It is currently 23 Sep 2017, 13:03

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

w, x, y, and z are integers. If w >x>y>z>0, is y a common

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

Hide Tags

Intern
Intern
avatar
Joined: 18 Aug 2012
Posts: 10

Kudos [?]: 9 [0], given: 1

GMAT 1: 730 Q50 V39
w, x, y, and z are integers. If w >x>y>z>0, is y a common [#permalink]

Show Tags

New post 27 Nov 2015, 01:11
Given to us : w > x > y > z > 0

In such type of questions, we have to start by reducing the given equations to a simple form and then test the simplified equations with a random number, so to quickly come to a required answer.

Using Statement 1

\(w/x=1/z+1/x\)

Simplifying the equation

\(w/x=(x+z)/xz\)
\(wz=x+z\)
\((w-1)z=x\) (Simplified Equation)

Now from the given equation \(w>x>y>z>0\), we definitely know that z minimum will be equal to 1. Substituting z=1 in the simplified equation, we get
\(w=x+1\).
From this equation, we can thus deduce that w and x are consecutive integers and it also satisfies w>x criteria. So if two numbers are consecutive to each other there can only be one number common to them (because these numbers become co-prime to each other, example 4 & 5) i.e. 1. but we definitely know y cannot be 1. It will definitely be greater than 1 because z=1 and y>z. So, y is not a common divisor of x and w.
Now, in case if z>1, then from the simplified equation, we will have x>w, which will contradict the given condition of (w>x>y>z>0).
Hence, statement 1 is sufficient is sufficient to answer the question that y is not a common divisor of x and w.

Using Statement 2

\(w^2-wy-2w=0\)

Simplifying the equation

\(w(w-y-2)=0\)
So, either \(w=0\) or \(w-y-2=0\)

w=0 is not possible because \(w>x>y>z>0\) is given to us.

Considering, \(w-y-2=0\), we get
\(w=y+2\).

Using this equation, we can conclude that there will be an integer between w and y, and that is definitely going to be x, because of the equation w>x>y>z>0.
For example, if w=6, then y becomes 4, then x has to be 5 to satisfy the equation.

So, from this statement we definitely know, that w,x and y are three consecutive integers.
Now three consecutive integers can only be co-prime to each other and can never have any common divisor in between them. There can only be one number common in between these numbers i.e. 1

So from this statement we can conclude that y is not the common divisor in between x and w.
Hence, Statment 2 is also sufficient to answer the Question.

So the Answer is D.

Kudos [?]: 9 [0], given: 1

Intern
Intern
User avatar
Joined: 11 Oct 2012
Posts: 42

Kudos [?]: 9 [0], given: 74

GMAT 1: 610 Q42 V32
GMAT ToolKit User Reviews Badge
w, x, y, and z are integers. If w >x>y>z>0, is y a common [#permalink]

Show Tags

New post 11 Mar 2016, 09:51
gmacforjyoab wrote:
enigma123 wrote:
w, x, y, and z are integers. If w > x > y > z > 0, is y a common divisor of w and x?

(1) w/x= z^-1+x^-1

(2) w^2-wy-2w=0



1 ) w/x = 1/z + 1/x
since W is greater than x , w/x should be greater than 1
hence 1/z +1/x should also be greater than 1. since x and z are integers grater than 0 , and z<x , the only way , 1/z +1/x can be >1 is if z=1
hence equation becomes - w/x= 1/1 + 1/x ======> w-1=x ..
hence x and w are consecutive integers and since y is not 1 and is >1 ( since z is 1) , the answer is NO
Sufficient

2) w^2-wy-2w=0
w(w-y-2) =0
since w != 0 w=y+2 .. w, x and y are consecutive integers . Same as statement 1 , the answer is NO.
Suff

-Jyothi


Thanks for the nice explanation !! Only this enabled me to understand the logic...
++ kudos

Kudos [?]: 9 [0], given: 74

BSchool Forum Moderator
User avatar
P
Joined: 12 Aug 2015
Posts: 2219

Kudos [?]: 806 [0], given: 595

GMAT ToolKit User Premium Member CAT Tests
Re: w, x, y, and z are integers. If w >x>y>z>0, is y a common [#permalink]

Show Tags

New post 13 Mar 2016, 23:05
Bunuel wrote:
ronr34 wrote:
PiyushK wrote:
Another concept, two consecutive numbers are co-prime thus they have only 1 as a common factor.

