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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 =
GMAT Difficulty: 600-700 Level Number Properties
Sunday 30 November 2014, by
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
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1. 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 =, 30 November 2014, 18:59, by hurtado claudio
Here the idea is to go expressing each factor from one to eight, decomposed into its primes:
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
Then
i = 7
k = 2
m = 1
p = 1
i + k + m + p = 11
Correct answer D
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