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Thu Jun 01, 2023 8:45 am
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B
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Difficulty:
65%
(hard)
Question Stats:
55% (02:33) correct
45%
(03:01)
wrong
based on 42
sessions
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Not Attempted Yet
If n is a positive integer, is \(3^n+3^8\) divisible by 4?
(1) n is a multiple of 3.
(2) \(3^2 +3^{n+2}\) is divisible by 4
(1) n is a multiple of 3.
(2) \(3^2 +3^{n+2}\) is divisible by 4
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
Thu Jun 01, 2023 10:19 am
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If n is a positive integer, is 3^n+3^8 divisible by 4?
(1) n is a multiple of 3.
If n=3, 3^3+3^8= 3^3(1+3^5)= 3^3(243+1). Since 244 is divisible by 4, answer is YES.
If n=6, 3^6+3^8= 3^6(1+3^2)= 3^3(1+9). Since 10 is indivisible by 4, answer is NO.
Statement I alone is not sufficient.
(2) 3^2+3^(n+2) is divisible by 4.
If n=1, 3^2+3^3= 3^2 (1+3)= 3^2*4.
Answer is YES.
If n=3, 3^2+3^5= 3^2 (1+27)= 3^2*28.
Answer is YES.
If n=5, 3^2+3^7= 3^2 (1+243)= 3^2*244.
Answer is YES.
Statement II alone is sufficient.
Option B is the correct answer
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(1) n is a multiple of 3.
If n=3, 3^3+3^8= 3^3(1+3^5)= 3^3(243+1). Since 244 is divisible by 4, answer is YES.
If n=6, 3^6+3^8= 3^6(1+3^2)= 3^3(1+9). Since 10 is indivisible by 4, answer is NO.
Statement I alone is not sufficient.
(2) 3^2+3^(n+2) is divisible by 4.
If n=1, 3^2+3^3= 3^2 (1+3)= 3^2*4.
Answer is YES.
If n=3, 3^2+3^5= 3^2 (1+27)= 3^2*28.
Answer is YES.
If n=5, 3^2+3^7= 3^2 (1+243)= 3^2*244.
Answer is YES.
Statement II alone is sufficient.
Option B is the correct answer
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Sat Jun 03, 2023 5:11 am
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Solution
(1) If n is even, then 3^n + 3^8 is not divisible by 4. If n is odd, 3^n + 3^8 is divisible -- insufficient
(2) 3^2 + 3^(n+2) = 9 * (1 + 3^n) -> (1 + 3^n) is divisible by 4, which means that n is always odd (works for n = 1, n = 3, n = 5 and so on). It means that 3^n + 3^8 [as per (1)] is divisible -- sufficient
Hope is helpful
(1) If n is even, then 3^n + 3^8 is not divisible by 4. If n is odd, 3^n + 3^8 is divisible -- insufficient
(2) 3^2 + 3^(n+2) = 9 * (1 + 3^n) -> (1 + 3^n) is divisible by 4, which means that n is always odd (works for n = 1, n = 3, n = 5 and so on). It means that 3^n + 3^8 [as per (1)] is divisible -- sufficient
Hope is helpful
