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

It is currently 16 Dec 2018, 15:04

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 in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • FREE Quant Workshop by e-GMAT!

     December 16, 2018

     December 16, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.
  • Free GMAT Prep Hour

     December 16, 2018

     December 16, 2018

     03:00 PM EST

     04:00 PM EST

    Strategies and techniques for approaching featured GMAT topics

If w, x, y and z are integers such that w/x and y/z are

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

Hide Tags

Manager
Manager
avatar
Joined: 21 Mar 2007
Posts: 72
If w, x, y and z are integers such that w/x and y/z are  [#permalink]

Show Tags

New post Updated on: 13 Mar 2012, 13:00
6
42
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

43% (01:46) correct 57% (02:04) wrong based on 1047 sessions

HideShow timer Statistics

If w, x, y and z are integers such that w/x and y/z are integers, is w/x + y/z odd?

(1) wx + yz is odd
(2) wz + yx is odd

Originally posted by japped187 on 01 Jun 2008, 04:41.
Last edited by Bunuel on 13 Mar 2012, 13:00, edited 1 time in total.
Edited the question and added the OA
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51229
Re: If w, x, y and z are integers such that w/x and y/z are  [#permalink]

Show Tags

New post 13 Mar 2012, 13:24
25
14
If w, x, y and z are integers such that w/x and y/z are integers, is w/x + y/z odd?

Given: \(\frac{w}{x}=integer\) and \(\frac{y}{z}=integer\). Hence, \(\frac{w}{x}+\frac{y}{z}=\frac{wz+yx}{xz}=integer\) and the question is whether this integer is odd.

(1) wx + yz is odd --> if \(w=x=1\) and \(y=z=2\) then \(\frac{w}{x}+\frac{y}{z}=2=even\) but if \(w=x=1\) and \(y=2\), \(z=1\) then \(\frac{w}{x}+\frac{y}{z}=3=odd\). Not sufficient.

(2) wz + yx is odd --> \(\frac{wz+yx}{xz}=\frac{odd}{xz}=integer\) --> \(odd=(xz)*integer\) --> all multiple must be odd in order the product to be odd, hence \(integer =odd\). Sufficient.

Answer: B.

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

Most Helpful Community Reply
Director
Director
avatar
Joined: 10 Sep 2007
Posts: 886
Re: if w,x,y,and z are integers...DS  [#permalink]

Show Tags

New post 01 Jun 2008, 08:00
6
2
I think question is asking w/x + y/z odd and not w/x + w/z odd or not? If this is the case then here is my explanation.
Rephrased question is wz+xy/xz is odd or not?

Statement 1:
wx + yz is odd, this implies one pair is odd and other pair is even. As even + odd = odd. But we are not sure which pair is even or odd. So this is not sufficient and answer cannot be A or D.

Statement 2;
wz + xy is odd, this numerator of question is odd. As given in question w/x + y/z is integer so wz+xy/xz is not a fraction and this implies wz+xy is divisible by xz. Only way a odd number divisible by another number is that divisor has to be odd as well. So odd divided by odd will yield odd. So question is answered.

Answer B.
General Discussion
Manager
Manager
avatar
Joined: 07 Nov 2009
Posts: 243
Re: If w, x, y, and z are integers such that w/x and y/z are  [#permalink]

Show Tags

New post 13 Mar 2012, 11:06
3
japped187 wrote:
If w, x, y, and z are integers such that w/x and y/z are integers, is w/x + w/z odd?

(1) wx + yz is odd
(2) wz + xy is odd


IMO A is also satisfactory ....
wx + yz is odd

Case 1
wx is odd & yz is even
wx is odd ==> w & x are odd (odd*odd = odd) ==> w/x is odd
yz is even ==> There can be 3 cases
y is even and z is odd = Not possible as we are given y/z is integer
y is odd and z is even = Not possible as we are given y/z is integer
y is even and z is even = Possible ==> y/z is even
w/x (odd) + y/z (even) = Odd

Case 2
wx is even & yz is odd can be proved in a similar manner.

