It is currently 19 Oct 2017, 07:56

STARTING SOON:

Live Chat with Cornell Adcoms in Main Chat Room  |  R1 Interview Invites: MIT Sloan Chat  |  UCLA Anderson Chat  |  Duke Fuqua Chat (EA Decisions)


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 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
S
Joined: 15 Dec 2015
Posts: 114

Kudos [?]: 111 [0], given: 70

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:

44% (01:16) correct 56% (01:30) wrong based on 34 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
[Reveal] Spoiler: OA

Kudos [?]: 111 [0], given: 70

Expert Post
1 KUDOS received
Math Forum Moderator
avatar
B
Joined: 20 Mar 2014
Posts: 2676

Kudos [?]: 1723 [1], given: 792

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
This post received
KUDOS
Expert's post
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.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Kudos [?]: 1723 [1], given: 792

Re: How many positive integers less than 1000 are there in which the sum o   [#permalink] 08 Aug 2017, 12:44
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  


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®.