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

It is currently 22 Oct 2014, 04:49

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, x is a factor of 2y

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 889
Followers: 6

Kudos [?]: 169 [0], given: 33

If x, y, and z are positive integers, x is a factor of 2y [#permalink] New post 24 Oct 2012, 03:48
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

76% (02:29) correct 24% (01:17) wrong based on 41 sessions
If x, y, and z are positive integers, x is a factor of 2y, and 3y is a factor of z, which of the following must also be an integer?

A) \frac{y}{x}

B) \frac{2y}{6}

C) \frac{xy}{3z}

D) \frac{zx}{3y}

E) \frac{zy}{3x}
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Oct 2012, 04:18, edited 2 times in total.
Renamed the topic and edited the question.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23369
Followers: 3607

Kudos [?]: 28758 [1] , given: 2846

Re: If x, y, and z are positive integers, x is a factor of 2y [#permalink] New post 24 Oct 2012, 04:17
1
This post received
KUDOS
Expert's post
LM wrote:
If x, y, and z are positive integers, x is a factor of 2y, and 3y is a factor of z, which of the following must also be an integer?

A) \frac{y}{x}

B) \frac{2y}{6}

C) \frac{xy}{3z}

D) \frac{zx}{3y}

E) \frac{zy}{3x}


x is a factor of 2y, means that \frac{2y}{x}=integer.

Similarly, 3y is a factor of z, means that \frac{z}{3y}=integer. Multiply both sides of this equation by integer x: \frac{z}{3y}*x=integer*x --> \frac{zx}{3y}=x*integer=integer*integer=integer.

Answer: D.

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

Moderator
Moderator
User avatar
Joined: 25 Apr 2012
Posts: 676
Location: India
GPA: 3.21
WE: Business Development (Other)
Followers: 18

Kudos [?]: 321 [0], given: 678

Premium Member CAT Tests
Re: If x, y, and z are positive integers, x is a factor of 2y [#permalink] New post 31 Oct 2012, 05:12
Bunuel wrote:
LM wrote:
If x, y, and z are positive integers, x is a factor of 2y, and 3y is a factor of z, which of the following must also be an integer?

A) \frac{y}{x}

B) \frac{2y}{6}

C) \frac{xy}{3z}

D) \frac{zx}{3y}

E) \frac{zy}{3x}


x is a factor of 2y, means that \frac{2y}{x}=integer.

Similarly, 3y is a factor of z, means that \frac{z}{3y}=integer. Multiply both sides of this equation by integer x: \frac{z}{3y}*x=integer*x --> \frac{zx}{3y}=x*integer=integer*integer=integer.

Answer: D.

Hope it's clear.



Hello Bunuel,

Can we simplify the options and then attempt the Questions

For Option 5, ZY/3X can be simplified as 3Y*Y/3X --> Y*Y/X which may or may not be true.
For example looking at option 4, ZX/3Y, if simplify it as ---> Z=3y and then the eqn becomes 3y*y/ 3y which gives x only

Please confirm
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23369
Followers: 3607

Kudos [?]: 28758 [0], given: 2846

Re: If x, y, and z are positive integers, x is a factor of 2y [#permalink] New post 01 Nov 2012, 06:13
Expert's post
mridulparashar1 wrote:
Bunuel wrote:
LM wrote:
If x, y, and z are positive integers, x is a factor of 2y, and 3y is a factor of z, which of the following must also be an integer?

A) \frac{y}{x}

B) \frac{2y}{6}

C) \frac{xy}{3z}

D) \frac{zx}{3y}

E) \frac{zy}{3x}


x is a factor of 2y, means that \frac{2y}{x}=integer.

Similarly, 3y is a factor of z, means that \frac{z}{3y}=integer. Multiply both sides of this equation by integer x: \frac{z}{3y}*x=integer*x --> \frac{zx}{3y}=x*integer=integer*integer=integer.

Answer: D.

Hope it's clear.



Hello Bunuel,

Can we simplify the options and then attempt the Questions

For Option 5, ZY/3X can be simplified as 3Y*Y/3X --> Y*Y/X which may or may not be true.
For example looking at option 4, ZX/3Y, if simplify it as ---> Z=3y and then the eqn becomes 3y*y/ 3y which gives x only

Please confirm


We are not given that z=3y, we are given that z=3y*integer (3y is a factor of z). Now, if we substitute z in \frac{zx}{3y}, we'l get: \frac{zx}{3y}=\frac{(3y*integer)*x}{3y}=integer*x=integer.

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

Re: If x, y, and z are positive integers, x is a factor of 2y   [#permalink] 01 Nov 2012, 06:13
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic If x, y, and z are positive integers such that x is a factor pinal2 4 16 Dec 2007, 09:51
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
The positive integers x,y, and z are such that x is a factor uvs_mba 3 01 Nov 2006, 21:37
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, x is a factor of 2y

  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®.