It is currently 20 Feb 2018, 09:39

Live Now:

Ace the Booth Interview - Live on YouTube


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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x, y, and z are positive integers such that x is a factor

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

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43830
If x, y, and z are positive integers such that x is a factor [#permalink]

Show Tags

New post 18 Mar 2014, 00:36
1
This post received
KUDOS
Expert's post
13
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

79% (01:28) correct 21% (01:20) wrong based on 636 sessions

HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

If x, y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?

(A) (x+z)/z
(B) (y+z)/x
(C) (x+y)/z
(D) (xy)/z
(E) (yz)/x

Problem Solving
Question: 172
Category: Arithmetic Properties of numbers
Page: 85
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!
[Reveal] Spoiler: OA

_________________

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

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43830
Re: If x, y, and z are positive integers such that x is a factor [#permalink]

Show Tags

New post 18 Mar 2014, 00:36
2
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
SOLUTION

If x, y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?

(A) (x+z)/z
(B) (y+z)/x
(C) (x+y)/z
(D) (xy)/z
(E) (yz)/x

Given: \(z\) goes into \(x\) and \(x\) goes into \(y\). Note that it's not necessarily means that \(z<x<y\), it means that \(z\leq{x}\leq{y}\) (for example all three can be equal x=y=z=1);

Now, in all options but B we can factor out the denominator from the nominator and reduce it. For example in A: \(\frac{x+z}{z}\) as \(z\) goes into \(x\) we can factor out it and reduce to get an integer result (or algebraically as \(x=zk\) for some positive integer \(k\) then \(\frac{x+z}{z}=\frac{zk+z}{z}=\frac{z(k+1)}{z}=k+1=integer\)).

But in B. \(\frac{y+z}{x}\) we can not be sure that we'll be able factor out \(x\) from \(z\) thus this option might not be an integer (for example x=y=4 and z=2).

Answer: B.

Alternately you could juts plug some smart numbers and the first option which would give a non-integer result would be the correct choice.
_________________

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

5 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1839
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If x, y, and z are positive integers such that x is a factor [#permalink]

Show Tags

New post 18 Mar 2014, 02:54
5
This post received
KUDOS
Answer = (B) \(\frac{(y+z)}{x}\)

Took x = 6; y = 12; z = 2

6 is a factor of 12, and 6 is a multiple of 2

Only option B contradicts the condition
_________________

Kindly press "+1 Kudos" to appreciate :)

2 KUDOS received
Manager
Manager
avatar
Joined: 21 Aug 2013
Posts: 99
Schools: ISB '15
Re: If x, y, and z are positive integers such that x is a factor [#permalink]

Show Tags

New post 19 Mar 2014, 21:20
2
This post received
KUDOS
IMO B.
let y = 10
then x = 2 or 5.
z can be 1 or 2

B satisfies.
_________________

Veritas Prep - 650
MGMAT 1 590
MGMAT 2 640 (V48/Q31)

Please help the community by giving Kudos.

1 KUDOS received
Director
Director
User avatar
G
Joined: 23 Jan 2013
Posts: 601
Schools: Cambridge'16
Re: If x, y, and z are positive integers such that x is a factor [#permalink]

Show Tags

New post 19 Mar 2014, 23:14
1
This post received
KUDOS
1
This post was
BOOKMARKED
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If x, y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?

(A) (x+z)/z
(B) (y+z)/x
(C) (x+y)/z
(D) (xy)/z
(E) (yz)/x

Problem Solving
Question: 172
Category: Arithmetic Properties of numbers
Page: 85
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!


We have integers Y,X and Z multiples of Z, all not equal to 0 and Y>=X>=Z

(A) (x+z)/z: we add multiples of Z and divide it by Z, it is always integer
(B) (y+z)/x: it is integer when Y=X=Z and Y>X=Z and not integer when Y>X>Z and Y=X>Z
(C) (x+y)/z: the same as in A
(D) (xy)/z: if one multiple of other, multiplying with any other guarantees multiple
(E) (yz)/x: the same as in D

For test strategy we could use picking but it has danger for testing B. We can choose B by exluding ACDE
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43830
Re: If x, y, and z are positive integers such that x is a factor [#permalink]

Show Tags

New post 23 Mar 2014, 07:11
Expert's post
1
This post was
BOOKMARKED
SOLUTION

If x, y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?

