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For a positive integer k written in decimal notation, #(k)

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GMAT Instructor
Joined: 04 Jul 2006
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For a positive integer k written in decimal notation, #(k) [#permalink]  27 Sep 2006, 01:35
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For a positive integer k written in decimal notation, #(k) is defined as the product of the digits of k. For instance, #(333)=27 and #(142)=8. If Y is the set of four digit whole numbers w such that #(w)=60, what percent of the elements of Y are greater than 5000?
Intern
Joined: 18 Sep 2006
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25%

The four digist are the factors of 60..so they could be (5322) or (1652) or (1453).
The numbers in each case that are greater than 5000 are 3 of 12, 4 of 24 and 4 of 24...so total 15 of 60 or 25%
Senior Manager
Joined: 11 May 2006
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i am getting 21/60

numbers could be permutation of 5322 or 1652 or 1453.
total numbers = !3/!2 + 2*3*2*1 + !3 = 21
Senior Manager
Joined: 11 Jul 2006
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10/21

Permutations of 4351 2651 , 2353 = 3 * 4!
Total possible combinations = 9P4 (we have to ignore 0)

3*4!/9P4 * 100 = 10/21
Manager
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Solution please I thought 25% as well.
Senior Manager
Joined: 28 Aug 2006
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lanuk wrote:
25%

The four digist are the factors of 60..so they could be (5322) or (1652) or (1453).
The numbers in each case that are greater than 5000 are 3 of 12, 4 of 24 and 4 of 24...so total 15 of 60 or 25%

Hey lanuk,

it must be 3 of 12, 6 of 24 and 6 of 24.........so total 15 out of 60 ie 25%.

I too got the same answer. So let's wait for the OA

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Last edited by cicerone on 25 Sep 2008, 00:17, edited 1 time in total.
Senior Manager
Joined: 28 Aug 2006
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kevincan wrote:
cicerone wrote:
lanuk wrote:
25%

The four digist are the factors of 60..so they could be (5322) or (1652) or (1453).
The numbers in each case that are greater than 5000 are 3 of 12, 4 of 24 and 4 of 24...so total 15 of 60 or 25%

Hey lanuk,

it must be 3 of 12, [color=red]6
of 24 and 6 of 24.........so total 15 out of 60 ie 25%.

I too got the same answer. So let's wait for the OA[/color]

Why only 6 of 24?

Hey kevin i got it...............

it is 21/60 ie 35%
Intern
Joined: 18 Sep 2006
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Yup Cicerone..you're right..should be 21/60...
3 +12(Both starting with 5 and 6 are greater than 5000) +6
Silly mistake
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