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alimad
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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.
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75% (hard)

Question Stats:

56% (02:05) correct 44% (02:42) wrong based on 577 sessions

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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

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Bunuel
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How many odd integers between 100 and 1000, do not contain the digit 19 May 2015, 05:29
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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
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How many odd integers between 100 and 1000, do not contain the digit 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
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How many odd integers between 100 and 1000, do not contain the digit 24 Jan 2009, 14:36
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Can someone tell my why we multiply 4*8*9, whats the logic behind multiplying versus another approach?

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Ali
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x2suresh
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How many odd integers between 100 and 1000, do not contain the digit 24 Jan 2009, 16:07
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x-ALI-x
Can someone tell my why we multiply 4*8*9, whats the logic behind multiplying versus another approach?

Thanks,
Ali
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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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How many odd integers between 100 and 1000, do not contain the digit 20 Mar 2025, 02:19
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Why inclusive is mentioned here? "In a set of numbers from 100 to 1000 inclusive"
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How many odd integers between 100 and 1000, do not contain the digit 20 Mar 2025, 02:34
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Aalto700
Why inclusive is mentioned here? "In a set of numbers from 100 to 1000 inclusive"
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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.
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How many odd integers between 100 and 1000, do not contain the digit 29 Mar 2026, 07:13
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