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 →

Combinatorics 01

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 504
Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members
Thanked: 114 times
by knight247 » Tue Sep 27, 2011 12:57 am
How many even 4 digit numbers can be formed by using the digits 0-9 so that no two digits are repeated?
A 2296
B 2396
C 2444
D 2456
E 2486

Don't have an OA. Detailed explanations would be appreciated
Last edited by knight247 on Tue Sep 27, 2011 1:24 am, edited 2 times in total.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Legendary Member
Posts: 966
Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members
Thanked: 230 times

by shankar.ashwin » Tue Sep 27, 2011 1:05 am
Its

9*9*8*7 = 4536 (for thousands, hundreds, tens and units place respectively)

You sure of options?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 142
Joined: Mon Jan 10, 2011 8:03 am
Thanked: 19 times

by krishnasty » Tue Sep 27, 2011 1:50 am
IMO A

This question can be solved in 2 parts.
part 1) when the unit digit is 0 (rememeber, any number ending with 0 is an even number)
9*8*7*1 = 504 ( 1 option for unit digit*9 digits for thousand digit, 8 for hundered and 7 for tens)

part 2) when the unit digit is any number from 2,4,6,8
8*8*7*4 = 1792( 4 option for unit digit, 8 for thousand,8 for hundered and 7 for tens)
tota; : 1792 +504 = 2296
---------------------------------------
Appreciation in thanks please!!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 966
Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members
Thanked: 230 times

by shankar.ashwin » Tue Sep 27, 2011 2:00 am
_ _ _ _

You know total Nos of possible 4 digit integers is 4536 (9*9*8*7)

To not consider separate cases including 0's, as the prev soln. Consider Nos of odd and subtract it with total, makes calc much easier.

For odd the units can be filled by (1,3,5,7 or 9)

_ _ _ 5

First can take 8 (exclude 0 and the last odd)
Second can take 8 (exclude first and last)
Third can take 7

So, 8*8*7*5 = 2240

Hence even = 4536-2240 = 2296
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Tue Sep 27, 2011 6:05 am
knight247 wrote:How many even 4 digit numbers can be formed by using the digits 0-9 so that no two digits are repeated?
A 2296
B 2396
C 2444
D 2456
E 2486
For most counting questions we can break the task into stages and apply the Fundamental Counting Principle (FCP).

Stage 1: Select units digit
Stage 2: Select tens digit
Stage 3: Select hundreds digit
Stage 4: Select thousands digit

Two important things:
1) When you use the FCP, always begins with the most restrictive stage
2) To handle the problematic situation where having a zero in the thousands position is no good, let's first determine the total number of 4-digit integers that may or may not have a zero in this position, and then we'll subtract the number of 4-digit integers that have a zero in this position.

4-digit integers that may or may not have a zero in the thousands position
Stage 1: can be accomplished in 5 ways (even digits only)
Stage 2: can be accomplished in 9 ways (once we select a digit for stage 1, there are 9 digits to choose from)
Stage 3: can be accomplished in 8 ways
Stage 4: can be accomplished in 7 ways
Total number of 4-digit integers = 5x9x8x7 = 2520

4-digit integers that have a zero in the thousands position
We'll begin the most restrictive stage, which is stage 4.
Stage 4: can be accomplished in 1 ways (must be zero)
Stage 1: can be accomplished in 4 ways (even digit other than 0)
Stage 2: can be accomplished in 8 ways
Stage 3: can be accomplished in 7 ways
Total number of 4-digit integers with zero in thousands position = 1x4x8x7 = 224

Final answer = 2520 - 225 = 2296, so the answer is A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1