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Intern  Joined: 05 Jan 2006
Posts: 2
How many four digit numbers divisible by 4 can be made with  [#permalink]

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13 00:00

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Question Stats: 92% (02:00) correct 8% (02:23) wrong based on 43 sessions

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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?
GMAT Club Legend  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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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
Director  Joined: 21 Sep 2003
Posts: 986
Location: USA
Re: How many four digit numbers divisible by 4 can be made with  [#permalink]

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3
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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- Bernard Edmonds
Manager  Joined: 04 Jan 2006
Posts: 51
Re: How many four digit numbers divisible by 4 can be made with  [#permalink]

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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)!)
SVP  Joined: 14 Dec 2004
Posts: 1516
Re: How many four digit numbers divisible by 4 can be made with  [#permalink]

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< 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
GMAT Club Legend  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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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  Joined: 05 Apr 2016
Posts: 26
Re: How many four digit numbers divisible by 4 can be made with  [#permalink]

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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
Non-Human User Joined: 09 Sep 2013
Posts: 11393
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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