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31 Mar 2023, 10:45
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
69% (01:58) correct
31%
(02:02)
wrong
based on 35
sessions
History
Date
Time
Result
Not Attempted Yet
If n is a positive integer, is \(3^4+3^{n+4}\) divisible by 5?
(1) n is an even integer.
(2) \(3^8 +3^{n+8}\) is divisible by 5.
(1) n is an even integer.
(2) \(3^8 +3^{n+8}\) is divisible by 5.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
31 Mar 2023, 13:27
Kudos
Bookmarks
Bunuel
Question:
\(3^4+3^{n+4}\)
\(3^4(1+3^{n})\)
\(3^4\) is not divisible by 5. Hence for the entire expression \(3^4(1+3^{n})\) to be divisible by 5, the term \((1+3^{n})\) should be divisible by 5.
Target Question: Is \(1+3^{n}\) divisible by 5 ?
Statement 1
(1) n is an even integer.
If n = 2; \(1+3^{n}\) = 10
Is \(1+3^{n}\) divisible by 5 ? - Yes !
If n = 4; \(1+3^{n}\) = 82
Is \(1+3^{n}\) divisible by 5 ? - No !
As we have multiple answers for the same target question, the statement alone is not sufficient.
Statement 2
(2) \(3^8 +3^{n+8}\) is divisible by 5.
\(3^8 +3^{n+8}\) is divisible by 5.
\(3^8(1 + 3^{n})\) is divisible by 5
\(3^8\) is divisible not by 5, therefore \((1 + 3^{n})\) must be divisible by 5 for the entire term to be divisible by 5.
Is \(1+3^{n}\) divisible by 5 ? - Yes !
The statement alone is sufficient to answer.
Option B
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