Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

700 Algrbra! Need help again. Thanks so much! [#permalink]
11 Feb 2010, 13:52

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

57% (01:17) correct
43% (01:17) wrong based on 6 sessions

Could anyone explain to me why the number 1 would work in the first situation? I understand why 3, 5, 7 or others work. But why 1 works, too? Thank you so much for this great help!!

Re: 700 Algrbra! Need help again. Thanks so much! [#permalink]
11 Feb 2010, 14:06

given, n is positive interger and n^2 - 1 = 8 * k + r -> r remainder what is r??

st 1) n is odd n^2-1 = (n+1) * (n-1) so n+1 and n-1 are consequetive even numbers... one of them will be multiple of 2 and the other will be multiple of 4. So n^2 - 1 will be evenly divided by 8 and r=0 Sufficient st 1) n is not divisible by 8. Not sufficient

Re: 700 Algrbra! Need help again. Thanks so much! [#permalink]
11 Feb 2010, 14:19

I like the approach in the post above best for this problem; when you see something like n^2 - 1 in a GMAT question, it will almost always be useful to use the difference of squares factorization: n^2 - 1 = (n+1)(n-1). A less elegant alternative is to write n = 2k + 1. Then n^2 - 1 = (2k + 1)^2 - 1 = 4k^2 + 4k + 1 - 1 = 4k^2 + 4k = 4(k)(k + 1), and since k and k+1 are consecutive integers, one of them must be divisible by 2, so 4(k)(k + 1) must be divisible by 4*2 = 8.

To answer the question in the original post, if n=1, then n^2 - 1 = 0. So the question becomes, what is the remainder when 0 is divided by 8? Well, 0 is divisible by every positive integer; the quotient is zero and the remainder is zero. If you think back to how you first learned division, this should hopefully be clear: if you have, say, 11 apples and 8 children, we can give each child 1 apple and we have 3 left over, so the quotient is 1 and the remainder is 3 when you divide eleven by eight. If we have 0 apples and 8 children, we can give each child 0 apples and we have 0 left over, so the quotient is 0 and the remainder is 0 when we divide zero by eight. _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Re: 700 Algrbra! Need help again. Thanks so much! [#permalink]
11 Feb 2010, 15:11

Thanks for the great help.

But I still feel very confused. The question is asking "what's the value of r"? I understand when n is 3,5,7, the r will be 1. However, if n is 1, r will be 0. In this case, we have two answers for r and we can't really tell the exact value for r, right? This is the reason why I don't think the first one work and the answer should be "E". Am I in the right path? Thanks for the help again.

Re: 700 Algrbra! Need help again. Thanks so much! [#permalink]
11 Feb 2010, 15:18

YTT wrote:

Thanks for the great help.

But I still feel very confused. The question is asking "what's the value of r"? I understand when n is 3,5,7, the r will be 1. However, if n is 1, r will be 0. In this case, we have two answers for r and we can't really tell the exact value for r, right? This is the reason why I don't think the first one work and the answer should be "E". Am I in the right path? Thanks for the help again.

No, the remainder will be zero for any of the values 1, 3, 5, or 7 (or for any other odd value of n). If, say, n=5, then n^2 - 1 = 25 - 1 = 24, and the remainder when we divide 24 by 8 is zero. _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.