GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 21 Sep 2018, 22:52

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.

Close

Request Expert Reply

Confirm Cancel

If x, y, and z are positive integers, x is a factor of 2y

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 833
GMAT ToolKit User
If x, y, and z are positive integers, x is a factor of 2y  [#permalink]

Show Tags

New post Updated on: 24 Oct 2012, 05:18
4
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

66% (01:38) correct 34% (01:40) wrong based on 236 sessions

HideShow timer Statistics

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) \(\frac{zy}{3x}\)

Originally posted by LM on 24 Oct 2012, 04:48.
Last edited by Bunuel on 24 Oct 2012, 05:18, edited 2 times in total.
Renamed the topic and edited the question.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49300
Re: If x, y, and z are positive integers, x is a factor of 2y  [#permalink]

Show Tags

New post 24 Oct 2012, 05:17
2
1
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 the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 698
Location: India
GPA: 3.21
WE: Business Development (Other)
Premium Member Reviews Badge
Re: If x, y, and z are positive integers, x is a factor of 2y  [#permalink]

Show Tags

New post 31 Oct 2012, 06:12
1
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.”

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49300
Re: If x, y, and z are positive integers, x is a factor of 2y  [#permalink]

Show Tags

New post 01 Nov 2012, 07:13
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 the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 21 Mar 2014
Posts: 35
Re: If x, y, and z are positive integers, x is a factor of 2y  [#permalink]

Show Tags

New post 19 Sep 2015, 02:35
if we take x=4, y=2 and z=12...
x(=2) is factor of 2y(=4)
and 3y(=6) is a factor of z(=12)......
D it is.......
_________________

kinaare paaon phailane lage hian,
nadi se roz mitti kat rahi hai....

Intern
Intern
avatar
B
Joined: 23 Sep 2014
Posts: 7
Premium Member
Re: If x, y, and z are positive integers, x is a factor of 2y  [#permalink]

Show Tags

New post 17 Jun 2017, 21:15
I have a doubt here. Option E is also possible.
The answer option is
zy/3x
z is divisible by 3y. that means z/3 will always yield an integer.
y/x will also give an integer.
When we multiply these 2 the result should be an integer as all x,y,z are integers. Please clarify if I am missing something.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49300
Re: If x, y, and z are positive integers, x is a factor of 2y  [#permalink]

Show Tags

New post 18 Jun 2017, 03:07
laasshetty wrote:
I have a doubt here. Option E is also possible.
The answer option is
zy/3x
z is divisible by 3y. that means z/3 will always yield an integer.
y/x will also give an integer.
When we multiply these 2 the result should be an integer as all x,y,z are integers. Please clarify if I am missing something.


You are not reading the question carefully.

The question asks: which of the following MUST also be an integer? Not COULD also be an integer?
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 23 Sep 2014
Posts: 7
Premium Member
Re: If x, y, and z are positive integers, x is a factor of 2y  [#permalink]

Show Tags

New post 18 Jun 2017, 21:32
Ok.. I get your point. Can you give me an example where E would not be an integer?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49300
Re: If x, y, and z are positive integers, x is a factor of 2y  [#permalink]

Show Tags

New post 18 Jun 2017, 21:48
laasshetty wrote:
Ok.. I get your point. Can you give me an example where E would not be an integer?


Yes.

\(x\) is a factor of \(2y\), means that \(\frac{2y}{x}=integer\). Say y = 2 and x = 1.

\(3y\) is a factor of \(z\), means that \(\frac{z}{3y}=integer\). Say z = 3 and y = 1.

E) \(\frac{zy}{3x}=\frac{3*1}{3*2}=\frac{1}{2} \neq integer\).

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12425
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If x, y, and z are positive integers, x is a factor of 2y  [#permalink]

Show Tags

New post 30 Jan 2018, 14:57
Hi All,

I'm a big fan of TESTing VALUES (which is showcased in several of the explanations) - it's perfect for these types of questions. In addition, the answer choices are written in such a way that you can answer this question using Number Property rules....

In the prompt, we're told that "3Y is a factor of Z." This is just a wordy way of saying Z/3Y is an INTEGER. We're also told that X, Y and Z are positive integers.

Looking at the answers, what do you notice about answer D?

ZX/3Y....

It's interesting that the letters in in the numerator are NOT in alphabetical order. I wonder why THAT is? Is it to hide the fact that this answer has Z/3Y in it? We already know that Z/3Y is an integer and we know that X is an integer too.

Answer D literally translates into (integer)(integer)....which is ALWAYS an integer.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2000
Re: If x, y, and z are positive integers, x is a factor of 2y  [#permalink]

Show Tags

New post 31 Jan 2018, 04:25
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) \(\frac{zy}{3x}\)


Solution



    • Given: x is factor of 2y.

      o Thus, we can write \(2y = k * x\), where k is an integer

      o \(\frac{x}{y} = \frac{2}{k}\)

    • Given: 3y is a factor of z.

      o Thus, we can write \(z = q * 3y\), where q is an integer

      o \(\frac{y}{z} = \frac{1}{3q}\)

    • Thus \(x : y : z = 2: k: 3qk\)

Now let us consider the options one by one and check which of the following MUST be an integer

    1. \(\frac{y}{x} = \frac{k}{2}\)
      a. We cannot be sure, since we do not know the value of k

    2. \(\frac{2y}{6} = \frac{k}{3}\)
      a. Again, we cannot be sure, since we do not know the value of k

    3. \(\frac{xy}{3z} = \frac{2k}{9qk} = \frac{2}{9q}\)
      a. Again, we cannot be sure, since we do not know the value of q

    4. \(\frac{zx}{3y} = \frac{3qk*2}{3k} = 2q\)
      a. This has to be an integer, since 2q is an integer

    At this point, we can stop and mark the answer as D, but just to be sure, let’s check the last option.

    5. \(\frac{zy}{3x} = \frac{3qk*k}{3*2}= \frac{qk^2}{2}\)
      a. We cannot be sure this is an integer, since we do not know the value of k or q.

Correct Answer: Option D

Regards,
Saquib
Quant Expert
e-GMAT
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Re: If x, y, and z are positive integers, x is a factor of 2y &nbs [#permalink] 31 Jan 2018, 04:25
Display posts from previous: Sort by

If x, y, and z are positive integers, x is a factor of 2y

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


cron

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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.