Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 18 Jul 2019, 14:43

### 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

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

Author Message
TAGS:

### Hide Tags

Director
Joined: 10 Feb 2006
Posts: 611
In a set of numbers from 100 to 1000 inclusive, how many integers are  [#permalink]

### Show Tags

Updated on: 19 May 2015, 05:28
5
00:00

Difficulty:

95% (hard)

Question Stats:

42% (02:14) correct 58% (02:39) wrong based on 221 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

_________________
GMAT the final frontie!!!.

Originally posted by alimad on 13 May 2008, 18:56.
Last edited by Bunuel on 19 May 2015, 05:28, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
SVP
Joined: 07 Nov 2007
Posts: 1553
Location: New York
Re: In a set of numbers from 100 to 1000 inclusive, how many integers are  [#permalink]

### Show Tags

24 Jan 2009, 16:07
8
3
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
##### General Discussion
Current Student
Joined: 28 Dec 2004
Posts: 3086
Location: New York City
Schools: Wharton'11 HBS'12
Re: In a set of numbers from 100 to 1000 inclusive, how many integers are  [#permalink]

### Show Tags

13 May 2008, 19:54
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: 697
Re: In a set of numbers from 100 to 1000 inclusive, how many integers are  [#permalink]

### Show Tags

13 May 2008, 20:11
3
2
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: 202
Schools: Life
Re: In a set of numbers from 100 to 1000 inclusive, how many integers are  [#permalink]

### Show Tags

24 Jan 2009, 14:36
Can someone tell my why we multiply 4*8*9, whats the logic behind multiplying versus another approach?

Thanks,
Ali
Intern
Joined: 24 Mar 2013
Posts: 23
Re: In a set of numbers from 100 to 1000 inclusive, how many integers are  [#permalink]

### Show Tags

18 May 2015, 16:43
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 9606 times ]

Math Expert
Joined: 02 Sep 2009
Posts: 56257
Re: In a set of numbers from 100 to 1000 inclusive, how many integers are  [#permalink]

### Show Tags

19 May 2015, 05:29
1
1
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)

_________________
Manager
Joined: 20 Feb 2017
Posts: 164
Location: India
Concentration: Operations, Strategy
WE: Engineering (Other)
Re: In a set of numbers from 100 to 1000 inclusive, how many integers are  [#permalink]

### Show Tags

26 Sep 2018, 08:22
consider all three digit number between 100-1000
XYZ

Z can take only 4 values : 1,3,7 and 9 (It cannot take 5)
y can take 9 values : 0,1,2,3,4,6,7,8,9 (It cannot take 5)
X can take 8 values : 1,2,3,4,6,7,8,9 (IT cannot take 0 and 5)
Hence the answer : 4*9*8= 288
_________________
If you feel the post helped you then do send me the kudos (damn theya re more valuable than \$)
Re: In a set of numbers from 100 to 1000 inclusive, how many integers are   [#permalink] 26 Sep 2018, 08:22
Display posts from previous: Sort by