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# How many 4 digit positive integers are there in which all 4

Author Message
Director
Joined: 24 Oct 2005
Posts: 555
Location: NYC
How many 4 digit positive integers are there in which all 4  [#permalink]

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20 Jun 2007, 18:35
2
11
How many 4 digit positive integers are there in which all 4 digits are even?

1. 625
2. 600
3. 500
4 400
5 256

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VP
Joined: 10 Jun 2007
Posts: 1360
Re: How many 4 digit positive integers?  [#permalink]

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20 Jun 2007, 18:41
1
2
bewakoof wrote:
How many 4 digit positive integers are there in which all 4 digits are even?

1. 625
2. 600
3. 500
4 400
5 256

I got 500.

Say integer = ABCD
A can be 2,4,6,8
B,C,D can be 0,2,4,6,8
So 4*5*5*5 = 500
Director
Joined: 16 May 2007
Posts: 527

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21 Jun 2007, 08:20
1
can you explain why you have multiplied 4*5*5*5?
Manager
Joined: 12 Apr 2007
Posts: 159

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21 Jun 2007, 16:54
1
trahul4 wrote:
can you explain why you have multiplied 4*5*5*5?

Think of having to fill four slots. The thousands, hundreds, tens, and units slots.

Since it is a 4 digit number, 0 cannot be the first digit. So the first digit can be 2, 4, 6, or 8. Four possibilities.

For the other 3 digits, there are 5 possibilities: 0, 2, 4, 6, and 8.

therefore, 4x5x5x5
Current Student
Joined: 03 Oct 2006
Posts: 84
Re: How many 4 digit positive integers?  [#permalink]

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21 Jun 2007, 18:10
bkk145 wrote:
bewakoof wrote:
How many 4 digit positive integers are there in which all 4 digits are even?

1. 625
2. 600
3. 500
4 400
5 256

I got 500.

Say integer = ABCD
A can be 2,4,6,8
B,C,D can be 0,2,4,6,8
So 4*5*5*5 = 500

Me too. These types of questions are prevalent in the GMATClub challenges, but I haven't seen problems of this type in the OG.
Non-Human User
Joined: 09 Sep 2013
Posts: 8817
Re: How many 4 digit positive integers are there in which all 4  [#permalink]

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28 Oct 2018, 16:22
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Re: How many 4 digit positive integers are there in which all 4 &nbs [#permalink] 28 Oct 2018, 16:22
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