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How many 3-digit numbers do not have an even digit or a zero?

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How many 3-digit numbers do not have an even digit or a zero?  [#permalink]

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New post 04 Apr 2019, 00:25
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (01:22) correct 20% (01:26) wrong based on 41 sessions

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How many 3-digit numbers do not have an even digit or a zero?  [#permalink]

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New post 04 Apr 2019, 01:14

Solution


To find:
    • The number of 3-digit numbers do not have an even digit

Approach and Working:
    • Let the three-digit number is abc and a, b, and c must be odd.
      o Hence, we need to find the number of values that a, b, and c can take.

Total values of a, b, and c:

    • a can be 1, or 3, or 5, or 7, or 9.
      o Values a can take = 5

    • Similarly, b and c can take 5 values.

Thus, total ways to form abc = 5 * 5 * 5 = 125

Hence, the correct answer is option E.

Answer: E

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Re: How many 3-digit numbers do not have an even digit or a zero?  [#permalink]

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New post 04 Apr 2019, 03:23
Bunuel wrote:
How many 3-digit numbers do not have an even digit?

(A) 20
(B) 30
(C) 60
(D) 80
(E) 125


solve using combination technique
total integers not even ; 1,3,5,7,9 ; 5
so 3 terms being all odd ;
5*5*5 = 125
IMO E
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Re: How many 3-digit numbers do not have an even digit or a zero?  [#permalink]

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New post 05 Apr 2019, 00:55
Archit3110 wrote:
Bunuel wrote:
How many 3-digit numbers do not have an even digit?

(A) 20
(B) 30
(C) 60
(D) 80
(E) 125


solve using combination technique
total integers not even ; 1,3,5,7,9 ; 5
so 3 terms being all odd ;
5*5*5 = 125
IMO E


Hi Archit, can you please explain your method further? Thanks!
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Re: How many 3-digit numbers do not have an even digit or a zero?  [#permalink]

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New post 05 Apr 2019, 02:01
swatato wrote:
Archit3110 wrote:
Bunuel wrote:
How many 3-digit numbers do not have an even digit?

(A) 20
(B) 30
(C) 60
(D) 80
(E) 125


solve using combination technique
total integers not even ; 1,3,5,7,9 ; 5
so 3 terms being all odd ;
5*5*5 = 125
IMO E


Hi Archit, can you please explain your method further? Thanks!


swatato
list down all odd integers from 0-9 ; 1,3,5,7,9 i.e 5 in total
question has asked How many 3-digit numbers do not have an even digit ; it means that all integers have to be odd and can be repeated
so combination ; 5*5*5 ; 125
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Re: How many 3-digit numbers do not have an even digit or a zero?  [#permalink]

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New post 07 Apr 2019, 19:10
Bunuel wrote:
How many 3-digit numbers do not have an even digit?

(A) 20
(B) 30
(C) 60
(D) 80
(E) 125


There are five possible choices for each of the digits (1, 3, 5, 7 and 9). The number of 3-digit numbers with all odd digits is 5 x 5 x 5 = 125.

Answer: E
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Re: How many 3-digit numbers do not have an even digit or a zero?   [#permalink] 07 Apr 2019, 19:10
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