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

 It is currently 20 Aug 2018, 09:35

### 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 positive integer and r is the remainder when

Author Message
Intern
Joined: 12 Jun 2009
Posts: 23
If n is a positive integer and r is the remainder when  [#permalink]

### Show Tags

28 Jul 2009, 17:18
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

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.

The answer is BOTH statements TOGETHER are sufficient, but Neither statement alone is not sufficient. I've been working on this for a few days but can't see how the answer is derived.
Any smart people out there know the reason behind the answer?

--== 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.
Retired Moderator
Joined: 05 Jul 2006
Posts: 1731
Re: a tricky data sufficiency prob  [#permalink]

### Show Tags

28 Jul 2009, 18:19
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.

from 1

(n-1)(n+1) are both even and ve 2^3 at least as factor however r can be anything, THINK OF THE PAIRS: (2,4)(4,6)(8,10(10,12)

from 2

insuff
n = 5 thus (n-1)(n+1) = 4*6 or if n= 2 then (n-1)(n+1) = 1*3

both

n = 1,5,7,9,..etc

thus surely r is 0 as (n-1)(n+1) must be multiples of 2^3*3 AND r = 0

C
Manager
Joined: 30 May 2009
Posts: 202
Re: a tricky data sufficiency prob  [#permalink]

### Show Tags

28 Jul 2009, 20:47
Yes answer should be C. We always get 0 remainder when both (1) and (2) are true.

However Yezz there is a small typo in your example....n=1,5,7,9....n cannot be 9 because 9 is divisible by 3.
n = 1,5,7,11,13 etc......

yezz wrote:

n = 1,5,7,9,..etc

thus surely r is 0 as (n-1)(n+1) must be multiples of 2^3*3 AND r = 0

C
Manager
Joined: 30 Jun 2009
Posts: 51
Re: a tricky data sufficiency prob  [#permalink]

### Show Tags

28 Jul 2009, 21:18
Yes, remainder is always 0 if both are true.

If you get stuck the tip is to simplify q. stem, pick number that suits each statement. The way I see it is to work out remainder of (n^2 -1)/24 by picking numbers.

Statement one - pick 2 odd numbers (e.g. 9 and 7 and get two different remainders)
Statement two - pick one even/one odd (7 and 10 and get two different remainders)

Two together get 5,7,11,13 - you see a pattern - all 0 as remainder
Senior Manager
Joined: 25 Jun 2009
Posts: 285
Re: a tricky data sufficiency prob  [#permalink]

### Show Tags

29 Jul 2009, 01:08
treemonkey wrote:
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.

The answer is BOTH statements TOGETHER are sufficient, but Neither statement alone is not sufficient. I've been working on this for a few days but can't see how the answer is derived.
Any smart people out there know the reason behind the answer?

Check this thread , this has been discussed !

Retired Moderator
Joined: 05 Jul 2006
Posts: 1731
Re: a tricky data sufficiency prob  [#permalink]

### Show Tags

29 Jul 2009, 02:25
sdrandom1 wrote:
Yes answer should be C. We always get 0 remainder when both (1) and (2) are true.

However Yezz there is a small typo in your example....n=1,5,7,9....n cannot be 9 because 9 is divisible by 3.
n = 1,5,7,11,13 etc......

yezz wrote:

n = 1,5,7,9,..etc

thus surely r is 0 as (n-1)(n+1) must be multiples of 2^3*3 AND r = 0

C

Thanks Sdran.... U ve got my back bro,, thanks

--== 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.
Re: a tricky data sufficiency prob &nbs [#permalink] 29 Jul 2009, 02:25
Display posts from previous: Sort by

# 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®.