integer

[sunilrawat]

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.

[cans]

(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

[golfstream700]

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

[gmatboost]

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.

[golfstream700]

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).

[Anurag@Gurome]

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.

[boymeetsworld]

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