Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43830

If x, y, and z are positive integers such that x is a factor [#permalink]
Show Tags
18 Mar 2014, 00:36
1
This post received KUDOS
Expert's post
13
This post was BOOKMARKED
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 EditionIf 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 ProjectEach 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!
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Sep 2009
Posts: 43830

Re: If x, y, and z are positive integers such that x is a factor [#permalink]
Show Tags
18 Mar 2014, 00:36
2
This post received KUDOS
Expert's post
5
This post was BOOKMARKED
SOLUTIONIf 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 noninteger 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? Extrahard Quant Tests with Brilliant Analytics



SVP
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
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



Manager
Joined: 21 Aug 2013
Posts: 99

Re: If x, y, and z are positive integers such that x is a factor [#permalink]
Show Tags
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.



Director
Joined: 23 Jan 2013
Posts: 601

Re: If x, y, and z are positive integers such that x is a factor [#permalink]
Show Tags
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 EditionIf 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 ProjectEach 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



Math Expert
Joined: 02 Sep 2009
Posts: 43830

Re: If x, y, and z are positive integers such that x is a factor [#permalink]
Show Tags
23 Mar 2014, 07:11
SOLUTIONIf 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 noninteger 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? Extrahard Quant Tests with Brilliant Analytics



Intern
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
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
Joined: 20 Dec 2013
Posts: 129

Re: If x, y, and z are positive integers such that x is a factor [#permalink]
Show Tags
06 Apr 2014, 01:42
[quote="Bunuel"] The Official Guide For GMAT® Quantitative Review, 2ND EditionIf 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



eGMAT Representative
Joined: 04 Jan 2015
Posts: 806

Re: If x, y, and z are positive integers such that x is a factor [#permalink]
Show Tags
02 Jun 2015, 01:22
3
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
GivenWe 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. ApproachSince \(x\) 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.egmat.com



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11036
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: If x, y, and z are positive integers such that x is a factor [#permalink]
Show Tags
03 Jun 2015, 15:16
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: 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
CoFounder & 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!***********************



Veritas Prep GMAT Instructor
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
03 Jun 2015, 20:09
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIf 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 ProjectEach 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
Joined: 21 May 2015
Posts: 265
Concentration: Operations, Strategy

Re: If x, y, and z are positive integers such that x is a factor [#permalink]
Show Tags
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
Joined: 10 Mar 2013
Posts: 584
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: If x, y, and z are positive integers such that x is a factor [#permalink]
Show Tags
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
Joined: 05 Jul 2015
Posts: 107
Concentration: Real Estate, International Business
GPA: 3.3

Re: If x, y, and z are positive integers such that x is a factor [#permalink]
Show Tags
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
Joined: 09 Aug 2016
Posts: 69

Re: If x, y, and z are positive integers such that x is a factor [#permalink]
Show Tags
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 noninteger 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 noninteger result would be the correct choice



Manager
Joined: 09 Mar 2016
Posts: 226

If x, y, and z are positive integers such that x is a factor [#permalink]
Show Tags
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



PS Forum Moderator
Joined: 25 Feb 2013
Posts: 926
Location: India
GPA: 3.82

Re: If x, y, and z are positive integers such that x is a factor [#permalink]
Show Tags
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 dave13In 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) \(\frac{(y+z)}{x}=\frac{y}{x}+\frac{z}{x}=integer+noninteger=noninteger\) (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



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11036
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: If x, y, and z are positive integers such that x is a factor [#permalink]
Show Tags
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
CoFounder & 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






