gmat prep remainder question

[unc42]

Hey I understand why "c" is the answer, but for curiousity sake I cannot actually figure out what the value of r would be and how to solve it. Any help on this?

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"

Correct answer is Both statements TOGETHER are sufficient.

Thanks for any help!

[sudhir3127]

Hey I understand why "c" is the answer, but for curiousity sake I cannot actually figure out what the value of r would be and how to solve it. Any help on this?

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"

Correct answer is Both statements TOGETHER are sufficient.

Thanks for any help!

yes its C. try plugging in any prime number other than 2/3 ...u will be good

Hope that helps..

[LSB]

Could you pls explain the answer. Trial and error leads to the conclusion that if 2 & 3 are not factors of N. Then the remainder will always be zero (if we use any other prime as N or factors of N). Why is that?

[Ian Stewart]

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"

(1) says that n is odd. Thus n-1 and n+1 are both even. In fact, one of them must be divisible by 4, because every second even number is divisible by 4. So from (1) we know that (n-1)(n+1) is divisible by 8.

(2) says that n is not divisible by 3. Notice that n-1, n, and n+1 are three consecutive integers. If you have any three consecutive integers, exactly one of them must be divisible by 3. So if n is not divisible by 3, either n-1 or n+1 is.

Using both (1) and (2) together, we know (n-1)(n+1) is divisible by both 3 and 8, and therefore by 24.

[mberkowitz]

can you pls explain how we know what r is based off of what you found?

[Ian Stewart]

I showed that (n-1)(n+1) is divisible by 24, using both statements. If (n-1)(n+1) is divisible by 24, the remainder is zero when you divide (n-1)(n+1) by 24.

[shahab03]

what is the remainder when 0/24 and when 1/24?

thanks

[Ian Stewart]

what is the remainder when 0/24 and when 1/24?

thanks

When 0 is divided by 24, the remainder is 0 (and the quotient is 0).

When 1 is divided by 24, the remainder is 1 (and the quotient is 0).

[maihuna]

Great Ian, the last time I solve it was using lot of numbers, using prime factorization and the given statement its fabulous to come to conckusion. You rocks as usual.

[manishpal]

lol great quest asked by shahabo3..heads off to u dear

what is the remainder when 0/24 and when 1/24?

thanks

When 0 is divided by 24, the remainder is 0 (and the quotient is 0).

When 1 is divided by 24, the remainder is 1 (and the quotient is 0).

[ilovemgmat]

Thanks for posting the question!

[sam117]

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"

(1) says that n is odd. Thus n-1 and n+1 are both even. In fact, one of them must be divisible by 4, because every second even number is divisible by 4. So from (1) we know that (n-1)(n+1) is divisible by 8.

(2) says that n is not divisible by 3. Notice that n-1, n, and n+1 are three consecutive integers. If you have any three consecutive integers, exactly one of them must be divisible by 3. So if n is not divisible by 3, either n-1 or n+1 is.

Using both (1) and (2) together, we know (n-1)(n+1) is divisible by both 3 and 8, and therefore by 24.

If n=1, (n-1)=0 and (n+1)= 2 . (n-1)(n+1)=0 which is not divisible by 8. Please help.

[Ian Stewart]

If n=1, (n-1)=0 and (n+1)= 2 . (n-1)(n+1)=0 which is not divisible by 8. Please help.

Zero *is* divisible by 8. If you divide 0 by 8, you get 0, which is an integer, so by the definition of divisibility, 0 is divisible by 8. In fact, 0 is divisible by every positive integer.