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21 Nov 2014, 01:42
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
60% (02:28) correct
40%
(02:34)
wrong
based on 262
sessions
History
Date
Time
Result
Not Attempted Yet
The highest common factor of \((3^{13} + 9^5)\) and \((3^{13} - 9^5)\) is
A: \(3^{13}\)
B: \(3^{12} - 9^5\)
C: \(2*3^{12}\)
D: \(3^{11} - 9^5\)
E: \(3^{11}\)
A: \(3^{13}\)
B: \(3^{12} - 9^5\)
C: \(2*3^{12}\)
D: \(3^{11} - 9^5\)
E: \(3^{11}\)
Updated on: 24 Nov 2014, 21:17
Originally posted by Ashishmathew01081987 on 21 Nov 2014, 07:52.
Last edited by Ashishmathew01081987 on 24 Nov 2014, 21:17, edited 1 time in total.
Last edited by Ashishmathew01081987 on 24 Nov 2014, 21:17, edited 1 time in total.
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[quote="PareshGmat"]The highest common factor of \((3^{13} + 9^5)\) and \((3^{13} - 9^5)\) is
A: \(3^{13}\)
B: \(3^{12} - 9^5\)
C: \(2*3^{12}\)
D: \(3^{11} - 9^5\)
E: \(3^{11}\)[/quo
A: \(3^{13}\)
B: \(3^{12} - 9^5\)
C: \(2*3^{12}\)
D: \(3^{11} - 9^5\)
E: \(3^{11}\)[/quo
21 Nov 2014, 09:22
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Bookmarks
Let's simplify both expressions first:
\((3^13+3^10)=3^13(3^3+1)=3^10*28=3^10*2*2*7\)
\((3^13-3^10)=3^13(3^3-1)=3^10*26=3^10*2*13\)
Clearly, the common factor is \(3^10*2\), but none of the answer choices matches it. So, we need to try to simplify the answer choices. Once we get to D, we get \(3^11-9^5=3^11-3^10=3^10(3-1)=3^10*2\)
Sorry for my formulas being off - new to this formatting thing.
\((3^13+3^10)=3^13(3^3+1)=3^10*28=3^10*2*2*7\)
\((3^13-3^10)=3^13(3^3-1)=3^10*26=3^10*2*13\)
Clearly, the common factor is \(3^10*2\), but none of the answer choices matches it. So, we need to try to simplify the answer choices. Once we get to D, we get \(3^11-9^5=3^11-3^10=3^10(3-1)=3^10*2\)
Sorry for my formulas being off - new to this formatting thing.
+1 Kudos for identifying it 