Please advice if i am wrong.
Manager
Manager
avatar
Joined: 07 Nov 2009
Posts: 243
Re: If w, x, y and z are integers such that w/x and y/z are  [#permalink]

Show Tags

New post 14 Mar 2012, 00:02
1
Hi Bunuel,

I agree with ur exp .. but is there a problem with my algebraic method ?
Senior Manager
Senior Manager
avatar
B
Joined: 24 Aug 2009
Posts: 469
Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: If w, x, y and z are integers such that w/x and y/z are  [#permalink]

Show Tags

New post 20 Sep 2012, 05:33
5
Other way to look at the problem

As w/x is integer we can say w=xa+0 , where a= any integer------> xa/x = a
Same way y/z is integer we can say y=zb+0 , where b= any integer------->zb/z = b

So the basically the question is, "Is a+b Odd"

1) wx + yz ----> x^2a + z^2b = odd------> a+b may be or may not be odd ---> Insufficient
2) wz + yx -----> xza + xzb ----> xz(a+b) = odd--->it means that both xz & (a+b) are odd ---->Sufficient

Answer B

Hope it helps.
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Director
Director
User avatar
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 595
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
GMAT ToolKit User Premium Member Reviews Badge
Re: If w, x, y and z are integers such that w/x and y/z are  [#permalink]

Show Tags

New post 20 Sep 2012, 06:16
2
rohitgoel15 wrote:
IMO A is also satisfactory ....
wx + yz is odd

Case 1
wx is odd & yz is even
wx is odd ==> w & x are odd (odd*odd = odd) ==> w/x is odd
yz is even ==> There can be 3 cases
y is even and z is odd = Not possible as we are given y/z is integer
y is odd and z is even = Not possible as we are given y/z is integer
y is even and z is even = Possible ==> y/z is even
w/x (odd) + y/z (even) = Odd

Case 2
wx is even & yz is odd can be proved in a similar manner.

Please advice if i am wrong.


rohitgoel15 wrote:
Hi Bunuel,

I agree with ur exp .. but is there a problem with my algebraic method ?


Yes there is a problem in statement:
y is even and z is odd = Not possible as we are given y/z is integer
Even/Odd can be integer, Consider eg Y=6 , z=3.. Hence that solution is incorrect.
_________________

Lets Kudos!!! ;-)
Black Friday Debrief

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51229
Re: If w, x, y and z are integers such that w/x and y/z are  [#permalink]

Show Tags

New post 19 Jul 2013, 00:22
1
Intern
Intern
avatar
Joined: 17 Jul 2013
Posts: 6
Location: United States
Concentration: Operations, Strategy
GPA: 3.18
WE: Engineering (Telecommunications)
Re: If w, x, y and z are integers such that w/x and y/z are  [#permalink]

Show Tags

New post 31 Jul 2013, 06:33
1
St 2 can also be proved in the following way.

w/x + y/z = something

=> (wz+xy)/xz = something
=> wz+xy = A -----------------------> Is xz*something odd ??

As per st 2 , wz+xy = odd .

Hence B

Hope there are no loopholes in my understanding.


Cheers :evil:
Intern
Intern
avatar
Joined: 20 Mar 2013
Posts: 10
Re: If w, x, y and z are integers such that w/x and y/z are  [#permalink]

Show Tags

New post 02 Aug 2013, 07:33
2
Hi All,

Problem helps us to understand the following:
For \(\frac{w}{x}\) to be an integer, both w and x need to be either even or odd. Same is the case with y and z, both either need to be even or odd.
We need, w/x + y/z to be of the following format:

ODD + EVEN, so of the two terms, one of them has to be even and the other to be odd.

Now, lets look the statements..

Statement (1): \(wx+yz\) is odd

From this statement we can deduce that either wx is odd and yz is even OR wx is even and yz is odd. Lets assume that wx is odd and yz is even. For the term wx to be odd and w/x to be an integer, both w and x needs to be odd.
However, even though yz is even since both y and z are even, it doesn't guarantee that y/z will be even. (6/2 = 3)

So from statement 1, what we get is ODD + EVEN/ODD, hence not sufficient.

Statement (2): \(wz+yx\) is odd

We can simply multiply and divide by xz as below:

(w/x + y/z) * xz = ODD

Now since we know that only ODD * ODD = ODD, we can be certain that w/x + y/z is odd, hence sufficient.

