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

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Director
Joined: 10 Feb 2006
Posts: 657
In a set of numbers from 100 to 1000 inclusive, how many integers are [#permalink]

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13 May 2008, 18:56
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Difficulty:

95% (hard)

Question Stats:

45% (02:01) correct 55% (01:52) wrong based on 110 sessions

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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

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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.
Current Student
Joined: 28 Dec 2004
Posts: 3357
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]

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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: 774
Re: In a set of numbers from 100 to 1000 inclusive, how many integers are [#permalink]

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13 May 2008, 20:11
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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: 228
Schools: Life
Re: In a set of numbers from 100 to 1000 inclusive, how many integers are [#permalink]

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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
SVP
Joined: 07 Nov 2007
Posts: 1799
Location: New York
Re: In a set of numbers from 100 to 1000 inclusive, how many integers are [#permalink]

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24 Jan 2009, 16:07
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
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Manager
Joined: 02 Aug 2007
Posts: 228
Schools: Life
Re: In a set of numbers from 100 to 1000 inclusive, how many integers are [#permalink]

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24 Jan 2009, 16:11
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
Re: In a set of numbers from 100 to 1000 inclusive, how many integers are [#permalink]

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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

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Math Expert
Joined: 02 Sep 2009
Posts: 39673
Re: In a set of numbers from 100 to 1000 inclusive, how many integers are [#permalink]

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19 May 2015, 05:29
1
KUDOS
Expert's post
1
This post was
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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)

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Posts: 15976
Re: In a set of numbers from 100 to 1000 inclusive, how many integers are [#permalink]

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03 Jun 2016, 03:34
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Re: In a set of numbers from 100 to 1000 inclusive, how many integers are   [#permalink] 03 Jun 2016, 03:34
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