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14 Apr 2021, 02:00
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A
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Difficulty:
35%
(medium)
Question Stats:
64% (01:33) correct
36%
(01:27)
wrong
based on 81
sessions
History
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If n is a positive integer, is n(n − 1)(n + 1) divisible by 4?
(1) n is an odd integer.
(2) n(n + 1) is divisible by 6.
(1) n is an odd integer.
(2) n(n + 1) is divisible by 6.
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:
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14 Apr 2021, 02:29
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If n is a positive integer, is n(n − 1)(n + 1) divisible by 4?
(1) n is an odd integer.
n+1 is even and n-1 is also even
so expression n(n-1)(n+1) will be divisible by 4
Hence, sufficient
(2) n(n + 1) is divisible by 6.
this means n may or may not be even
if n is even and not divisible by 4
Expression will be not divisible by 4 and in cases when n is divisible by 4 expression will also be divisible by 4
Hence not sufficient IMO
Answer should be A
(1) n is an odd integer.
n+1 is even and n-1 is also even
so expression n(n-1)(n+1) will be divisible by 4
Hence, sufficient
(2) n(n + 1) is divisible by 6.
this means n may or may not be even
if n is even and not divisible by 4
Expression will be not divisible by 4 and in cases when n is divisible by 4 expression will also be divisible by 4
Hence not sufficient IMO
Answer should be A
16 Apr 2021, 00:00
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If n is a positive integer, is n(n − 1)(n + 1) divisible by 4?
We are asked whether the product of 3 consecutive integers (n-1, n and n+1) is divisible by 4
(1) n is an odd integer. Since n is odd then both n-1 and n+1 are even hence (n-1)n(n+1) is divisible by 4. Sufficient.
(2) n(n + 1) is divisible by 6. If n=2 then n(n − 1)(n + 1)=6 and the answer is NO but if n=3 then n(n − 1)(n + 1)=24 and the answer is YES. Not sufficient.
Answer: A.
We are asked whether the product of 3 consecutive integers (n-1, n and n+1) is divisible by 4
(1) n is an odd integer. Since n is odd then both n-1 and n+1 are even hence (n-1)n(n+1) is divisible by 4. Sufficient.
(2) n(n + 1) is divisible by 6. If n=2 then n(n − 1)(n + 1)=6 and the answer is NO but if n=3 then n(n − 1)(n + 1)=24 and the answer is YES. Not sufficient.
Answer: A.
