Problem : Data Sufficiency

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6983manish: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Mon Mar 07, 2011 12:27 am; Thanked: 6 times

by 6983manish » Fri Mar 25, 2011 12:08 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: Beat The GMAT — Data Sufficiency | Fri Mar 25, 2011 12:08 am

HSPA: Legendary Member; Posts: 1101; Joined: Fri Jan 28, 2011 7:26 amFollowed by: 13 members; Thanked: 47 times; GMAT Score:640

by HSPA » Fri Mar 25, 2011 1:26 am

A) n is not divisible by 2 hence n is odd and
n-1, n+1 are always even as n is odd

Let n = 1,3,5,7
n=1 ; 0/24 = 0
n=3 ; 2*4/24 = 8
n =5; 4*6/24 = 0
n=7; 6*8/24 = 0
Not sufficient , I got two values 0,8

B) n is not divisible by 3... so either n-1 or n+1 is divisible by 3

either C or E now....
Combined: either or both n-1 and n+1 is having 2 and 3 as factors;

I am getting answer as C and r= 8

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rajasekaran: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Tue Jan 04, 2011 3:01 am

by rajasekaran » Fri Mar 25, 2011 2:38 am

Hi HSPA - Could you please clarify how you determined remainder as 8,

' Combined: either or both n-1 and n+1 is having 2 and 3 as factors;

I am getting answer as C and r= 8 '

On merging 1 & 2, agree that it (n+1) & (n-1) has got 2 and 3 as factors.

Then, I believe that (n+1)(n-1) is always divisible by 24 (got a factor of 2 & 3) and remainder is 0.

By sub. numbers to the equation.

Let's assume n= 5,

(n-1) (n+1) / 24 = 0 is the remainder

Let's assume n=41 , (n-1) (n+1) / 24=0 is the remainder.

am i missing something.????

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HSPA: Legendary Member; Posts: 1101; Joined: Fri Jan 28, 2011 7:26 amFollowed by: 13 members; Thanked: 47 times; GMAT Score:640

by HSPA » Fri Mar 25, 2011 3:26 am

Hi Rajasekar,

thanks for correcting : answer is C and r=0..
I mis wrote the remainder considering n = 3 but B says n cannot be divisible by 3.

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