Last visit was: 01 May 2026, 23:47 It is currently 01 May 2026, 23:47
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
alimad
User avatar
Joined: 10 Feb 2006
Last visit: 09 Jul 2014
Posts: 466
Own Kudos:
4,433
 [56]
Posts: 466
Kudos: 4,433
 [56]
How many odd integers between 100 and 1000, do not contain the digit Updated on: 20 Mar 2025, 02:35
Originally posted by alimad on 13 May 2008, 18:56.
Last edited by Bunuel on 20 Mar 2025, 02:35, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
1
Kudos
Add Kudos
55
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

57% (02:05) correct 43% (02:42) wrong based on 582 sessions

History

Date
Time
Result
Not Attempted Yet
How many odd integers between 100 and 1000, do not contain the digit "5"?

A. 180
B. 196
C. 286
D. 288
E. 324

M03-12

Experience GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 01 May 2026
Posts: 110,001
Own Kudos:
812,367
 [15]
Given Kudos: 105,976
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 110,001
Kudos: 812,367
 [15]
How many odd integers between 100 and 1000, do not contain the digit 19 May 2015, 05:29
9
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
Official Solution:

How many odd integers between 100 and 1000, do not contain the digit "5"?

A. 180
B. 196
C. 286
D. 288
E. 324


Let's examine the possible options for each digit in these numbers:

The hundreds digit has 8 options: 1, 2, 3, 4, 6, 7, 8, or 9 (excluding 0 and 5).

The tens digit has 9 options: 0, 1, 2, 3, 4, 6, 7, 8, or 9 (excluding 5).

The units digit has 4 odd options: 1, 3, 7, or 9 (excluding 0, 2, 4, 5, 6, and 8).

Consequently, the total number of odd integers between 100 and 1000 that do not contain the digit "5" is \(8 * 9 * 4 = 32 * 9 = 288.\)


Answer: D
General Discussion
User avatar
[email protected]
User avatar
Joined: 14 Jan 2007
Last visit: 04 Feb 2009
Posts: 312
Own Kudos:
956
 [8]
Posts: 312
Kudos: 956
 [8]
How many odd integers between 100 and 1000, do not contain the digit 13 May 2008, 20:11
5
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
Should be 288.
We have to find the total number of 3-digit odd numbers not having 5 as a digit.
Units digits will be among 1,3,7,9
Tenth digits will be among 0,1,2,3,4,6,7,8,9
Hundredth digits will be among 1,2,3,4,6,7,8,9
So total numbers = 4*9*8 =288
User avatar
xALIx
User avatar
Joined: 02 Aug 2007
Last visit: 29 Apr 2009
Posts: 136
Own Kudos:
264
Schools:Life
Posts: 136
Kudos: 264
How many odd integers between 100 and 1000, do not contain the digit 24 Jan 2009, 14:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can someone tell my why we multiply 4*8*9, whats the logic behind multiplying versus another approach?

Thanks,
Ali
User avatar
x2suresh
User avatar
Joined: 07 Nov 2007
Last visit: 18 Aug 2012
Posts: 711
Own Kudos:
3,148
Given Kudos: 5
Location: New York
Posts: 711
Kudos: 3,148
How many odd integers between 100 and 1000, do not contain the digit 24 Jan 2009, 16:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
x-ALI-x
Can someone tell my why we multiply 4*8*9, whats the logic behind multiplying versus another approach?

Thanks,
Ali
Show more

we need to find odd numbers without digit 5 from 100 to 1000 (i.e same as odd numbers without digit 5 from 100 to 999)

let say number= XYZ
Z= units digit
Y= tenths digit
X= Hundredth's digit

For any 3 digit number to be odd, Unit digit must be odd
So Z can be filled with 1,3,7,9 (we are exlcuding digit 5) = 4 ways.
Y can be filled with 0,1,2,3,4,6,7,8,9 (we are ecluding digit 5) = 9 ways
X can be filled with 1,2,3,4,6,7,8,9 (we are exlcuding digits 0 and 5 .. ) = 8 ways

No of ways= 4*9*8= 288
User avatar
Aalto700
User avatar
Joined: 06 Dec 2021
Last visit: 11 Jan 2026
Posts: 53
Own Kudos:
14
Given Kudos: 80
Location: Finland
Concentration: Accounting, Entrepreneurship
Schools: HBS '27 (WD)
GPA: 4
WE:Account Management (Consulting)
Schools: HBS '27 (WD)
Posts: 53
Kudos: 14
How many odd integers between 100 and 1000, do not contain the digit 20 Mar 2025, 02:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Why inclusive is mentioned here? "In a set of numbers from 100 to 1000 inclusive"
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 01 May 2026
Posts: 110,001
Own Kudos:
812,367
 [1]
Given Kudos: 105,976
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 110,001
Kudos: 812,367
 [1]
How many odd integers between 100 and 1000, do not contain the digit 20 Mar 2025, 02:34
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Aalto700
Why inclusive is mentioned here? "In a set of numbers from 100 to 1000 inclusive"
Show more

The word "inclusive" is mentioned to clarify that both 100 and 1000 are part of the set. However, it doesn't actually affect the count in this case because neither 100 nor 1000 is odd or contains the digit "5".

The new edition of this question corrects this.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,009
Own Kudos:
1,122
Posts: 39,009
Kudos: 1,122
How many odd integers between 100 and 1000, do not contain the digit 29 Mar 2026, 07:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
110001 posts
Krunaal
Tuck School Moderator
852 posts