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02 Dec 2019, 00:40
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Difficulty:
75%
(hard)
Question Stats:
51% (02:07) correct
49%
(02:07)
wrong
based on 131
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Let n be a positive integer. Is n^2 + 1 divisible by n + 1?
(1) n > 13
(2) n is prime
Are You Up For the Challenge: 700 Level Questions
(1) n > 13
(2) n is prime
Are You Up For the Challenge: 700 Level Questions
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
02 Dec 2019, 04:22
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Let n be a positive integer. Is n^2 + 1 divisible by n + 1?
\(n^2+1=(n+1)^2-2n\). So we have to check whether 2n is divisible by n+1 or \(\frac{2n}{n+1}\) is an integer. This can only happen when n=1, as n and n+1 are co-prime.
Thus the question is whether \(n=1\).
(1) n > 13
No, so n^2+1 is NOT divisible by n+1.
Suff
(2) n is prime
No \(n\neq{1}\), so n^2+1 is NOT divisible by n+1.
Suff
D
\(n^2+1=(n+1)^2-2n\). So we have to check whether 2n is divisible by n+1 or \(\frac{2n}{n+1}\) is an integer. This can only happen when n=1, as n and n+1 are co-prime.
Thus the question is whether \(n=1\).
(1) n > 13
No, so n^2+1 is NOT divisible by n+1.
Suff
(2) n is prime
No \(n\neq{1}\), so n^2+1 is NOT divisible by n+1.
Suff
D
04 Jan 2022, 09:46
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