What is r?

[ayankm]

If n is a positive integer and r is remainder when (n-1)(n+1) is divided by 24, what is the value of r?

a. n is divisible by 2
b. n is not divisible by 3

I am getting the value of r as 3 or 15 by combining both the information given and marked the answer as -E-.
However, OA is given as -C-

[jeffedwards]

What is the source?

I get the same as you.

First, I simplified the top part of the fraction
(n-1)(n+1) = (n^2) - (1^2) or (n^2) - 1

Now let's just skip down and combine both statements. We know that n could equal 2,4,8,10,14 and so on

Plug in for the first couple numbers
For 2 we get a remainder of 3
For 4 we get a remainder of 15

Since we have two different answers combining the statements, this shouldn't be sufficient. Is there a piece of information we are overlooking or missing?

[ayankm]

What is the source?

I get the same as you.

Hello Jeff,

I quoted this problem from the document '198 700+ problems'. This is available for download from this community.
However, I have no idea regarding the original source of this problem.

[jeffedwards]

What is the source?

I quoted this problem from the document '198 700+ problems'. This is available for download from this community.
However, I have no idea regarding the original source of this problem.

Dang, doesn't that bug you. Got to love the OG...at least we know the answers in the guide are right. Some other sources i don't fully trust. Well it'd be neat to see what the truth is. Thanks ayankm

[ayankm]

Ohh yes it does...
More so because its less 2 weeks for my GMAT and I am getting quite a few DS problems wrong.
Oh my!!

[jeffedwards]

You know I took the GMAT over three years ago...just did it on a whim without a lot of prep (this time i'm going to rock it). Anyway, i practiced from the official guide and it seemed as though many of the questions on the actual test were the same as in the guide, just with different numbers. The OG may be easier than some other materials, but it will align your thinking with that of the GMAT test makers, just an idea. oh and good luck!!!

[kevincanspain]

If n is a positive integer and r is remainder when (n-1)(n+1) is divided by 24, what is the value of r?

a. n is divisible by 2
b. n is not divisible by 3

I am getting the value of r as 3 or 15 by combining both the information given and marked the answer as -E-.
However, OA is given as -C-

A should read n is NOT divisible by 2

[jeffedwards]

A should read n is NOT divisible by 2

Wow, yep getting that piece of information sure does help; thanks.

Now, I'm sure you got this too, but I'll respond anyway.

We can list out a few numbers that meet that criteria...1,5,7,11,13,17,19....

All of these numbers give a remainder of 0. Pretty cool. I don't know the rule behind this, but since I can't think of any irregular
numbers to try, such as zero, negative, or a decimal - because it must be a positive number. I would say both are sufficient, giving the remainder of 0 every time.