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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sunilrawat
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cans
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(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
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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Cans!!
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Cans!!
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golfstream700
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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
For all prime numbers, r is 0 at (n^2-1)/24
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gmatboost
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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.
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
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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).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.
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(1) n is odd.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.
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
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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
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
