integer

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sunilrawat: Master | Next Rank: 500 Posts; Posts: 112; Joined: Sun Jun 13, 2010 9:20 am; Thanked: 5 times; GMAT Score:640

by sunilrawat » Sat Sep 24, 2011 8:31 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

OA C
Please also specify what the value should be.

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Sat Sep 24, 2011 8:41 am

(n-1)(n+1)/24
A) if n=3, r = 8, if n=5, r=0 insufficient
B) if n=2,r=3 and if r=5,r=0. insufficient
A&B) if n not divisible by 2, (n-1),(n+1) are 2 even consecutive integers. thus their product is divisible by 8. and also n not divisible by 3, thus one of (n-1) or (n+1) divides 3. thus r=0
IMO C

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golfstream700: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Wed Oct 27, 2010 12:45 pm

by golfstream700 » Sun Sep 25, 2011 1:53 pm

if n is not divisible by 2 and 3, possible numbers of n are prime numbers.

For all prime numbers, r is 0 at (n^2-1)/24

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gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members; Location: New York City; Thanked: 130 times; GMAT Score:780

by gmatboost » Tue Sep 27, 2011 10:11 pm

There are other numbers that are not divisible by 2 no 3, but are not prime, like 25 and 35, etc.

Cans is correct, I would just add that you can use the reasoning provided in the A&B section to also answer A and B alone, rather than plugging in.

Statement 1 tells you that (n-1)(n+1) is divisible by 8, but not necessarily by 24.
Statement 2 tells you that (n-1)(n+1) is divisible by 3, but not necessarily by 24.

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golfstream700: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Wed Oct 27, 2010 12:45 pm

by golfstream700 » Wed Sep 28, 2011 12:31 am

gmatboost wrote:There are other numbers that are not divisible by 2 no 3, but are not prime, like 25 and 35, etc.

Cans is correct, I would just add that you can use the reasoning provided in the A&B section to also answer A and B alone, rather than plugging in.

Statement 1 tells you that (n-1)(n+1) is divisible by 8, but not necessarily by 24.
Statement 2 tells you that (n-1)(n+1) is divisible by 3, but not necessarily by 24.

the divisors of 25 and 35 are still prime numbers. if divisors of 25 in the question are divisible to 24, 25 should be divisible to 25 ((n^2-1)/24).

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Sep 28, 2011 6:18 pm

sunilrawat 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. n is not divisible by 2

2. n is not divisible by 3

OA C
Please also specify what the value should be.

(1) n is odd.
Hence, (n - 1) and (n + 1) are even consecutive integers, i.e. one of them is divisible by 2 and the other one is by 4. Therefore we can only conclude that (n - 1)(n + 1) is divisible by 8; NOT sufficient.

(2) As (n - 1), n, and (n + 1) are three consecutive integers and n is not divisible by 3, either (n - 1) or (n + 1) is divisible by 3. Therefore we can only conclude that (n - 1)(n + 1) is divisible by 3; Not sufficient.

Combining (1) and (2), (n - 1)(n + 1) is divisible by 8 and 3 and hence by 24.
Therefore, the value r is 0; Sufficient.

The correct answer is C.

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boymeetsworld: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Fri Jun 03, 2011 10:55 am

by boymeetsworld » Thu Sep 29, 2011 3:32 pm

Anurag@Gurome

For statement (1), what if N = 1? Then can we still say (N-1)(N+1) is divisible by 8?

(1-1)(1+1) = 0

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