WP Carey(Arizona),Foster(Uwashngton)
Joined: 27 Jun 2011
Posts: 894
Followers: 62

Kudos [?]: 156 [0], given: 57

GMAT ToolKit User Reviews Badge
Re: m25#02 [#permalink] New post 22 Oct 2011, 08:16
1
This post was
BOOKMARKED
There is no need to calculate 10! since on the other hand we have 10! + 20.

So for the difference we need how many are divisible by 3 ..so total no. of integers 20 + 1= 21

So the answer is 7.
_________________

General GMAT useful links-->

Indian Bschools Accepting Gmat | My Gmat Daily Diary | All Gmat Practice CAT's | MBA Ranking 2013 | How to Convert Indian GPA/ Percentage to US 4 pt. GPA scale | GMAT MATH BOOK in downloadable PDF format| POWERSCORE CRITICAL REASONING BIBLE - FULL CHAPTER NOTES | Result correlation between GMAT and GMAT Club's Tests | Best GMAT Stories - Period!

More useful links-->

GMAT Prep Software Analysis and What If Scenarios| GMAT and MBA 101|Everything You Need to Prepare for the GMAT|New to the GMAT Club? <START HERE>|GMAT ToolKit: iPhone/iPod/iPad/Android application|

Verbal Treasure Hunt-->

"Ultimate" Study Plan for Verbal on the GMAT|Books to Read (Improve Verbal Score and Enjoy a Good Read)|Best Verbal GMAT Books 2012|Carcass Best EXTERNAL resources to tackle the GMAT Verbal Section|Ultimate GMAT Grammar Book from GC club [Free Download]|Ultimate Sentence Correction Encyclopedia|Souvik's The Most Comprehensive Collection Of Everything Official-SC|ALL SC Rules+Official Qs by Experts & Legendary Club Members|Meaning/Clarity SC Question Bank by Carcass_Souvik|Critical Reasoning Shortcuts and Tips|Critical Reasoning Megathread!|The Most Comprehensive Collection Of Everything Official- CR|GMAT Club's Reading Comprehension Strategy Guide|The Most Comprehensive Collection Of Everything Official- RC|Ultimate Reading Comprehension Encyclopedia|ALL RC Strategy+Official Q by Experts&Legendary Club Members

----
---
--
-


1 KUDOS = 1 THANK


Kick Ass Gmat

Re: m25#02   [#permalink] 22 Oct 2011, 08:16
Display posts from previous: Sort by

m25#02

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page    1   2    Next  [ 30 posts ] 

Moderators: WoundedTiger, Bunuel



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®.