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# How many 4-digit numbers divisible by 4 can be formed from using

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Manager
Joined: 03 Nov 2019
Posts: 54
How many 4-digit numbers divisible by 4 can be formed from using  [#permalink]

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15 Dec 2019, 11:37
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Difficulty:

65% (hard)

Question Stats:

39% (02:39) correct 61% (02:16) wrong based on 18 sessions

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How many 4-digit numbers divisible by 4 can be formed from using the digits: 0, 1, 2, 3, 4 (without repetition) ?

A) 36
B) 30
C) 24
D) 40
E) 50
VP
Joined: 19 Oct 2018
Posts: 1295
Location: India
Re: How many 4-digit numbers divisible by 4 can be formed from using  [#permalink]

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15 Dec 2019, 19:16
Let a 4 digit number 'abcd'.

Case 1- Unit digit is 0
Tens digit must be even; we have 2 choices (2 and 4).

we are left with 3 options for a and 2 for b.

Total combinations= 3*2*2*1=12

Case 2- unit digit is 2
Tens digit must be odd; we have 2 choices (1 and 3).

we have 2 options for a (exclude 0) and 2 for b.

Total combinations= 2*2*2*1=8

Case 3- unit digit is 4.
Tens digit must be even.

1. tens digit is 0
we have 3 options for a and 2 for b

2. tens digit is 2
we have 2 options for a(exclude 0) and 2 for b

Total combinations= (3*2*1*1)+(2*2*1*1)= 10

Total 4-digit numbers divisible by 4 can be formed from using the digits: 0, 1, 2, 3, 4 (without repetition)= 12+8+10=30

Ansh777 wrote:
How many 4-digit numbers divisible by 4 can be formed from using the digits: 0, 1, 2, 3, 4 (without repetition) ?

A) 36
B) 30
C) 24
D) 40
E) 50
Math Expert
Joined: 02 Aug 2009
Posts: 8336
How many 4-digit numbers divisible by 4 can be formed from using  [#permalink]

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15 Dec 2019, 20:48
Ansh777 wrote:
How many 4-digit numbers divisible by 4 can be formed from using the digits: 0, 1, 2, 3, 4 (without repetition) ?

A) 36
B) 30
C) 24
D) 40
E) 50

Divisiblity by 4 depends on last two digits

1) when the units digit is divisible by 4( so 0 or 4), then the tens digit should be even( 0, 2 or 4)
So if units digit is 0, then tens digit can be 2 or 4. The first and second digit can be filled in remaining 3*2 ways.
Thus 3*2*2*1=12 ways
If units digit is 4, then two ways$$xy04–3*2*1*1=6$$ ways and $$xy24-2*2*1*1=4$$ ways

2) when the units digit is even but not divisible by 4 (that is 2),then tens digit has to be odd (that is 1 or 3).
Ways = xyz2.
z can be any of 1 or 3.
x any of the remaining 3 except digit 0, and
y remaining 2.
Thus 2*2*2*1=8 ways

Total 12+6+4+8=30

B
_________________
How many 4-digit numbers divisible by 4 can be formed from using   [#permalink] 15 Dec 2019, 20:48
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