It is currently 21 Sep 2017, 09:08

Happening Now:

Live Chat with Amy Mitson, Sr. Associate Director of Admissions at Tuck Dartmouth


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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

How many positive integers less than 10,000 are there in

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

Hide Tags

Manager
Manager
User avatar
Joined: 10 Jun 2015
Posts: 126

Kudos [?]: 29 [0], given: 0

Re: How many positive integers less than 10,000 are there in [#permalink]

Show Tags

New post 16 Jun 2015, 23:59
Bunuel wrote:
How many positive integers less than 10,000 are there in which the sum of the digits equals 5?

(A) 31
(B) 51
(C) 56
(D) 62
(E) 93

from 0 to 9, 5 ( 1 number)
from 10 to 99, we have 14,23,32,41,50 (5 numbers)
from 100 to 999, we have 104,113. 122,131, 140, 203,212,221, 230,302, 311,320,401,410,500 (15 numbers)
from 1000 to 9999, we have 1004,1040,1103,1112, 1121,1130,1202,1211,1220,1301,1310,1400, 2003,2012,2021,2030,2102,2111,2120,2201,2210,2300,3002.3011.3020,3101,3110,3200,4001,4010,4100,5000 (32 numbers)
So we have only 53 numbers.
Can anyone tell the numbers which I miss?

Kudos [?]: 29 [0], given: 0

Intern
Intern
avatar
B
Joined: 02 Feb 2016
Posts: 5

Kudos [?]: 5 [0], given: 7

Location: India
Concentration: Technology, General Management
WE: Analyst (Computer Software)
Premium Member
Re: How many positive integers less than 10,000 are there in [#permalink]

Show Tags

New post 19 May 2016, 00:21
As it says integers less than 100,000,why only four digit numbers are considered ? Why not three digits,two digits and single digit integers considered?

Kudos [?]: 5 [0], given: 7

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41660

Kudos [?]: 124306 [0], given: 12077

Re: How many positive integers less than 10,000 are there in [#permalink]

Show Tags

New post 19 May 2016, 03:34
shaktirdas19 wrote:
As it says integers less than 100,000,why only four digit numbers are considered ? Why not three digits,two digits and single digit integers considered?


They are considered. If you read the whole thread you'll find the answer to your question.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 124306 [0], given: 12077

Director
Director
avatar
S
Joined: 12 Dec 2016
Posts: 808

Kudos [?]: 7 [0], given: 744

Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
GMAT ToolKit User Premium Member CAT Tests
Re: How many positive integers less than 10,000 are there in [#permalink]

Show Tags

New post 16 Apr 2017, 14:47
Bunuel wrote:
Ramsay wrote:
Sorry guys,

Could someone please explain the following:

"There are 8C3 ways to determine where to place the separators"

I'm not familiar with this shortcut/approach.

Ta


Consider this: we have 5 \(d\)'s and 3 separators \(|\), like: \(ddddd|||\). How many permutations (arrangements) of these symbols are possible? Total of 8 symbols (5+3=8), out of which 5 \(d\)'s and 3 \(|\)'s are identical, so \(\frac{8!}{5!3!}=56\).

With these permutations we'll get combinations like: \(|dd|d|dd\) this would be 3 digit number 212 OR \(|||ddddd\) this would be single digit number 5 (smallest number less than 10,000 in which sum of digits equals 5) OR \(ddddd|||\) this would be 4 digit number 5,000 (largest number less than 10,000 in which sum of digits equals 5)...

Basically this arrangements will give us all numbers less than 10,000 in which sum of the digits (sum of 5 d's=5) equals 5.

Hence the answer is \(\frac{8!}{5!3!}=56\).

Answer: C (56).

This can be done with direct formula as well:

The total number of ways of dividing n identical items (5 d's in our case) among r persons or objects (4 digt places in our case), each one of whom, can receive 0, 1, 2 or more items (from zero to 5 in our case) is \({n+r-1}_C_{r-1}\).

In our case we'll get: \({n+r-1}_C_{r-1}={5+4-1}_C_{4-1}={8}C3=\frac{8!}{5!3!}=56\)

Also see the image I found in the net about this question explaining the concept:
Attachment:
pTNfS-2e270de4ca223ec2741fa10b386c7bfe.jpg


hello, i complete understand the formula, but what i still do not understand is how why there are only 5 numbers? It should be 6 if o is included

Kudos [?]: 7 [0], given: 744

Intern
Intern
avatar
B
Joined: 28 Jan 2017
Posts: 29

Kudos [?]: 19 [0], given: 14

Re: How many positive integers less than 10,000 are there in [#permalink]

Show Tags

New post 21 Jul 2017, 10:10
X1 + X2 +X3 +X4 =5

The number of solutions of this equation for X1 X2, X3 and X4>=0 : n+r-1(C)r-1

Here r=4 and n=5
Hence solution: 8C3

Kudos [?]: 19 [0], given: 14

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 17586

Kudos [?]: 270 [0], given: 0

Premium Member
Re: How many positive integers less than 10,000 are there in whi [#permalink]

Show Tags

New post 09 Aug 2017, 22:05
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 270 [0], given: 0

Intern
Intern
User avatar
B
Joined: 30 Jun 2017
Posts: 18

Kudos [?]: 7 [0], given: 80

Location: India
Concentration: Technology, General Management
WE: Consulting (Computer Software)
GMAT ToolKit User CAT Tests
Re: How many positive integers less than 10,000 are there in [#permalink]

Show Tags

New post 06 Sep 2017, 22:41
walker wrote:
there is a shortcut. For the problem, 4 digits are equally important in 0000-9999 set and it is impossible to build a number using only one digit (like 11111) So, answer has to be divisible by 4. Only 56 works.

Image Posted from GMAT ToolKit


Hi walker,

Can you please explain this?

Kudos [?]: 7 [0], given: 80

Re: How many positive integers less than 10,000 are there in   [#permalink] 06 Sep 2017, 22:41

Go to page   Previous    1   2   3   4   [ 67 posts ] 

    Similar topics Author Replies Last post
Similar
Topics:
6 How many positive integers less than 200 are there such that they are PareshGmat 2 23 Aug 2016, 10:05
24 EXPERTS_POSTS_IN_THIS_TOPIC How many positive integers less than 200 are there such that bmwhype2 6 20 Jan 2017, 11:24
1 How many positive integers less than 10,000 are there in which the sum braxus 2 01 Oct 2011, 18:21
31 EXPERTS_POSTS_IN_THIS_TOPIC How many positive integers less than 10,000 are such that the product PTK 18 11 Aug 2017, 04:41
12 EXPERTS_POSTS_IN_THIS_TOPIC How many positive integers less than 10,000 are such that the product Bunuel 10 25 May 2015, 08:21
Display posts from previous: Sort by

How many positive integers less than 10,000 are there in

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


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