In a set of numbers from 100 to 1000 inclusive, how many integers are : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 17 Jan 2017, 04:00

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In a set of numbers from 100 to 1000 inclusive, how many integers are

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Director
Joined: 10 Feb 2006
Posts: 658
Followers: 3

Kudos [?]: 459 [0], given: 0

In a set of numbers from 100 to 1000 inclusive, how many integers are [#permalink]

### Show Tags

13 May 2008, 17:56
00:00

Difficulty:

95% (hard)

Question Stats:

40% (02:12) correct 60% (01:53) wrong based on 95 sessions

### HideShow timer Statistics

In a set of numbers from 100 to 1000 inclusive, how many integers are odd and do not contain the digit "5"?

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

M03-12
[Reveal] Spoiler: OA

_________________

GMAT the final frontie!!!.

Last edited by Bunuel on 19 May 2015, 04:28, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Current Student
Joined: 28 Dec 2004
Posts: 3384
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 15

Kudos [?]: 281 [0], given: 2

Re: In a set of numbers from 100 to 1000 inclusive, how many integers are [#permalink]

### Show Tags

13 May 2008, 18:54
In a set of numbers from 100 to 1000 inclusive, how many integers are odd and do not contain the digit "5"?

180
196
286
288
324

lets see..in all there are 450 odd numbers!

of which 105, 115, 125, 135..10 such number per 100 numbrs 10+10(from 15X) 20-1=19 such numbers cause i already counted 155 twice..
19*8=152 such numbers..plus 100 from 5XX..so total to be excluded 152+100-450=198..

I would guess the number is 196..
Director
Joined: 14 Jan 2007
Posts: 777
Followers: 2

Kudos [?]: 136 [0], given: 0

Re: In a set of numbers from 100 to 1000 inclusive, how many integers are [#permalink]

### Show Tags

13 May 2008, 19:11
2
This post was
BOOKMARKED
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
Manager
Joined: 02 Aug 2007
Posts: 231
Schools: Life
Followers: 3

Kudos [?]: 56 [0], given: 0

Re: In a set of numbers from 100 to 1000 inclusive, how many integers are [#permalink]

### Show Tags

24 Jan 2009, 13:36
Can someone tell my why we multiply 4*8*9, whats the logic behind multiplying versus another approach?

Thanks,
Ali
SVP
Joined: 07 Nov 2007
Posts: 1820
Location: New York
Followers: 34

Kudos [?]: 860 [3] , given: 5

Re: In a set of numbers from 100 to 1000 inclusive, how many integers are [#permalink]

### Show Tags

24 Jan 2009, 15:07
3
KUDOS
x-ALI-x wrote:
Can someone tell my why we multiply 4*8*9, whats the logic behind multiplying versus another approach?

Thanks,
Ali

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
_________________

Smiling wins more friends than frowning

Manager
Joined: 02 Aug 2007
Posts: 231
Schools: Life
Followers: 3

Kudos [?]: 56 [0], given: 0

Re: In a set of numbers from 100 to 1000 inclusive, how many integers are [#permalink]

### Show Tags

24 Jan 2009, 15:11
x2suresh wrote:

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

Enough said, very well put!
Intern
Joined: 24 Mar 2013
Posts: 28
Followers: 0

Kudos [?]: 5 [0], given: 131

Re: In a set of numbers from 100 to 1000 inclusive, how many integers are [#permalink]

### Show Tags

18 May 2015, 15:43
x2suresh wrote:
x-ALI-x wrote:
Can someone tell my why we multiply 4*8*9, whats the logic behind multiplying versus another approach?

Thanks,
Ali

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

Dear x2suresh,
Clearly your approach sets the benchmark!
Please share more of such examples. Thanks.
My approach was cumbersome and time consuming:
Attachments

1234.jpg [ 36.49 KiB | Viewed 2516 times ]

Math Expert
Joined: 02 Sep 2009
Posts: 36530
Followers: 7070

Kudos [?]: 92960 [1] , given: 10541

Re: In a set of numbers from 100 to 1000 inclusive, how many integers are [#permalink]

### Show Tags

19 May 2015, 04:29
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
In a set of numbers from 100 to 1000 inclusive, how many integers are odd and do not contain the digit "5"?

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

M03-12

Examine what digits these set members can contain:

First digit (hundreds): 8 choices (1, 2, 3, 4, 6, 7, 8, 9 - cannot be 0 or 5)
Second digit (tens): 9 choices (0, 1, 2, 3, 4, 6, 7, 8, 9 - cannot be 5)
Last digit (units): 4 choices (1, 3, 7, 9 - cannot be 0, 2, 4, 5, 6, 8)

The answer is 8∗9∗4=32∗9=288.

_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13423
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: In a set of numbers from 100 to 1000 inclusive, how many integers are [#permalink]

### Show Tags

03 Jun 2016, 02:34
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: In a set of numbers from 100 to 1000 inclusive, how many integers are   [#permalink] 03 Jun 2016, 02:34
Similar topics Replies Last post
Similar
Topics:
1 How many positive integers, from 2 to 100, inclusive, are not 1 27 Oct 2016, 09:38
5 How many even number in the range between 10 to 100 inclusive are not 2 21 Aug 2016, 08:48
8 How many integers from 1 to 100 (both inclusive) have odd number of 3 15 Jul 2015, 17:32
12 What is the number of integers from 1 to 1000 (inclusive) 8 16 Jan 2012, 08:56
38 How many positive integers, from 2 to 100, inclusive, are no 11 09 Feb 2011, 16:31
Display posts from previous: Sort by

# In a set of numbers from 100 to 1000 inclusive, how many integers are

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO 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®.