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18 Apr 2016, 00:57
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
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Question Stats:
77% (01:03) correct
23%
(01:18)
wrong
based on 397
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What is the greatest positive integer n such that 3^n is a factor of 36^100?
A. 100
B. 200
C. 300
D. 600
E. 900
A. 100
B. 200
C. 300
D. 600
E. 900
18 Apr 2016, 01:01
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Bunuel
Hi,
the Q basically asks us the number of 3 in \(36^{100}\)...
so lets factorize it--
\(36^{100} = (3^2*2^2)^{100} = 3^{2*100} * 2^{2*100} = 3^{200} * 2^{200}\)..
so n=200
B
18 Apr 2016, 12:21
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Bunuel
\(36^{100}\) = \((3^{2}*2^{2})^{100}\) =\(3^{200} * 2^{200}\)
So, The Highest power of 3^n will be 3^200
Or, \(3^n\)= \(3^{200}\)
Hence n = 200