So my response, B
Director
Director
avatar
Joined: 29 Nov 2012
Posts: 759
Re: If w, x, y and z are integers such that w/x and y/z are  [#permalink]

Show Tags

New post 10 Oct 2013, 06:16
1
Statement 1 is indeed tricky... Statement 2 is easy.
Manager
Manager
avatar
Status: Student
Joined: 26 Aug 2013
Posts: 190
Location: France
Concentration: Finance, General Management
Schools: EMLYON FT'16
GMAT 1: 650 Q47 V32
GPA: 3.44
Re: If w, x, y and z are integers such that w/x and y/z are  [#permalink]

Show Tags

New post 27 Dec 2013, 06:48
1
HI,

Just for further discussion,

if AB is odd, is A/B also odd? What is the rule on this type of construction?

Thanks
_________________

Think outside the box

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51229
Re: If w, x, y and z are integers such that w/x and y/z are  [#permalink]

Show Tags

New post 29 Dec 2013, 03:43
Paris75 wrote:
HI,

Just for further discussion,

if AB is odd, is A/B also odd? What is the rule on this type of construction?

Thanks


You could try some examples to answer your own question.

For integers a and b, ab is odd only if both are odd. Now, odd/odd can be odd or not an integer at all. For example, 3/1=3=odd but 1/3 is not an integer at all.
_________________

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
S
Joined: 17 Dec 2012
Posts: 632
Location: India
Re: If w, x, y and z are integers such that w/x and y/z are  [#permalink]

Show Tags

New post 29 Dec 2013, 19:27
1
japped187 wrote:
If w, x, y and z are integers such that w/x and y/z are integers, is w/x + y/z odd?

(1) wx + yz is odd
(2) wz + yx is odd



Plug in approach requiring minimal thinking:

Take the case that is to be proved i.e, w/x + y/z is odd and then take the contrary case i.e, w/x + y/z is even for both the statements

(i) Case to be proved : wx+ yz is odd and w/x + y/z is odd.

The former is satisfied by odd + even and the latter again by odd+ even

Thus this will be satisfied say, if the following is satisfied: wx and w/x are both odd and y/z and yz are both even. an example is w=15 , x=3 and y=4 and z=2

How about the contrary case for (i). i.e., wx+ yz is odd but w/x + y/z is even.

The former is satisfied by odd+ even and the latter by odd+odd or even +even

This will be satisfied say, if wx and w/x are both odd and yz is even and y/z is odd. An example is w=9 x=3 and y=6 z=2

since the case to be proved and the contrary are both satisfied (i) is not sufficient

(ii) Case to be proved: wz+yx is odd and w/x and y/z is odd

The former is satisfied by odd+ even and the latter again by odd+ even

Thus this will be satisfied say, if the following is satisfied: wz and w/x are both odd and y/z and yx are both even. an example is w=15 , x=3 and y=12 and z=1

How about the contrary case for (i). i.e., wx+ yz is odd but w/x + y/z is even.

The former is satisfied by odd+ even and the latter by odd+odd or even +even

This will be satisfied say, if wz and w/x are both odd and yx is even and y/z is odd.

We find this cannot be satisfied

Since the contrary case cannot be proved for (ii) , this alone is sufficient and the answer is B.
_________________

Srinivasan Vaidyaraman
Sravna Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

CEO
CEO
User avatar
P
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2711
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: If w, x, y and z are integers such that w/x and y/z are  [#permalink]

Show Tags

New post 25 Aug 2016, 21:32
1
1
japped187 wrote:
If w, x, y and z are integers such that w/x and y/z are integers, is w/x + y/z odd?

(1) wx + yz is odd
(2) wz + yx is odd


Please find the solution as attached
Attachments

File comment: www.GMATinsight.com
1115.jpg
1115.jpg [ 115.29 KiB | Viewed 8974 times ]


_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Manager
Manager
User avatar
G
Joined: 10 Apr 2018
Posts: 180
If w, x, y and z are integers such that w/x and y/z are  [#permalink]

Show Tags

New post Updated on: 05 Sep 2018, 13:08
Hi,

Some important observations that could be helpful if we internalize this.

\(\frac{ODD}{EVEN}\) = never an integer and remainder is always odd.
\(\frac{3}{2}\) = never an integer value and reminder is 1,
\(\frac{191}{60}\) = never an integer remainder is 11.

