How many odd three-digit integers greater than 800 are there : PS Archive
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How many odd three-digit integers greater than 800 are there

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SVP
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How many odd three-digit integers greater than 800 are there [#permalink]

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11 Nov 2008, 01:40
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How many odd three-digit integers greater than 800 are there such that all their digits are different?

a) 40
b) 56
c) 72
d) 81
e) 104

Thanks
CEO
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 550

Kudos [?]: 3564 [1] , given: 360

Re: PS: How many odd three-digit integers [#permalink]

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11 Nov 2008, 01:59
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Expert's post
C

1. Let's consider 8xy set
2. y e [1,3,5,7,9] (5 possibilities), x has 10 possibilities - 2 possibilities (8 and y). The total number is 5*8=40
3. Let's consider 9xy set
4. y e [1,3,5,7] (4 possibilities), x has 10 possibilities - 2 possibilities (9 and y). The total number is 4*8=32
5 40+32=72
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Director
Joined: 01 Aug 2008
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Re: PS: How many odd three-digit integers [#permalink]

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11 Nov 2008, 07:48
Walker,
great explanation. Thanks.
SVP
Joined: 21 Jul 2006
Posts: 1538
Followers: 10

Kudos [?]: 744 [0], given: 1

Re: PS: How many odd three-digit integers [#permalink]

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12 Nov 2008, 02:56
walker wrote:
C

1. Let's consider 8xy set
2. y e [1,3,5,7,9] (5 possibilities), x has 10 possibilities - 2 possibilities (8 and y). The total number is 5*8=40
3. Let's consider 9xy set
4. y e [1,3,5,7] (4 possibilities), x has 10 possibilities - 2 possibilities (9 and y). The total number is 4*8=32
5 40+32=72

Great explanation walker! Thanks. The OA is C. I just have 1 question. Why did you have to start first from the left digit, then skipped the middle digit to go to the right digit, then back to the middle digit? Why couldn't you just go from left to middle, then from middle to right?

thanks
CEO
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 550

Kudos [?]: 3564 [0], given: 360

Re: PS: How many odd three-digit integers [#permalink]

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12 Nov 2008, 03:13
I saw that we have two different cases here: 8 and 9. 9 is odd and we cannot choose 9 as a unit digit. 8 is even and don't add a restriction to a unit digit. That is why I started with division of the problem by two cases: 8xy and 9xy
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SVP
Joined: 21 Jul 2006
Posts: 1538
Followers: 10

Kudos [?]: 744 [0], given: 1

Re: PS: How many odd three-digit integers [#permalink]

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12 Nov 2008, 03:18
walker wrote:
I saw that we have two different cases here: 8 and 9. 9 is odd and we cannot choose 9 as a unit digit. 8 is even and don't add a restriction to a unit digit. That is why I started with division of the problem by two cases: 8xy and 9xy

as always, you never failed to answer my questions. you're a legend
thanks!
Re: PS: How many odd three-digit integers   [#permalink] 12 Nov 2008, 03:18
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