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If n is a positive integer and r is the remainder when (n

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Senior Manager
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If n is a positive integer and r is the remainder when (n [#permalink] New post 17 Feb 2008, 08:14
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.

I am looking for a quick way to solve this...less than 2min solution. It took me over 4+ mins to solve on the test and still got it wrong...
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Re: Mat Set 22. Q15 [#permalink] New post 17 Feb 2008, 08:53
After you get very comfortable with the gmat, you will see that there is a pattern with that algebra:

n, n+1, n-1 are three consecutive numbers. Arranged in order:

n-1, n, n+1

This is really common.

A few things about this:
- Often these questions have to do with even/odd
- notice that each triplets alternates between two odd and one even and vice versa
- Any time there are two evens, the product of all three will be a multiple of 8
- in every triplet, the product of all three will always be divisible by 3 and by 6

This problem deals with 24, which has a lot to do with 6, 8, 24.

Now, you can simply make a list of a bunch of consecutive triplets and knock off the statements. In this problem, we are multiplying the first and last of each triplet, so you can do that quickly, too:

123: 3
234: 8
345: 15
456: 24
567: 35
678: 48
789: 63
8910: 80

Notice already that some of these are multiples of 24.

Statement 1 says that n is not even (i'm paraphrasing). So cut out all the ones where the middle number is even, ie, (n-1)(n+1) is not going to be odd. Still not enough, since there are different even ones.

Statement 2 says that n is not a multiple of 3. Cut those out, still not enough info.

Together, we now know that n is not even, and it is not a multiple of 3, so cut out 2,3,4; 8,9,10, etc..

WHat's left? All multiples of 24.

So the answer is C.

You can do this really quickly on paper.
Re: Mat Set 22. Q15   [#permalink] 17 Feb 2008, 08:53
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