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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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New post 21 Aug 2009, 05:07
3
3
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (01:42) correct 39% (02:01) wrong based on 140 sessions

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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

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.

The correct answer is C.

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.
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Re: GMAT CLUB tests - p&c problem  [#permalink]

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New post 21 Aug 2009, 05:27
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2
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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New post 21 Aug 2009, 05:14
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Please explain the solution!!

I am weak in P&C :o
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Re: GMAT CLUB tests - p&c problem  [#permalink]

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New post 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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New post 21 Aug 2009, 12:59
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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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New post 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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New post 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.

Answer: C.

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