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by arpitad » Tue Dec 20, 2011 2:40 pm
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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by neelgandham » Tue Dec 20, 2011 3:09 pm
n = 1*2*3*4*5*6*7*8
n = 2^7 * 3^2 * 5^1 * 7^1 = 2^i * 3^k * 5^m * 7^p
Equating the exponents
i+k+m+p = 7+ 2+ 1+ 1= 11
D it is !

Already solved here:https://www.beatthegmat.com/if-x-is-the- ... 13395.html
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by Anurag@Gurome » Tue Dec 20, 2011 7:45 pm
arpitad 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
x = 2^i 3^k 5^m 7^p
x = 8! = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 = 2^7 * 3^2 * 5^1 * 7^1
So, 2^7 * 3^2 * 5^1 * 7^1 = 2^i * 3^k * 5^m * 7^p
Equating the exponents on both sides,
i = 7, k = 2, m = 1, and p = 1
Therefore, i + k + m + p = 7 + 2 + 1 + 1 = 11

The correct answer is D.
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by ArunangsuSahu » Fri Dec 30, 2011 8:27 am
11. Convert to the terms as said in the question
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