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# How many odd three-digit integers greater than 800 are there

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

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21 Aug 2009, 05:07
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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. 60
C. 72
D. 81
E. 104

[Reveal] Spoiler:
If the number begins with 8, there are possibilities (5 possibilities for the last digit and 8 possibilities for the middle digit). If the number begins with 9, there are possibilities (4 possibilities for the last digit and 8 possibilities for the middle digit). In all, there are numbers that satisfy the constraints.

GMAC25 : i think there are 9 possiblities for middle digit, 0-9 and excluding 8, now how can we say that there are 5 possibilties for last digit when middle digit is 1 then possible last digit values are 3,5,7,9.

i am not able to understand this.
[Reveal] Spoiler: OA
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Re: GMAT CLUB tests - p&c problem [#permalink]

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21 Aug 2009, 05:14
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I am weak in P&C
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Re: GMAT CLUB tests - p&c problem [#permalink]

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21 Aug 2009, 05:27
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Last digit is always ODD:
case1: first digit is 8, then last digit has 5 options(1,3,5,7,9) and middle digit has 8 options as we have already chosen two digits for the first and the last positions.
total numbers = 1*8*5 = 40

case2: first digit is 9, then last digit has 4 options(1,3,5,7) and middle digit has 8 options again.
total numbers = 1*8*4 = 32
Ans:72

NOTE: last digit should always be one of 1,3,5,7,9
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Re: GMAT CLUB tests - p&c problem [#permalink]

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21 Aug 2009, 12:53
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thanks a lot .... this solution cleared my doubt.
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Re: GMAT CLUB tests - p&c problem [#permalink]

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21 Aug 2009, 12:59
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Expert's post
Also here: m25-76554.html

See this post for a listing of all discussions: gmat-club-tests-master-threads-all-tests-78599.html
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Re: GMAT CLUB tests - p&c problem [#permalink]

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07 Sep 2010, 18:02
Thank you for explanation. It is very helpful!
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Re: GMAT CLUB tests - p&c problem [#permalink]

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11 Sep 2010, 22:51
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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. 60
C. 72
D. 81
E. 104

In the range 800 - 900:
1 choice for the first digit: 8;
5 choices for the third digit: 1, 3, 5, 7, 9;
8 choices for the second digit: 10 digits - first digit - third digit = 8 digits.

1*5*8 = 40.

In the range 900 - 999:
1 choice for the first digit: 9;
4 choices for the third digit: 1, 3, 5, 7 (9 is out as it's first digit);
8 choices for the second digit: 10 digits - first digit - third digit = 8 digits.

1*4*8 = 32.

Total: 40+32 = 72.

Also discussed at: odd-3-digit-integers-94655.html and no-properties-71853.html?hilit=range%20choice%20first%20digit

Hope it helps.
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Re: How many odd three-digit integers greater than 800 are there [#permalink]

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23 Jan 2015, 02:34
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Re: How many odd three-digit integers greater than 800 are there [#permalink]

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22 May 2017, 21:54
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: How many odd three-digit integers greater than 800 are there   [#permalink] 22 May 2017, 21:54
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