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

It is currently 17 Aug 2018, 00:26

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

How many positive integers less than 1000 are there in which the sum o

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

Hide Tags

Manager
Manager
User avatar
G
Joined: 15 Dec 2015
Posts: 120
GMAT 1: 660 Q46 V35
GPA: 4
WE: Information Technology (Computer Software)
How many positive integers less than 1000 are there in which the sum o  [#permalink]

Show Tags

New post 08 Aug 2017, 12:32
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

54% (01:20) correct 46% (01:32) wrong based on 59 sessions

HideShow timer Statistics

How many positive integers less than 1000 are there in which the sum of the digits equals 4?

(A) 10
(B) 12
(C) 13
(D) 14
(E) 15
Current Student
avatar
S
Joined: 20 Mar 2014
Posts: 2643
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: How many positive integers less than 1000 are there in which the sum o  [#permalink]

Show Tags

New post 08 Aug 2017, 12:44
1
DH99 wrote:
How many positive integers less than 1000 are there in which the sum of the digits equals 4?

(A) 10
(B) 12
(C) 13
(D) 14
(E) 15


Straightforward if you divide possible numbers up into different 'buckets':

1. Single digit numbers
2. Double digit numbers
3. Triple digit numbers

For #1: we only have 1 option, 4

For #2: we have 13/31/22/40 = 4 options

For #3: we have 112 (and its combinations = 3!/2! = 3) + combinations of 202 (=2) + combinations of 103 (= 2*2*1 = 4) + 400 = 3+2+4+1 = 10

Thus, total possible positive integers less than 1000 with sum of digits = 4 is equal to 1+4+10 = 15.

E is the correct answer.

Hope this helps.
Senior Manager
Senior Manager
avatar
G
Joined: 02 Apr 2014
Posts: 484
GMAT 1: 700 Q50 V34
Re: How many positive integers less than 1000 are there in which the sum o  [#permalink]

Show Tags

New post 30 Apr 2018, 12:50
1
This is similiar to donut problem - Distributing n donuts among m children, such that each children may receive 0 to n donuts

we use formula: (n+m-1)!/(n!(m-1)!)

similiarly here,
we imagine 4 1's => 1 1 1 1 to be distributed among 3 places (since it is less than 1000, maximum 3 digits)
so total combinations: (4 + 3 - 1)!/ (4! * 2!) = 6!/(4! 2!) = 15
Re: How many positive integers less than 1000 are there in which the sum o &nbs [#permalink] 30 Apr 2018, 12:50
Display posts from previous: Sort by

How many positive integers less than 1000 are there in which the sum o

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

Events & Promotions

PREV
NEXT


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®.