(A) (x+z)/z
(B) (y+z)/x
(C) (x+y)/z
(D) (xy)/z
(E) (yz)/x

Given: \(z\) goes into \(x\) and \(x\) goes into \(y\). Note that it's not necessarily means that \(z<x<y\), it means that \(z\leq{x}\leq{y}\) (for example all three can be equal x=y=z=1);

Now, in all options but B we can factor out the denominator from the nominator and reduce it. For example in A: \(\frac{x+z}{z}\) as \(z\) goes into \(x\) we can factor out it and reduce to get an integer result (or algebraically as \(x=zk\) for some positive integer \(k\) then \(\frac{x+z}{z}=\frac{zk+z}{z}=\frac{z(k+1)}{z}=k+1=integer\)).

But in B. \(\frac{y+z}{x}\) we can not be sure that we'll be able factor out \(x\) from \(z\) thus this option might not be an integer (for example x=y=4 and z=2).

Answer: B.

Alternately you could juts plug some smart numbers and the first option which would give a non-integer result would be the correct choice.
_________________

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: 31 Mar 2014
Posts: 7
Location: Germany
GMAT 1: 600 Q47 V26
GMAT 2: 730 Q49 V41
Re: If x, y, and z are positive integers such that x is a factor [#permalink]

Show Tags

New post 06 Apr 2014, 01:19
A: z is obviously divisible by z and x is div by z, since x is a multiple of z (x = zn). So, x+z is div by z
B: y is div by x, since x is a factor of y. z is not div by x if x>z. for example: z=6 x=12. So, y+z is not necessarily div by x.
Manager
Manager
User avatar
Joined: 20 Dec 2013
Posts: 129
Re: If x, y, and z are positive integers such that x is a factor [#permalink]

Show Tags

New post 06 Apr 2014, 01:42
[quote="Bunuel"]The Official Guide For GMAT® Quantitative Review, 2ND Edition

If x, y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?

(A) (x+z)/z
(B) (y+z)/x
(C) (x+y)/z
(D) (xy)/z
(E) (yz)/x

If we plug in: x = 6, y = 12 and z = 3.

A - (9)/3
B - (15)/12 - NOT an integer
C - (18)/3
D - Integer
E - Integer

Hence answer will be B
_________________

76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org
http://www.youtube.com/perfectscores

Expert Post
3 KUDOS received
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 806
Re: If x, y, and z are positive integers such that x is a factor [#permalink]

Show Tags

New post 02 Jun 2015, 01:22
3
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
Given
We are given 3 positive integers \(x\), \(y\) and \(z\) such that \(x\) is a factor of \(y\) and \(x\) is a multiple of \(z\). We are asked to find that among the options given which of them is not necessarily an integer.

Approach
Since \(x\) is a factor of \(y\), we can say that \(\frac{y}{x}\) is an integer...........(1)

Also, as \(x\) is a multiple of \(z\) i.e. \(z\) is a factor of \(x\), we can say that \(\frac{x}{z}\) is an integer............(2)

From the above two deductions, we can say that \(\frac{y}{z}\) will also be an integer as \(x\) divides \(y\) completely and \(z\) divides \(x\) completely..............(3)

Our endeavor would be to reduce the expressions in the options to one or more of the above 3 forms.

Working Out
(A) \(\frac{x +z}{z} = \frac{x}{z} + 1\) . Since \(\frac{x}{z}\) is an integer, the expression will be an integer

(B) \(\frac{y+z}{x} = \frac{y}{x} + \frac{z}{x}\) . \(\frac{y}{x}\) is an integer but we can't say if \(\frac{z}{x}\) is also an integer. So the expression need not necessarily be an integer.

Although we have got our answer, I am reducing the other expressions for solution purpose.

(C) \(\frac{x+y}{z} = \frac{x}{z} + \frac{y}{z}\). Both \(\frac{x}{z}\) and \(\frac{y}{z}\) are integers, hence the expression will also be an integer

(D) \(\frac{xy}{z}\). Since \(\frac{x}{z}\) is an integer, the expression will also be an integer.

(E) \(\frac{yz}{x}\). Since \(\frac{y}{x}\) is an integer, the expression will also be an integer.

