BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Combinations

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Senior | Next Rank: 100 Posts
Posts: 66
Joined: Wed Jul 07, 2010 11:06 am
Thanked: 1 times
by baladon99 » Sun Apr 17, 2011 10:03 am
How many positive integers less than 10,000 are there in which sum of digits equals 5?

(a) 31
(b) 51
(c) 56
(d) 62
(e) 93

Can any one help to solve this problem ?

Thanks in advance,
Bala
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Senior | Next Rank: 100 Posts
Posts: 94
Joined: Tue Jun 30, 2009 4:51 pmFollowed by: 7 members
Thanked: 24 times
GMAT Score:750

by havok » Sun Apr 17, 2011 10:16 am
So I'll try to type and figure out this problem at the same time. It has to be less than 10,000, so it's going to be a number with one, two, three, or four digits.

* One Digits * 5 (1 Total)
* Two Digits * 50, 41, 32, 23, 14 (6 total)
* Three Digits * 500, 410, 401, 320, 302, 311, 230, 203, 221, 212, 140, 104, 113, 131, 122 (21 Total)
* Four Digits * 5000, 4100, 4010, 4001, 3200, 3020, 3002, 3110, 3101, 3011, 2300, 2030, 2003, 2120, 2102, 2210, 2201, 2120, 2102, 2111, 1400, 1040, 1004, 1130, 1103, 1220, 1202, 1310, 1301. (51 Total)

B. 51 (wrong), there should be a short cut to a correct answer?
Last edited by havok on Sun Apr 17, 2011 11:16 am, edited 1 time in total.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Thu Feb 19, 2009 10:16 pm
Location: CA, USA
Thanked: 2 times

by vvsmart » Sun Apr 17, 2011 10:29 am
Only 1 non-zero digit - 4
5, 50,500,5000 - 4

two non-zero digits - 24

23 - 2 ( 23 & 32)
230 - 4 (230, 203, 320, 302)
2300 - 6 (2003, 2030, 2300, 3200, 3020, 3002)

Total = 12

or calculate overall as 4!/2! = 12 ( find combinations for 4 digits where 2 are repeating 2, 3, 0, 0)

Similarly 12 options for 1,4,0,0

3 non-zero digits - 24

1,2,2,0
Total = 4!/2! = 12

1,3,1,0
Total = 4!/2! = 12

4 non-zero digits = 4

1,1,1,2
Total = 4!/3! = 4

Overall total = 56
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1