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How many four digit numbers divisible by 4 can be made with

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Intern
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How many four digit numbers divisible by 4 can be made with  [#permalink]

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New post 31 Jan 2006, 07:38
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How many four digit numbers divisible by 4 can be made with digits 1, 2, 3, 4, 5 if the repetition of digits is not allowed?
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Joined: 07 Jul 2004
Posts: 4560
Location: Singapore
Re: How many four digit numbers divisible by 4 can be made with  [#permalink]

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New post 31 Jan 2006, 09:14
A number is divisible by 4 if the last 2 numbers are divisible by 4 (divisible by 2 twice)

Ending can be
12
24
32
42
52

Case: Ending with 12,24,32,42,54
First digit - 3 choices
Second digit - 2 choices
Third digit - 1 choice
Fourth digit - 1 choice

6 possible choices for each ending (e.g. 3412,3512, 3212 ,4512 ,5312 ,5412)

Total number of 4 digit numbers divisible by 4 = 6 * 5 = 30
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Re: How many four digit numbers divisible by 4 can be made with  [#permalink]

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New post 31 Jan 2006, 09:24
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ywilfred wrote:
A number is divisible by 4 if the last 2 numbers are divisible by 4 (divisible by 2 twice)

Ending can be
12
24
32
42
52

Case: Ending with 12,24,32,42,54
First digit - 3 choices
Second digit - 2 choices
Third digit - 1 choice
Fourth digit - 1 choice

6 possible choices for each ending (e.g. 3412,3512, 3212 ,4512 ,5312 ,5412)

Total number of 4 digit numbers divisible by 4 = 6 * 5 = 30


I like your explanation. There seems to be a small error. Isn't it 12:30AM in Singapore?

only 12, 24, 32, 52 are divisible by 4

6*4 = 24
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Re: How many four digit numbers divisible by 4 can be made with  [#permalink]

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New post 31 Jan 2006, 10:32
12,24,32 and 52.
so 4*3! = 24.
(3! is because the first 2 digits of the 4 digit no. can be formed form the
3 remaining digits of 1,2,3,4,5. So 3P2 = 3! /(3-2)!)
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Re: How many four digit numbers divisible by 4 can be made with  [#permalink]

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New post 31 Jan 2006, 12:25
< than 1 min :)

Last two digits can only be: 12,24,32,52
Other 3 digits should be used to form 100th & 1000th position.

Total combinations = (2*3*1)*4 = 24
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Re: How many four digit numbers divisible by 4 can be made with  [#permalink]

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New post 31 Jan 2006, 19:00
giddi77 wrote:
ywilfred wrote:
A number is divisible by 4 if the last 2 numbers are divisible by 4 (divisible by 2 twice)

Ending can be
12
24
32
42
52

Case: Ending with 12,24,32,42,54
First digit - 3 choices
Second digit - 2 choices
Third digit - 1 choice
Fourth digit - 1 choice

6 possible choices for each ending (e.g. 3412,3512, 3212 ,4512 ,5312 ,5412)

Total number of 4 digit numbers divisible by 4 = 6 * 5 = 30


I like your explanation. There seems to be a small error. Isn't it 12:30AM in Singapore?

only 12, 24, 32, 52 are divisible by 4

6*4 = 24


Yup, it was about slightly over 12:30am. :)
Intern
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Re: How many four digit numbers divisible by 4 can be made with  [#permalink]

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New post 02 Jul 2016, 10:25
I got 24.
The only four-digit numbers divisible by 4 are the ones that end with 24, 12, 32 and 52 (a number is divisible by 4 if the last two digits are divisible by 4).
In each of these cases, the first two digits can be arranged in 3*2 ways, as the last two digits are fixed numbers (3*2*1*1).
So it's 6*4= 24
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Re: How many four digit numbers divisible by 4 can be made with  [#permalink]

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Re: How many four digit numbers divisible by 4 can be made with   [#permalink] 14 Sep 2018, 14:04
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