Hence, answer is Option B

Hope this helps :)

Regards
Harsh
_________________












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

Expert Post
1 KUDOS received
EMPOWERgmat Instructor
User avatar
D
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11036
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: If x, y, and z are positive integers such that x is a factor [#permalink]

Show Tags

New post 03 Jun 2015, 15:16
1
This post received
KUDOS
Expert's post
Hi All,

This question is perfect for TESTing VALUES. Since the prompt asks 'which of the following is NOT necessarily an integer?", we can take advantage of a great 'shortcut' - we just need to find ONE instance for any answer to NOT be an integer and we'll have the solution...

We're given a few facts to work with:
1) X, Y and Z are POSITIVE INTEGERS
2) X is a FACTOR of Y
3) X is a MULTIPLE of Z

Let's TEST VALUES.....

IF....
X = 2
Y = 2
Z = 1

Answer A: (X+Z)/Z = (2+1)/1 = 3 This is an integer
Answer B: (Y+Z)/X = (2+1)/2 = 3/2 This is NOT an integer, so this MUST be the answer. We don't even have to check the others.

Final Answer:
[Reveal] Spoiler:
B


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!***********************

Expert Post
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7942
Location: Pune, India
Re: If x, y, and z are positive integers such that x is a factor [#permalink]

Show Tags

New post 03 Jun 2015, 20:09
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If x, y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?

(A) (x+z)/z
(B) (y+z)/x
(C) (x+y)/z
(D) (xy)/z
(E) (yz)/x

Problem Solving
Question: 172
Category: Arithmetic Properties of numbers
Page: 85
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!


An easy approach would be to bring everything in terms of z.

x = za (where a is a positive integer)
y = xb = zab (where b is a positive integer)

(A) (x+z)/z = (za + z)/z = a + 1 (positive integer)
(B) (y+z)/x = (zab + z)/za = (ab + 1)/a (Not necessarily an integer)
(C) (x+y)/z = (zab + za)/z = ab + a (positive integer)
(D) (xy)/z = zazab/z = zaab (positive integer)
(E) (yz)/x = zabz/za = zb (positive integer)

Answer (B)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Senior Manager
Senior Manager
avatar
Joined: 21 May 2015
Posts: 265
Concentration: Operations, Strategy
GMAT 1: 750 Q50 V41
Re: If x, y, and z are positive integers such that x is a factor [#permalink]

Show Tags

New post 03 Jun 2015, 23:33
B
As x is factor y and z is a factor of x that means z is a factor of y too
Only B divides z/x which might not be an integer
_________________

Apoorv

I realize that i cannot change the world....But i can play a part :)

Director
Director
User avatar
Joined: 10 Mar 2013
Posts: 584
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
GMAT ToolKit User
Re: If x, y, and z are positive integers such that x is a factor [#permalink]

Show Tags

New post 27 Aug 2015, 05:57
z x y
z 3z 9z --> (B) (y+z)/x = 9z+z/3z=10z/3z
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Manager
Manager
User avatar
Joined: 05 Jul 2015
Posts: 107
Concentration: Real Estate, International Business
GMAT 1: 600 Q33 V40
GPA: 3.3
Re: If x, y, and z are positive integers such that x is a factor [#permalink]

Show Tags

New post 22 Nov 2015, 20:05
I decided to pick numbers with exponents. Y=2^3 X=2^2 Z=2

All the ones with Z on the bottom are obviously divisible with my numbers and Y is stated to be divisible by x

Had to check B) 10/4 Not an integer.
Manager
Manager
avatar
B
Joined: 09 Aug 2016
Posts: 69
Re: If x, y, and z are positive integers such that x is a factor [#permalink]

Show Tags

New post 24 Jan 2017, 07:02
Bunuel wrote:
SOLUTION

If x, y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?

(A) (x+z)/z
(B) (y+z)/x
(C) (x+y)/z
(D) (xy)/z
(E) (yz)/x

Given: \(z\) goes into \(x\) and \(x\) goes into \(y\). Note that it's not necessarily means that \(z<x<y\), it means that \(z\leq{x}\leq{y}\) (for example all three can be equal x=y=z=1);

Now, in all options but B we can factor out the denominator from the nominator and reduce it. For example in A: \(\frac{x+z}{z}\) as \(z\) goes into \(x\) we can factor out it and reduce to get an integer result (or algebraically as \(x=zk\) for some positive integer \(k\) then \(\frac{x+z}{z}=\frac{zk+z}{z}=\frac{z(k+1)}{z}=k+1=integer\)).

