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15 May 2017, 04:05
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
40% (02:33) correct
60%
(02:21)
wrong
based on 91
sessions
History
Date
Time
Result
Not Attempted Yet
If n is a positive integer. Is n^3-n divisible by 24?
1) 2n has twice as many factors as n has
2) n has exactly 2 distinct positive factors
source: https://www.GMATinsight.com
1) 2n has twice as many factors as n has
2) n has exactly 2 distinct positive factors
source: https://www.GMATinsight.com
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
15 May 2017, 04:57
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GMATinsight
Hi,
\(n^3-n=n(n^2-1)=n(n-1)(n+1)\)
(n-1)*n*(n+1) means three CONSECUTIVE integers..
Points to consider here..
1) ATLEAST one number will be multiple of 2 and one number multiple of 3..
2) If n is even number, n-1 and n+1 will be odd... So \(n^3-n\) is div by ATLEAST 2*3=6..
3) If n is Odd, one of n-1 or n+1 is multiple of 2 and other multiple of atleast 4.. So \(n^3-n\) is div by ATLEAST 2*4*3=24..
Let's see the statements..
1) 2n has twice as many factors as n has
This is possible ONLY when n is odd, so point (3) tells us that n^3-n is div by 24
Sufficient
2) n has exactly 2 distinct positive factors
This means n is prime number.
If n is 2, n^3-n=2^3-2=6.. so ans is NO
If n is 3,5 or any other odd prime number, ans will be YES as per point (3) above.
Insufficient
A
08 Sep 2018, 06:00
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