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If n is a positive integer and r is the remainder when

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If n is a positive integer and r is the remainder when [#permalink]

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New post 28 Jul 2009, 17:18
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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) 2 is not a factor of n.
(2) 3 is not a factor of n.

The answer is BOTH statements TOGETHER are sufficient, but Neither statement alone is not sufficient. I've been working on this for a few days but can't see how the answer is derived.
Any smart people out there know the reason behind the answer?

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Re: a tricky data sufficiency prob [#permalink]

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New post 28 Jul 2009, 18:19
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) 2 is not a factor of n.
(2) 3 is not a factor of n.

from 1

(n-1)(n+1) are both even and ve 2^3 at least as factor however r can be anything, THINK OF THE PAIRS: (2,4)(4,6)(8,10(10,12)

from 2

insuff
n = 5 thus (n-1)(n+1) = 4*6 or if n= 2 then (n-1)(n+1) = 1*3

both

n = 1,5,7,9,..etc

thus surely r is 0 as (n-1)(n+1) must be multiples of 2^3*3 AND r = 0

C

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Re: a tricky data sufficiency prob [#permalink]

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New post 28 Jul 2009, 20:47
Yes answer should be C. We always get 0 remainder when both (1) and (2) are true.

However Yezz there is a small typo in your example....n=1,5,7,9....n cannot be 9 because 9 is divisible by 3.
n = 1,5,7,11,13 etc......

yezz wrote:

n = 1,5,7,9,..etc

thus surely r is 0 as (n-1)(n+1) must be multiples of 2^3*3 AND r = 0

C

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Re: a tricky data sufficiency prob [#permalink]

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New post 28 Jul 2009, 21:18
Yes, remainder is always 0 if both are true.

If you get stuck the tip is to simplify q. stem, pick number that suits each statement. The way I see it is to work out remainder of (n^2 -1)/24 by picking numbers.

Statement one - pick 2 odd numbers (e.g. 9 and 7 and get two different remainders)
Statement two - pick one even/one odd (7 and 10 and get two different remainders)

Two together get 5,7,11,13 - you see a pattern - all 0 as remainder

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Re: a tricky data sufficiency prob [#permalink]

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New post 29 Jul 2009, 01:08
treemonkey wrote:
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) 2 is not a factor of n.
(2) 3 is not a factor of n.

The answer is BOTH statements TOGETHER are sufficient, but Neither statement alone is not sufficient. I've been working on this for a few days but can't see how the answer is derived.
Any smart people out there know the reason behind the answer?



Check this thread , this has been discussed !

ds-problem-8-please-take-a-stab-anyone-thx-81450.html

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Re: a tricky data sufficiency prob [#permalink]

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New post 29 Jul 2009, 02:25
sdrandom1 wrote:
Yes answer should be C. We always get 0 remainder when both (1) and (2) are true.

However Yezz there is a small typo in your example....n=1,5,7,9....n cannot be 9 because 9 is divisible by 3.
n = 1,5,7,11,13 etc......

yezz wrote:

n = 1,5,7,9,..etc

thus surely r is 0 as (n-1)(n+1) must be multiples of 2^3*3 AND r = 0

C


Thanks Sdran.... U ve got my back bro,, thanks :)

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Re: a tricky data sufficiency prob   [#permalink] 29 Jul 2009, 02:25
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