But in B. \(\frac{y+z}{x}\) we can not be sure that we'll be able factor out \(x\) from \(z\) thus this option might not be an integer (for example x=y=4 and z=2).

Answer: B.

Alternately you could juts plug some smart numbers and the first option which would give a non-integer result would be the correct choice.


My opinion is that in GMAT terms the right solution is ONLY the:

"Alternately you could juts plug some smart numbers and the first option which would give a non-integer result would be the correct choice
Manager
Manager
User avatar
S
Joined: 09 Mar 2016
Posts: 226
If x, y, and z are positive integers such that x is a factor [#permalink]

Show Tags

New post 23 Jan 2018, 10:08
Hey everyone,

this question took me 7 minutes to solve correctly, is there any shortcut for dummies to solve this quckly ? :? :)

here is my solution :) its only 30sec read, please read it below you wont get bored :)

Let y be 6
Then x = 2 or x =3
Z =1 or z =2

x is a factor of y -----> 2 is factor of 6
x is a multiple of z -----> 2 is multiple of 1

so let`s test them; this is the most exciting part of problem solving process :)


(A) (x+z)/z ( 2+2)/2 or (2+1)1
(B) (y+z)/x (6+1)/2= non integer or (6+2)/2 integer
(C) (x+y)/z 2+6/1 or 2+6/2
(D) (xy)/z 2*6/1 or 3*6/2
(E) (yz)/x 6*1/2 , 6*1/2 6*2/3 etc 
1 KUDOS received
PS Forum Moderator
avatar
P
Joined: 25 Feb 2013
Posts: 926
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: If x, y, and z are positive integers such that x is a factor [#permalink]

Show Tags

New post 23 Jan 2018, 10:58
1
This post received
KUDOS
1
This post was
BOOKMARKED
dave13 wrote:
Hey everyone,

this question took me 7 minutes to solve correctly, is there any shortcut for dummies to solve this quckly ? :? :)

here is my solution :) its only 30sec read, please read it below you wont get bored :)

Let y be 6
Then x = 2 or x =3
Z =1 or z =2

x is a factor of y -----> 2 is factor of 6
x is a multiple of z -----> 2 is multiple of 1

so let`s test them; this is the most exciting part of problem solving process :)


(A) (x+z)/z ( 2+2)/2 or (2+1)1
(B) (y+z)/x (6+1)/2= non integer or (6+2)/2 integer
(C) (x+y)/z 2+6/1 or 2+6/2
(D) (xy)/z 2*6/1 or 3*6/2
(E) (yz)/x 6*1/2 , 6*1/2 6*2/3 etc 


Hi dave13

In fact what your method i.e. substitution works best for this question and is the fastest route. try \(z=1\), \(x=2\) & \(y=4\). remember from question stem you should have realized that \(y>x>z\), hence you should pick the smallest number for \(z\) for easy calculation and then work upwards.

Algebraic approach -

given \(y=kx\) (where \(k\) is a constant) and \(x=qz\) (where \(q\) is a constant). In the options I could see that only \(x\) & \(z\) are in the denominators so

\(\frac{y}{x}=k=integer\) and \(\frac{x}{z}=q=integer\). with this understanding scan the options

A) \(\frac{(x+z)}{z}=\frac{x}{z}+\frac{z}{z}=integer+1=integer\)

(B) \(\frac{(y+z)}{x}=\frac{y}{x}+\frac{z}{x}=integer+non-integer=non-integer\)

(C) \(\frac{(x+y)}{z}=\frac{x}{z}+\frac{y}{z}=integer+integer=integer\)

(D) \(\frac{(xy)}{z}=y*\frac{x}{z}=y*integer=integer\)

(E) \(\frac{(yz)}{x}=\frac{y}{x}*z=integer*z=integer\)

Hence our answer is B
Expert Post
EMPOWERgmat Instructor
User avatar
D
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11036
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: If x, y, and z are positive integers such that x is a factor [#permalink]

Show Tags

New post 23 Jan 2018, 12:20
Hi niks18,

You have to be careful about the assumptions you make about the given information. At NO point does the prompt state that Y > X.

In my approach, I used X=2, Y=2, Z=1 and found the correct answer WITHOUT having to check 3 of the options.

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!***********************

Re: If x, y, and z are positive integers such that x is a factor   [#permalink] 23 Jan 2018, 12:20
Display posts from previous: Sort by

If x, y, and z are positive integers such that x is a factor

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.