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

It is currently 20 Aug 2014, 06:59

Starting Soon:

Live Q&A Session with Cambridge Admissions Team   ||    Join Chat Room to Attend the Session


Close

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
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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Positive integer n divisible by 4 and 21

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 08 Jul 2009
Posts: 6
Followers: 0

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

Positive integer n divisible by 4 and 21 [#permalink] New post 19 Jul 2009, 09:00
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions
This question and answer explanation is from a Manhattan GMAT practice test. I don't understand why they don't take into account the 7 as one of the prime factors. Can anyone explain this? Thanks for your help.

If positive integer n is divisible by both 4 and 21, then n must be divisible by which of the following?

8 - 2, 2, 2

12 - 2, 2, 3

18, 2, 3, 3

24 - 2, 2, 2, 3

48- , 2, 2, 2, 2,

If n is divisible by both 4 and 21, its prime factors include 2, 2, 3, and 7. Therefore, any integer that can be constructed as the product of these prime factors is also a factor of n. In this case, 12 is the only integer that can definitively be constructed from the prime factors of n, since 12 = 2 x 2 x 3.

The correct answer is B.
Manhattan GMAT Discount CodesKaplan GMAT Prep Discount CodesGMAT Pill GMAT Discount Codes
Manager
Manager
avatar
Joined: 19 Jun 2009
Posts: 141
Location: India
Concentration: Strategy, General Management
GMAT 1: 650 Q51 V27
GMAT 2: 710 Q48 V39
GPA: 3.2
WE: Engineering (Computer Hardware)
Followers: 5

Kudos [?]: 17 [0], given: 21

Re: Positive integer n divisible by 4 and 21 [#permalink] New post 19 Jul 2009, 10:08
You are confused.

Read the question again, carefully.

If you still don't get it, here it is -

Now, prime factors :

4= 2, 2.
21=3,7.

'n' is divisible by 4 & 21.
Consider, Y is divisor after dividing 'n' by 4 & 21.
Let's write 'n' as

n = 4 x 21 x Y = 2 x 2 x 3 x 7 x Y.

Now, question asks for a number that divides 'n'. If there is a number that divides 'n' for sure, it must not have any additional prime factors than (2,2,3,7). Consider the possibility that Y might even be 1, so we don't consider Y here.

All other options except '12'=2 x 2 x 3, have those additional prime factors.

This is complete logic. Quick way to solve the problem -

Divide 4 x 21 by each option given. The one which gives integer divisor, is your answer. :P
_________________

I am ready to fall, but not before I fly.

Manager
Manager
User avatar
Joined: 27 Jun 2008
Posts: 160
Followers: 2

Kudos [?]: 18 [0], given: 11

GMAT Tests User
Re: Positive integer n divisible by 4 and 21 [#permalink] New post 21 Jul 2009, 23:16
well explained alpeshvc.
Manager
Manager
User avatar
Joined: 14 Nov 2008
Posts: 200
Schools: Stanford...Wait, I will come!!!
Followers: 2

Kudos [?]: 28 [0], given: 3

GMAT Tests User
Re: Positive integer n divisible by 4 and 21 [#permalink] New post 23 Jul 2009, 03:31
In Other way, the first number,apart from 0, is LCM of 4 and 21. This is 84.
so out of the following only 12 divides it. Thanks.
nss123 wrote:
This question and answer explanation is from a Manhattan GMAT practice test. I don't understand why they don't take into account the 7 as one of the prime factors. Can anyone explain this? Thanks for your help.

If positive integer n is divisible by both 4 and 21, then n must be divisible by which of the following?

8 - 2, 2, 2

12 - 2, 2, 3

18, 2, 3, 3

24 - 2, 2, 2, 3

48- , 2, 2, 2, 2,

If n is divisible by both 4 and 21, its prime factors include 2, 2, 3, and 7. Therefore, any integer that can be constructed as the product of these prime factors is also a factor of n. In this case, 12 is the only integer that can definitively be constructed from the prime factors of n, since 12 = 2 x 2 x 3.

The correct answer is B.
Re: Positive integer n divisible by 4 and 21   [#permalink] 23 Jul 2009, 03:31
    Similar topics Author Replies Last post
Similar
Topics:
If n is a positive integer, is n^3 - n divisible by 4? (1) n btm3 2 18 Jun 2011, 21:09
If n is positive integer, is (n^3 - n) divisible by 4? 1. n LoyalWater 5 08 Sep 2008, 13:34
1 Experts publish their posts in the topic If n is a positive integer, is n3 n divisible by 4? 1. n = sondenso 6 24 Feb 2008, 17:59
If n is a positive integer, is n^3 - n divisible by 4? (1) n mexicanhoney 2 07 Oct 2007, 12:20
If n is a positive integer, is n^3 - n divisible by 4? (1) n TeHCM 15 24 Oct 2005, 21:12
Display posts from previous: Sort by

Positive integer n divisible by 4 and 21

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.