GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Jul 2018, 23:43

### GMAT Club Daily Prep

#### 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

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

# If n is a postive integer and r is the remainder when (n+1)

Author Message
Manager
Joined: 12 Aug 2008
Posts: 57
If n is a postive integer and r is the remainder when (n+1) [#permalink]

### Show Tags

11 Jan 2009, 15:44
If n is a postive integer and r is the remainder when (n+1)(n-1) is divided by 24, what is the value of r?

(1) n is not divisible by 2

(2) n is not divisible by 3

Edited by Gmat Tiger (GT): No OA with the question; post OA only after 4/5 responses.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Manager
Joined: 04 Jan 2009
Posts: 229

### Show Tags

11 Jan 2009, 18:25
sid3699 wrote:

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

(1) n is not divisible by 2

(2) n is not divisible by 3

Edited by Gmat Tiger (GT): No OA with the question; post OA only after 4/5 responses.

individually n is not divisible by 2=>
n belongs to 3, 5,7,9,11,13,15,17,19,................ (odd numbers)
n^2-1:8,24,48,80.
so r can be 0 or non-zero. hence not sufficient.
(2) n belongs to the series:
2,4,5,7,8,10,11,13,...........
n^2-1:3,15,24,48,63,
again remainder is not determinate. hence not sufficient.
(1) & (2) together define the following series:
5,7,11,13,17,19,23,25,29,31,35,37,..............
n^2-1:24,48,120,168,.......
hence sufficient.
I have perhaps proved this whole thing; but anyone has an easier way?
_________________

-----------------------
tusharvk

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1345

### Show Tags

12 Jan 2009, 02:36
sid3699 wrote:

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

(1) n is not divisible by 2

(2) n is not divisible by 3

Edited by Gmat Tiger (GT): No OA with the question; post OA only after 4/5 responses.

There is an easier way, yes, if you know a few basic properties from number theory.

First, if you take three consecutive integers:

n-1, n, n+1

it will always be true that exactly one of these integers is divisible by 3 (since multiples of 3 are separated by 3 on the number line).

Second, say n-1 and n+1 are two consecutive even numbers. Then it must be true that one of them is a multiple of 4, since every second even number is a multiple of 4.

Now to the question: n-1, n, n+1 are three consecutive integers. If we use both statements, we know that n is not a multiple of 3 , so either n-1 or n+1 must be a multiple of 3. We also know that n is odd, so n-1 and n+1 are both even, and one of them is a multiple of 4. So the product (n-1)(n+1) must be divisible by 3*2*4 = 24, and if (n-1)(n+1) is a multiple of 24, the remainder will be zero when we divide it by 24.

Since neither statement is sufficient alone, the answer is C.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Manager
Joined: 04 Jan 2009
Posts: 229

### Show Tags

12 Jan 2009, 06:40
great man. I always tend to go back to deriving it.

Do you happen to have any website\notes\links where such properties are summarized?
IanStewart wrote:
sid3699 wrote:

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

(1) n is not divisible by 2

(2) n is not divisible by 3

Edited by Gmat Tiger (GT): No OA with the question; post OA only after 4/5 responses.

There is an easier way, yes, if you know a few basic properties from number theory.

First, if you take three consecutive integers:

n-1, n, n+1

it will always be true that exactly one of these integers is divisible by 3 (since multiples of 3 are separated by 3 on the number line).

Second, say n-1 and n+1 are two consecutive even numbers. Then it must be true that one of them is a multiple of 4, since every second even number is a multiple of 4.

Now to the question: n-1, n, n+1 are three consecutive integers. If we use both statements, we know that n is not a multiple of 3 , so either n-1 or n+1 must be a multiple of 3. We also know that n is odd, so n-1 and n+1 are both even, and one of them is a multiple of 4. So the product (n-1)(n+1) must be divisible by 3*2*4 = 24, and if (n-1)(n+1) is a multiple of 24, the remainder will be zero when we divide it by 24.

Since neither statement is sufficient alone, the answer is C.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

-----------------------
tusharvk

Re: From GMAT Prep   [#permalink] 12 Jan 2009, 06:40
Display posts from previous: Sort by

# If n is a postive integer and r is the remainder when (n+1)

Moderator: chetan2u

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.