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 →

Digits

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 301
Joined: Tue Apr 22, 2008 6:07 am
Thanked: 2 times
by beater » Fri Feb 13, 2009 7:57 pm
Of the 3-digit integers greater than 700, how many have 2 digits that are equal to each other and the remaining digit different from the other 2 ?

(A) 90
(B) 82
(C) 80
(D) 45
(E) 36

Could someone please show me how to solve this using combinatorics
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Site Admin
Posts: 2567
Joined: Thu Jan 01, 2009 10:05 amFollowed by: 550 members
Thanked: 712 times
GMAT Score:770

by DanaJ » Fri Feb 13, 2009 10:27 pm
https://www.beatthegmat.com/counting-int ... 16933.html
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 80
Joined: Mon Feb 02, 2009 6:36 am
Thanked: 10 times

Re: Digits

by billzhao » Sat Feb 14, 2009 1:31 am
beater wrote:Of the 3-digit integers greater than 700, how many have 2 digits that are equal to each other and the remaining digit different from the other 2 ?

(A) 90
(B) 82
(C) 80
(D) 45
(E) 36

Could someone please show me how to solve this using combinatorics
There are three situations:
1.All the digits are the same.
2.Two of the three are the same.
3.Every digit is distinct.

So we can use subtraction.

Total number of 3-digit integer: 3*10*10 = 300
Total number of 3-digit integer with all the digits are the same: 3*1*1=3 (i.e. 777,888,999)
Total number of 3-digit integer with every digit is distinct: 3*9*8=216
Total number of 3-digit integer with 2 digits that are equal to each other: 300-3-216=81

Then we need to exclude 700. So the answer is 81-1=80
Yiliang
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1