\(\frac{ODD}{ODD}\) = either Odd Integer or never integer, then remainder can be either Odd or even
\(\frac{3}{1}\)= Odd integer remainder 0,
\(\frac{3}{5}\)= not an integer , remainder is 3,
\(\frac{5}{3}\)= not an integer and reminder is 2.


\(\frac{EVEN}{EVEN}\)= either Integer ( could be even or could be odd ) or could not be an integer, then remainder is always even.
\(\frac{6}{2}\)= 3 which is odd integer and remainder is 0 which is even .
\(\frac{12}{6}\)= 6 which is even integer and remainder is 0 which is even.
\(\frac{14}{4}\)= not an integer value and remainder is 2 which is even

\(\frac{EVEN}{ODD}\)= even integer or not an integer,then remainder is even or odd.
\(\frac{12}{3}\)= 4 even integer and remainder is 0
\(\frac{12}{5}\)= not an integer & reminder is 2 which is even
\(\frac{12}{7}\)= not an integer & remainder is 5 which is Odd


Now back to question,
we are given that w,x,y,z are integers and \(\frac {w}{x}\)and \(\frac{y}{z}\) are integers is \(\frac {w}{x}\)+ \(\frac{y}{z}\) = odd?

So lets say \(\frac{w}{x}\)= a , & \(\frac{y}{z}\) = b
then is a+b = odd integer . { note a, b are integers, and integer+integer= integer}
if we rearrange the terms \(\frac{wz+xy}{zx}\) = odd integer

we know that \(\frac{wz+xy}{zx}\)= integer,then we can write wz+xy= zx( integer). let this integer be denoted by k.

wz+xy= zx(k) -------(i)

Stm1 :wx+yz is odd.

adding wx+yz on both sides of equation(i)
then, wx+yz+wz+xy= k(zx)+wx+yz
so odd+ wz+xy= k(zx)+odd
or odd-odd+wz+xy= k(zx)
or even +wz+xy= k(zx)

so if wz+xy = odd then yes, if wz+xy = even then no.
So stmt 1 Insufficient .


Stmt 2: wz+xy = odd.
substituting in equation (i) we have
odd= k(zx) ,this implies k(zx) is odd { Note neither K, nor z or x is even}
So stmt 2 Sufficient .

Though , i did not use the observations above, but felt useful sharing as many Friends out here were using this approach.

Probus

Originally posted by Probus on 29 Aug 2018, 22:20.
Last edited by Probus on 05 Sep 2018, 13:08, edited 1 time in total.
Senior Manager
Senior Manager
avatar
S
Joined: 29 Jun 2017
Posts: 402
Re: If w, x, y and z are integers such that w/x and y/z are  [#permalink]

Show Tags

New post 30 Aug 2018, 07:49
japped187 wrote:
If w, x, y and z are integers such that w/x and y/z are integers, is w/x + y/z odd?

(1) wx + yz is odd
(2) wz + yx is odd


very hard.
from 1.
case 1; wx is odd and yz is even
w, x is odd and y or z is even
from here we can not know
case 2
similar to case 1,
so we can not know.
Intern
Intern
User avatar
B
Joined: 05 Oct 2017
Posts: 35
Location: Bangladesh
Concentration: Accounting, Social Entrepreneurship
Re: If w, x, y and z are integers such that w/x and y/z are  [#permalink]

Show Tags

New post 28 Oct 2018, 10:51
Bunuel wrote:
If w, x, y and z are integers such that w/x and y/z are integers, is w/x + y/z odd?

Given: \(\frac{w}{x}=integer\) and \(\frac{y}{z}=integer\). Hence, \(\frac{w}{x}+\frac{y}{z}=\frac{wz+yx}{xz}=integer\) and the question is whether this integer is odd.

(1) wx + yz is odd --> if \(w=x=1\) and \(y=z=2\) then \(\frac{w}{x}+\frac{y}{z}=2=even\) but if \(w=x=1\) and \(y=2\), \(z=1\) then \(\frac{w}{x}+\frac{y}{z}=3=odd\). Not sufficient.

