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

It is currently 24 Oct 2014, 11:10

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

If x, y, and z are positive integers, and (x!+x)/z=y, then

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 08 Nov 2009
Posts: 48
Followers: 0

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

If x, y, and z are positive integers, and (x!+x)/z=y, then [#permalink] New post 19 Dec 2009, 14:26
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

24% (02:46) correct 76% (01:44) wrong based on 86 sessions
If x, y, and z are positive integers, and \frac{x!+x}{z}=y, then what is the value of z?

(1) x is a factor of y
(2) z < x

[Reveal] Spoiler:
With the first clue I get to the form (x-1)!/c+1/c=z, where c is a positive integer, but I don't know how to use the second clue.
[Reveal] Spoiler: OA
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23409
Followers: 3613

Kudos [?]: 28906 [1] , given: 2871

Re: PR1012 - Factorials 4 [#permalink] New post 21 Dec 2009, 03:05
1
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
Marco83 wrote:
I would like an explanation on how to solve this exercise without plugging numbers.

If x, y, and z are positive integers, and (x!+x)/z=y, then what is the value of z?

I) x is a factor of y

II) z<x


With the first clue I get to the form (x-1)!/c+1/c=z, where c is a positive integer, but I don't know how to use the second clue.


First note that for n>1, n!+1 has no factor k<=n, but 1. As n!=2*3*...*n, which means that every integer less than or equal to n is a factor of n!, but if we add 1 to n!, sum, n!+1, obviously won't be evenly divisible by these factors.

For example:
n=3, n!+1=7, 7 has no factor <=3, except 1.
n=4, n!+1=25, 25 has no factor <=4, except 1.
n=5, n!+1=121, 121 has no factor <=5, except 1.

Back to the question:

If x, y, and z are positive integers, and \frac{x!+x}{z}=y, then what is the value of z?

(1) x is a factor of y --> xk=y --> x!+x=yz=xkz --> (x-1)!+1=kz --> z=1 OR z>x-1. Not sufficient.

For example:
x=4, (x-1)!+1=7=kz, z=1 OR z=7>4-1=3
x=5, (x-1)!+1=25=kz, z=1 OR z=5>5-1=4 OR z=25>5-1=4
x=6, (x-1)!+1=121=kz, z=1 OR z=11>5-1=4 OR z=121>5-1=4

(2) z<x. Clearly insufficient.

For example:
x=4, x!+x=28=yz, z=1 OR z=2 OR z=4 OR z=14 OR z=28.

(1)+(2) z=1 OR z>x-1 AND z<x --> As z<x and z is an integer, z>x-1 can not be true, hence z=1.

Answer: C.
_________________

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

Manager
Manager
avatar
Joined: 22 Jul 2009
Posts: 206
Location: Manchester UK
Followers: 2

Kudos [?]: 49 [0], given: 6

Re: PR1012 - Factorials 4 [#permalink] New post 22 Dec 2009, 07:34
@bunuel i dont get why z > x-1 please can you explain?
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23409
Followers: 3613

Kudos [?]: 28906 [1] , given: 2871

Re: PR1012 - Factorials 4 [#permalink] New post 22 Dec 2009, 08:12
1
This post received
KUDOS
Expert's post
sagarsabnis wrote:
@bunuel i dont get why z > x-1 please can you explain?


We know that n!+1 has no factor k, such as k<=n, but 1. Refer to the explanation in my previous post.

We have (x-1)!+1=kz, which means that z is a factor of (x-1)!+1, hence either z equals to 1 OR z>x-1, as z can not be <=x-1 (see above).

Hope it's clear.
_________________

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

Manager
Manager
avatar
Joined: 22 Jul 2009
Posts: 206
Location: Manchester UK
Followers: 2

Kudos [?]: 49 [0], given: 6

Re: PR1012 - Factorials 4 [#permalink] New post 22 Dec 2009, 10:39
now its clear...thanks
CEO
CEO
User avatar
Joined: 09 Sep 2013
Posts: 2855
Followers: 207

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

Premium Member
Re: If x, y, and z are positive integers, and (x!+x)/z=y, then [#permalink] New post 29 Aug 2014, 02:17
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: If x, y, and z are positive integers, and (x!+x)/z=y, then   [#permalink] 29 Aug 2014, 02:17
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic If x, y, and z are positive integers, is x - y - z positive ? clipea12 2 14 Sep 2014, 22:42
The positive integers x, y and z Countdown 0 03 Jul 2013, 04:08
4 Experts publish their posts in the topic If x, y and z are positive integers such that x is a factor lumone 9 29 Nov 2007, 10:01
The positive integers x, y and z are such that x is a factor arjsingh1976 2 02 Dec 2006, 11:33
If x,y, and z are positive integers such that x is a factor tareks 7 31 Jan 2005, 17:23
Display posts from previous: Sort by

If x, y, and z are positive integers, and (x!+x)/z=y, then

  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®.