1> After reducing option 1 we have Z = X/(W-1) for Z to be an integer (1) and X<W, W and Z must be consecutive numbers.
And two consecutive numbers have only one common factor that is 1, bcz Y>Z>0 and Z is also an integer then Y can not be 1. Therefore, Y can not be a common divisor for both.

2> After reducing option 2.
W=Y+2 it means W,X,Y all are consecutive integers and co prime to each other. thus, again Y can not be common divisor for W and X and neither it is equal to one as restricted by given data.

Therefore, Ans D.

PiyushK - I think you meant "W and X must be consecutive numbers"... not "W and Z" :)
Bunuel - In your solution, for st. 1, you wrote
Bunuel wrote:
since w>x>z then z=1 (if z>1 then x>w which contradicts given condition)
. How did you reach this conclusion?


w > x > y > z > 0, is y a common divisor of w and x?

We have that z(w-1)=x and w>x>z>0. If z>1, say if z=2, then 2(w-1)=x. Now tell me can in this case x be less than w?



I did not understand one concept here
What if W=-10
w-1=-11
z=100
=> z*(w-1) = -200
so x=-200
also x<w is satisfied..


Regards
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 806 [0], given: 595

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124641 [0], given: 12079

Re: w, x, y, and z are integers. If w >x>y>z>0, is y a common [#permalink]

Show Tags

New post 13 Mar 2016, 23:28

Kudos [?]: 124641 [0], given: 12079

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 17622

Kudos [?]: 271 [0], given: 0

Premium Member
Re: w, x, y, and z are integers. If w >x>y>z>0, is y a common [#permalink]

Show Tags

New post 15 Mar 2017, 01:44
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 271 [0], given: 0

Expert Post
Director
Director
User avatar
B
Joined: 17 Dec 2012
Posts: 601

Kudos [?]: 508 [0], given: 16

Location: India
Re: w, x, y, and z are integers. If w >x>y>z>0, is y a common [#permalink]

Show Tags

New post 09 Aug 2017, 22:30
What is tested is whether one is able to identify a specific set of consecutive integers.

Statement 1: z has to be 1 because w/x is greater than 1. z is the smallest integer and greater than 0. If z=1, we can see that w=x+1. A number cannot be a common divisor of two consecutive integers unless it is 1. y is not 1. Sufficient.

Statement 2: We can see W=y+2 and so w=x+1. Now the same reasoning as that for statement 1 applies. Sufficient.
_________________

Srinivasan Vaidyaraman
Sravna
http://www.sravnatestprep.com/regularcourse.php

Free Online Coaching
Standardized Approaches

Kudos [?]: 508 [0], given: 16

Re: w, x, y, and z are integers. If w >x>y>z>0, is y a common   [#permalink] 09 Aug 2017, 22:30

Go to page   Previous    1   2   [ 26 posts ] 

    Similar topics Author Replies Last post
Similar
Topics:
34 EXPERTS_POSTS_IN_THIS_TOPIC If w+x<0, is w-y>0? gmatbull 29 13 Mar 2017, 10:37
7 EXPERTS_POSTS_IN_THIS_TOPIC If w + x < 0, is w - y > 0 ? uzzy12 6 20 Jun 2017, 09:53
EXPERTS_POSTS_IN_THIS_TOPIC If w < x < y < z, is wxyz > 0? (1) wz > 0 (2) xy > 0 Bunuel 3 25 Dec 2016, 00:09
94 EXPERTS_POSTS_IN_THIS_TOPIC If w, x, y and z are integers such that w/x and y/z are japped187 17 16 Sep 2017, 10:26
1 EXPERTS_POSTS_IN_THIS_TOPIC w, x, y, and z are integers. If w > x > y > z > 0, is y a co ashiima 5 04 Jan 2012, 13:37
Display posts from previous: Sort by

w, x, y, and z are integers. If w >x>y>z>0, is y a common

  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®.