(2) wz + yx is odd --> \(\frac{wz+yx}{xz}=\frac{odd}{xz}=integer\) --> \(odd=(xz)*integer\) --> all multiple must be odd in order the product to be odd, hence \(integer =odd\). Sufficient.

Answer: B.

Hope it's clear.


I don't understand the following part:
"all multiple must be odd in order the product to be odd"

Posted from my mobile device
_________________

....and now go, make glorious MISTAKES and make PROFIT from those mistakes. You are already NAKED. There is NO reason not to FOLLOW your heart.

Intern
Intern
User avatar
B
Joined: 05 Oct 2017
Posts: 35
Location: Bangladesh
Concentration: Accounting, Social Entrepreneurship
Re: If w, x, y and z are integers such that w/x and y/z are  [#permalink]

Show Tags

New post 29 Oct 2018, 03:07
1
japped187 wrote:
If w, x, y and z are integers such that w/x and y/z are integers, is w/x + y/z odd?

(1) wx + yz is odd
(2) wz + yx is odd

another way to think about this problem is:

Given
w/x is an integer so w=x * a
y/z is an integer so y=z * b
is w/x + y/z odd?
bt putting values
w/x + y/z = (x*a)/x+(z*b)/z= (a+b)= odd?
now the given statements

a. wx + yz = odd

putting these values
(x *a) x+ (z*b)z is odd
so this is a x^2 +bz^2
dont have any info about individual terms so not sufficient

b. wz + xy = odd
(x *a) z+ (z*b)x is odd
so this is xza+xzb = odd
xz(a+b)= odd
now we know that
Odd x Odd = Odd
so (a+b) = odd
hence sufficient

Posted from my mobile device
_________________

....and now go, make glorious MISTAKES and make PROFIT from those mistakes. You are already NAKED. There is NO reason not to FOLLOW your heart.

Senior Manager
Senior Manager
avatar
S
Joined: 04 Aug 2010
Posts: 310
Schools: Dartmouth College
If w, x, y and z are integers such that w/x and y/z are  [#permalink]

Show Tags

New post 29 Oct 2018, 03:12
japped187 wrote:
If w, x, y and z are integers such that w/x and y/z are integers, is w/x + y/z odd?

(1) wx + yz is odd
(2) wz + yx is odd


\(\frac{w}{x} + \frac{y}{z} = \frac{{wz + xy}}{xz}\)
Since \(\frac{w}{x}\) and \(\frac{y}{z}\) are integers, their SUM on the left side of the equation above must also be an integer.
Implication:
\(\frac{wz + xy}{xz}\) = INTEGER

Statement 1: wx + yz = odd
Case 1: w=1, x=1, y=2 and z=2, with the result that wx + yz = 1*1 + 2*2 = 5
In this case, \(\frac{w}{x} +\frac{y}{z} = \frac{1}{1} + \frac{2}{2} = 2\), so the answer to the question stem is NO.

Case 2: w=1, x=1, y=2, and z=1, with the result that wx + yz = 1*1 + 2*1 = 3
In this case, \(\frac{w}{x} + \frac{y}{z} = \frac{1}{1} + \frac{2}{1} = 3\), so the answer to the question stem is YES.
INSUFFICIENT.

Statement 2: wz + xy = ODD
Consider the following cases:
15 is an integer and \(\frac{15}{3}\) is an integer, so \(\frac{15}{3}\) is a FACTOR OF 15.
21 is an integer and \(\frac{21}{7}\)is an integer, so \(\frac{21}{7}\) is a FACTOR OF 21.
Using the same reasoning:
wz + xy is an integer and \(\frac{wz + xy}{xz}\) is an integer, so \(\frac{wz + xy}{xz}\) is a FACTOR of wz + xy.
Since wz + xy is odd, all of its factors must be odd.
Thus,\(\frac{wz + xy}{xz}\) must be odd.
Since \(\frac{wz + xy}{xz} = \frac{w}{x} + \frac{y}{z}\) = ODD, the answer to the question stem is YES.


_________________

GMAT and GRE Tutor
Over 1800 followers
Click here to learn more
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

GMAT Club Bot
If w, x, y and z are integers such that w/x and y/z are &nbs [#permalink] 29 Oct 2018, 03:12
Display posts from previous: Sort by

If w, x, y and z are integers such that w/x and y/z are

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


Copyright

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®.