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(n - 1) (n + 1) is divided by 24

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by sanju09 » Wed Apr 08, 2009 5:55 am
If n is a positive integer and r is the remainder when (n - 1) (n + 1) is divided by 24, what is the value of r?

(1) n is not divisible by 2.

(2) n is not divisible by 3.



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Source: — Data Sufficiency |
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by scoobydooby » Wed Apr 08, 2009 6:20 am
1) n not divisible by 2=> n is odd=> (n-1) and (n+1) must be consective even numbers.

if n=1, 0*2/24 leaves remainder 0
if n=3, 2*4/24 leaves remainder 8
not sufficient


2) n not divisible by 3=> n can be even or 1, 5, 7, 11, 13....

if n=5, 4*6/24 leaves remainder 0
if n=2, 1*3/24 leaves remainder 3
not sufficient

together,
n must be odd and not divisible by 3=> n can be 1, 5, 7, 11, 13...
if n=7, 6*8/24 leaves remainder 0
if n=11, 10*12/24 leaves remainder 0

hence C.
Last edited by scoobydooby on Wed Apr 08, 2009 9:44 am, edited 1 time in total.
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by rossmj » Wed Apr 08, 2009 6:50 am
Scooby good solution. Additionally, based on both statements n could equal 1 which would result in a remainder of 0.
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by pjasak » Wed Apr 08, 2009 9:28 am
Scooby,

No problem with the math and logic until the very last. How do you know that for every prime number, n, (n-1)*(n+1) is evenly divisible by 24?

Thanks
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by scoobydooby » Wed Apr 08, 2009 9:42 am
@ pjasak: thanks for pointing out. sorry, did a bad generalization. will edit the post.

@ rossmj: thanks, true. missed that out.
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