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by eustudent » Mon Jun 01, 2009 9:00 pm
If N is a positive integer and R is the reminder when (N-1)(N+1) is divided by 24,w hat is the value of R?

1) N is not divisible by 2

2) N is not divisible by 3

Answer is C

Ok, considering both statements together, N could be 7, 13, 19, etc.
Then R will have several values, therefore E should be the right answer.

I believe, this problem is mistaken because we cannot find the value of R with the information given.
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Source: — Data Sufficiency |
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by ontherocks27 » Tue Jun 02, 2009 8:56 am
Statement 1:

If N is not divisible by 2 then the numbers could be

0,1,2 (Remainder for (n-1)(n+1) = 0)
2,3,4 (Remainder for (n-1)(n+1) = 8)
4,5,6 (Remainder for (n-1)(n+1) = 0)
6,7,8 (Remainder for (n-1)(n+1) = 0)
8,9,10 (Remainder for (n-1)(n+1) = 8)

we see a trend that anytime N is divisible by 3, the remainder is 8. rest of the times, remainder is 0.

so 2 possibilities are 0 and 8,

Hence Insufficient

Statement 2:

If N is not divisible by 3 then the numbers could be

0,1,2 (Remainder for (n-1)(n+1) = 0)
1,2,3 (Remainder for (n-1)(n+1) = 3)
3,4,5 (Remainder for (n-1)(n+1) = 15)
4,5,6 (Remainder for (n-1)(n+1) = 0)
6,7,8 (Remainder for (n-1)(n+1) = 0)

we see a trend that anytime N is divisible by 2, the remainder is something other than 0. Rest of the times, remainder is 0

Hence, Insufficient

Combining, N is not divisible by both 2 and 3 - Hence, the remainder must always be 0. Thus C.
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by ontherocks27 » Tue Jun 02, 2009 8:58 am
Also, it'll be great if somebody can suggest a quicker way of doing this - My method took me a long time.

Thanks
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by Osirus@VeritasPrep » Tue Jun 02, 2009 6:34 pm
This may not help anybody but a guessing tip may be to always choose C when you see a problem like this. I still don't know how to do these problems but in each of the three problems the answer has been C. It may just be a coincidence but if you really don't know how to do it and you get it on the actual test, it may be something to keep in mind.
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