PS - counting : PS Archive
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# PS - counting

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Joined: 19 Mar 2007
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17 Jul 2007, 23:53
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The sum = ?

Last edited by nick_sun on 28 Jun 2008, 02:21, edited 1 time in total.
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Re: PS - counting (Gset 27 - 17) [#permalink]

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18 Jul 2007, 00:01
nick_sun wrote:
If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2^i * 3^k * 5^m * 7^p, then i + k + m + p =

A. 4
B. 7
C. 8
D. 11
E. 12

8! = 8*7*6*5*4*3*2*1 = 2^i * 3^k * 5^m * 7^p

i=7, k=2, m=1, p=1

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18 Jul 2007, 01:43
Quote:
If x is the product of the positive integers from 1 to 8, inclusive

x=8.7.6.5.4.3.2.1=8!

Quote:
if i, k, m, and p are positive integers such that x = 2^i * 3^k * 5^m * 7^p

we can simplify x as 2^7.3^2.5^1.7^1
Equating the values of x
we have i=7,k=2,m=1,p=1
Quote:
then i + k + m + p =

18 Jul 2007, 01:43
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