Scoretop No. 4 - Exponents

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Scoretop No. 4 - Exponents

by akay » Sun Aug 26, 2007 5:54 am
A lot of the questions from Scoretop seem incomplete. Anyways here goes...

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
Source: — Problem Solving |

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Re: Scoretop No. 4 - Exponents

by beny » Sun Aug 26, 2007 6:04 am
akay wrote:A lot of the questions from Scoretop seem incomplete. Anyways here goes...

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
x=1*2*3*4*5*6*7*8
=1*2*3*(2*2)*5*(2*3)*7*(2*2*2)
=2^7*3^2*5^1*7^1
i=7, k=2, m=1, p=1

i+k+m+p=11

Answer D.

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by akay » Sun Aug 26, 2007 6:36 am
beny thanks. factorization, never thought about it :(