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

It is currently 23 Oct 2014, 04:34

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

M27-01 - Anyone got a more expansive answer?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Manager
Manager
User avatar
Joined: 02 May 2012
Posts: 109
Location: United Kingdom
WE: Account Management (Other)
Followers: 0

Kudos [?]: 14 [0], given: 34

M27-01 - Anyone got a more expansive answer? [#permalink] New post 13 Aug 2012, 12:22
Hi GMATers

This question has stumped me. Has anyone got a more detailed explanation for this? I can't follow the OG to save myself!

If n is a positive integer and p is a prime number, is p a factor of n!?
(1) p is a factor of (n+2)!−n!

(2) p is a factor of (n+2)!n!

Thanks

B
_________________

In the study cave!

Kaplan Promo CodeKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
2 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 73

Kudos [?]: 529 [2] , given: 43

Re: M27-01 - Anyone got a more expansive answer? [#permalink] New post 13 Aug 2012, 14:01
2
This post received
KUDOS
bradfris wrote:
Hi GMATers

This question has stumped me. Has anyone got a more detailed explanation for this? I can't follow the OG to save myself!

If n is a positive integer and p is a prime number, is p a factor of n!?
(1) p is a factor of (n+2)!−n!

(2) p is a factor of (n+2)!n!

Thanks

B


(1) p is a factor of (n+2)!-n!=n![(n+1)(n+2)-1]=n!(n^2+3n+1).
p not necessarily a factor of n!, it can be a factor of n^2+3n+1, which is greater than 1.
Not sufficient.

(2) p is a factor of (n+2)!n!=(n!)^2(n+1)(n+2)=(n!)^2(n^2+3n+2)
Again, p not necessarily a factor of n!,it can be a factor of n^2+3n+2, which is greater than 1.
Not sufficient.

(1) and (2) If p is not a factor of n! then necessarily p has to be a factor of both n^2+3n+1 and n^2+3n+2. But these are two consecutive positive integers, so only 1 can be a factor of both. p being a prime, is greater than 1. It follows that necessarily p must be a factor of n!.
Sufficient.

Answer C

If (2) should be \frac{(n+2)!}{n!}, then the above should be replaced by:

(2) \frac{(n+2)!}{n!}=(n+1)(n+2). For example n+1 can be a prime, and if p=n+1, certainly p is not a factor of n!.
Not sufficient.

(1) and (2) together - stays the same as above:
If p is not a factor of n! then necessarily p has to be a factor of both n^2+3n+1 and n^2+3n+2. But these are two consecutive positive integers, so only 1 can be a factor of both. p being a prime, is greater than 1. It follows that necessarily p must be a factor of n!.
Sufficient.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.


Last edited by EvaJager on 14 Aug 2012, 06:23, edited 1 time in total.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23393
Followers: 3609

Kudos [?]: 28822 [1] , given: 2852

Re: M27-01 - Anyone got a more expansive answer? [#permalink] New post 14 Aug 2012, 00:11
1
This post received
KUDOS
Expert's post
bradfris wrote:
Hi GMATers

This question has stumped me. Has anyone got a more detailed explanation for this? I can't follow the OG to save myself!

If n is a positive integer and p is a prime number, is p a factor of n!?
(1) p is a factor of (n+2)!−n!

(2) p is a factor of (n+2)!n!

Thanks

B


The second statement should read: p is a factor of (n+2)!/n!.

Below is OE for this question:

If n is a positive integer and p is a prime number, is p a factor of n!?

(1) p is a factor of (n+2)!-n! --> if n=2 then (n+2)!-n!=22 and for p=2 then answer will be YES but for p=11 the answer will be NO. Not sufficient.

(2) p is a factor of (n+2)!/n! --> \frac{(n+2)!}{n!}=(n+1)(n+2) --> if n=2 then (n+1)(n+2)=12 and for p=2 the answer will be YES but for p=3 the answer will be NO. Not sufficient.

(1)+(2) (n+2)!-n!=n!((n+1)(n+2)-1). Now, (n+1)(n+2)-1 and (n+1)(n+2) are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1. So, as from (2) p is a factor of (n+1)(n+2) then it cannot be a factor of (n+1)(n+2)-1, thus in order p to be a factor of n!*((n+1)(n+2)-1), from (1), then it should be a factor of the first multiple of this expression: n!. Sufficient.

Answer: C.

Discussed here: devil-s-dozen-129312.html

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Current Student
User avatar
Joined: 23 Oct 2010
Posts: 384
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 13

Kudos [?]: 146 [0], given: 73

GMAT ToolKit User
Re: M27-01 - Anyone got a more expansive answer? [#permalink] New post 15 Aug 2012, 10:02
Bunuel wrote:

(1)+(2) (n+2)!-n!=n!((n+1)(n+2)-1).

didnt get it. how comes (n+1)(n+2)?
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 73

Kudos [?]: 529 [0], given: 43

Re: M27-01 - Anyone got a more expansive answer? [#permalink] New post 15 Aug 2012, 10:23
LalaB wrote:
Bunuel wrote:

(1)+(2) (n+2)!-n!=n!((n+1)(n+2)-1).

didnt get it. how comes (n+1)(n+2)?


(n+2)!=n!(n+1)(n+2)
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Current Student
User avatar
Joined: 23 Oct 2010
Posts: 384
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 13

Kudos [?]: 146 [0], given: 73

GMAT ToolKit User
Re: M27-01 - Anyone got a more expansive answer? [#permalink] New post 15 Aug 2012, 10:27
EvaJager I meant WHY (n+2)!=n!(n+1)(n+2)
perhaps I am tired and need some rest to get it
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 73

Kudos [?]: 529 [0], given: 43

Re: M27-01 - Anyone got a more expansive answer? [#permalink] New post 15 Aug 2012, 10:38
LalaB wrote:
EvaJager I meant WHY (n+2)!=n!(n+1)(n+2)
perhaps I am tired and need some rest to get it


(n+2)!=1*2*...*n*(n+1)*(n+2)=n!*(n+1)*(n+2)

By definition, n!=1*2*...*n, for any positive integer n, and 0!=1.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

1 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 73

Kudos [?]: 529 [1] , given: 43

Re: M27-01 - Anyone got a more expansive answer? [#permalink] New post 15 Aug 2012, 10:39
1
This post received
KUDOS
LalaB wrote:
EvaJager I meant WHY (n+2)!=n!(n+1)(n+2)
perhaps I am tired and need some rest to get it


(n+2)!=1*2*...*n*(n+1)*(n+2)=n!*(n+1)*(n+2)

By definition, n!=1*2*...*n, for any positive integer n, and 0!=1.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Current Student
User avatar
Joined: 23 Oct 2010
Posts: 384
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 13

Kudos [?]: 146 [0], given: 73

GMAT ToolKit User
Re: M27-01 - Anyone got a more expansive answer? [#permalink] New post 15 Aug 2012, 10:42
EvaJager ,
ah got it. thnx
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

Re: M27-01 - Anyone got a more expansive answer?   [#permalink] 15 Aug 2012, 10:42
    Similar topics Author Replies Last post
Similar
Topics:
Anyone got 800 Here? ecashzone 4 11 Nov 2011, 09:40
1 Would anyone have the answers Seshouan 11 22 Oct 2009, 13:47
Does anyone know the answer? ronibr 2 19 Jul 2007, 13:08
1000 PS and DS answers. Anyone? asaf 4 16 Jul 2007, 04:54
Display posts from previous: Sort by

M27-01 - Anyone got a more expansive answer?

  Question banks Downloads My Bookmarks Reviews Important topics  

Moderators: WoundedTiger, Bunuel



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®.