Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 26 May 2017, 20:26

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Director
Affiliations: FRM Charter holder
Joined: 02 Dec 2006
Posts: 730
Schools: Stanford, Chicago Booth, Babson College
Followers: 16

Kudos [?]: 85 [0], given: 4

If n is a positive integer and r is the remainder when (n [#permalink]

### Show Tags

23 Jan 2007, 07:47
00:00

Difficulty:

(N/A)

Question Stats:

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

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If n is a positive integer and r is the remainder when (n â€“ 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.
SVP
Joined: 01 May 2006
Posts: 1796
Followers: 9

Kudos [?]: 154 [0], given: 0

### Show Tags

23 Jan 2007, 08:08
(C) for me

24 = 3*4*2 = 3*2*2*2

Stat1
n is not divisible by 2 implies that n is odd.

and that,
o either (n-1) or (n+1) is divisable by 4
o both (n-1) and (n+1) is divisable by 2

(n+1)(n-1) is divisble by 8 and it could be divisable by 3 or not. In the first case, the remainder would be 0 once divided by 24. In the second case, the remainder would not be 0.

INSUFF.

Stat2
n is not divisible by 3 implies. Does not help.

o If n=1, (n+1)*(n-1) = 0 that is divisable by 24 and remainder = 0
o If n=2, (n+1)*(n-1) = 3*1 = 3 that is not divisable by 24 and remainder = 3

INSUFF.

Both (1) and (2)
We will have:
o either (n-1) or (n+1) is divisable by 4
o both (n-1) and (n+1) is divisable by 2
and
o either (n-1) or (n+1) is divisable by 3

4*2*3=24

SUFF.

n is in the set {1, 5, 7, 11, 13, 17...}
VP
Joined: 22 Oct 2006
Posts: 1438
Schools: Chicago Booth '11
Followers: 9

Kudos [?]: 192 [0], given: 12

### Show Tags

01 Feb 2007, 10:36
I agree with C,

my approach

Stat 1 tells us that N is not even, since it is not a factor of 2

therefore (n-1)(n+1) are 2 consecutive even integers

but this could mean anything 2 and 4, 4 and 6 this will yield different remainders

Stat 2 tells us that 3 is not a factor of N, so therefore N could be anything

11 and 13, 17 and 19

all yield different remainders

Combining , we know that (n-1)(n+1) are consective even postive #'s

so could be (0,2) (2,4) (4,6) (6,8) (8,10)

taking statement 2 into account

SINCE out of any 3 consective integers, one MUST be a factor of 3 then either (n-1) or (n+1) is a factor of 3

picking numbers in my set we realize that all consecutive even numbers that contain a factor of 3, yields a 0 remainder for the number 24

C !!!
01 Feb 2007, 10:36
Display posts from previous: Sort by

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

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO 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®.