Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 06 May 2015, 15:28

### 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

# n' is a natural number. State whether n (n&#9516;&#9619; -

Author Message
TAGS:
Director
Joined: 13 Nov 2003
Posts: 971
Location: Florida
Followers: 1

Kudos [?]: 32 [0], given: 0

n' is a natural number. State whether n (n&#9516;&#9619; - [#permalink]  25 Nov 2003, 22:15
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
'n' is a natural number. State whether n (n┬▓ - 1) is divisible by 24.

(1) 3 divides 'n' completely without leaving any remainder.

(2) 'n' is odd.

A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Director
Joined: 13 Nov 2003
Posts: 793
Location: BULGARIA
Followers: 1

Kudos [?]: 27 [0], given: 0

as far as I know natural numbers=positive integers without 0, so from A n could be 3,6,9,and so on. The outcome is 24,210,720, so A is not sufficient, B states n is odd 3,9,15 .. which gives 24,720,3360 which are all divisible by 24 so IMO B is sufficient
SVP
Joined: 03 Feb 2003
Posts: 1608
Followers: 6

Kudos [?]: 76 [0], given: 0

agree with B

n(n┬▓-1)=n(n-1)(n+1)=(n-1)n(n+1)

(1) n is div by 3.

consider n=3: 2*3*4=24 is div by 24
consider n=6: 5*6*7 is not

(2) n is odd

n=2k+1
(n-1)n(n+1) is divisible by 6
moreover =2k(2k+1)(2k+2)=8k^3+12k^2+4k divisible by 4
thus divisible by 24

B.
Manager
Joined: 26 Aug 2003
Posts: 233
Location: United States
Followers: 1

Kudos [?]: 2 [0], given: 0

I'd say B too.

(1) Since n is divisible by 3, (n┬▓ - 1) has to be divisible by 8 for the quanitity in question. We also know that n > 3. But not all values of n are such that (n┬▓ - 1) will be evenly divisible by 8. Not suff.
(2) If n is odd then n(n┬▓ - 1) is divisible by 24 for all values of n.
Director
Joined: 13 Nov 2003
Posts: 971
Location: Florida
Followers: 1

Kudos [?]: 32 [0], given: 0

good explanation, stolyar. right answer is B
I just substituted values and got the answer...
Director
Joined: 28 Oct 2003
Posts: 503
Location: 55405
Followers: 1

Kudos [?]: 10 [0], given: 0

To stolyar's point,

The product of three consecutive numbers will always be divisible by 24 if the middle number is odd. Because:

one of three consecutive numbers is always divisible by three (for obvious reasons)
every other even number is divisible by four.
The even number that's not divisible by four, when multiplied with the one that is, gives you a multiple of 8.
Similar topics Replies Last post
Similar
Topics:
4 If n is an odd natural number and n! ends with 32 zeros, the 3 08 Jan 2014, 08:31
1 A natural number N has 4 factors , Sum of the factors of N 2 31 Jul 2013, 08:28
2 If n is the integer, whether 30 is a factor of n? 3 26 Jan 2012, 05:38
3 State whether n (n² - 1) is divisible by 24 1 28 Aug 2009, 23:03
If n is a natural number, is n ! < ^x ? I. n is an 1 23 Jun 2006, 15:59
Display posts from previous: Sort by