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What is the highest prime factor in the expression
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Updated on: 12 Dec 2017, 11:55
Updated on: 12 Dec 2017, 11:55
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49% (00:59) correct
49% (01:04) wrong based on 14 sessions
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What is the highest prime factor in the expression
\(\frac{3^{18} - 3^{12}}{3^5}\)
A) 3
B) 7
C) 11
D) 13
E) 19
\(\frac{3^{18} - 3^{12}}{3^5}\)
A) 3
B) 7
C) 11
D) 13
E) 19
Originally posted by shadowcatradz on 20 Feb 2017, 09:57.
Last edited by Carcass on 12 Dec 2017, 11:55, edited 3 times in total.
Last edited by Carcass on 12 Dec 2017, 11:55, edited 3 times in total.
Edited by Carcass
Re: What is the highest prime factor in the expression
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20 Feb 2017, 12:31
20 Feb 2017, 12:31
1
Expert Reply
Explanation
Take the expression
\(\frac{3^1^8 - 3^1^2}{3^5}\) or \(3^1^2\frac{3^6 - 1}{3^5}\)= \(3^7 \times 728\).
Clearly the highest prime factor of the expression \(\frac{3^1^8 - 3^1^2}{3^5}\) also is the highest prime factor of 728.
Try \(\frac{728}{19}\). Doesn't work!
Try \(\frac{728}{13}\). Works!
Hence D is the right answer.
Take the expression
\(\frac{3^1^8 - 3^1^2}{3^5}\) or \(3^1^2\frac{3^6 - 1}{3^5}\)= \(3^7 \times 728\).
Clearly the highest prime factor of the expression \(\frac{3^1^8 - 3^1^2}{3^5}\) also is the highest prime factor of 728.
Try \(\frac{728}{19}\). Doesn't work!
Try \(\frac{728}{13}\). Works!
Hence D is the right answer.
gmatclubot
Re: What is the highest prime factor in the expression [#permalink]
20 Feb 2017, 12:31
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