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

It is currently 09 Dec 2019, 21:26

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

On the number line above, is the product of w, x, y and z negative?

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

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
B
Joined: 14 Feb 2016
Posts: 68
On the number line above, is the product of w, x, y and z negative?  [#permalink]

Show Tags

New post Updated on: 25 Feb 2016, 08:45
1
3
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

91% (00:53) correct 9% (00:46) wrong based on 188 sessions

HideShow timer Statistics

Image
On the number line above, is the product of w, x, y, and z negative?

(1) z is positive.
(2) The product of w and x is positive

Correct answer: statement (1) and (2) together are not sufficient.

Therefore, my question how would one come to find out if the product of the line above is negative?
What's the underlying concept/method to apply?

Please help. My math knowledge is extremely basic and I have to study from the ground up. Therefore I am looking to understand what math concept I must master in order to easily answer such a question.


Attachment:
number line.png
number line.png [ 2.81 KiB | Viewed 6127 times ]

Originally posted by CLIMBTHELADDER on 25 Feb 2016, 07:28.
Last edited by Bunuel on 25 Feb 2016, 08:45, edited 2 times in total.
Renamed the topic and edited the question.
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2560
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Re: On the number line above, is the product of w, x, y and z negative?  [#permalink]

Show Tags

New post 25 Feb 2016, 08:31
1
1
aadirenpronk wrote:
[<------w------x--y----z------->

On the number line above, is the product of w, x, y and z negative?

1) z is positive

2) the product of w and x is positive

Correct answer: statement (1) and (2) together are not sufficient.

Therefore, my question how would one come to find out if the product of the line above is negative?
What's the underlying concept/method to apply?

Please help. My math knowledge is extremely basic and I have to study from the ground up. Therefore I am looking to understand what math concept I must master in order to easily answer such a question.


Follow posting guidelines (link in my signatures). Do add the OA with your questions and format the analyses in the main question. Any and all analyses should either be put in the next post or put under "spoilers".

Refer below for the solution. The concepts tested are : Number properties (number line).

You are given the number line with the following important interpretation: w<x<y<z. Now, without knowing where is 0 wrt these 4 variables, we can not know what will be the sign of w*x*y*z .

Per statement 1, z>0 doesnt help. What if w,x,y are all positive ---> you will get wxyz >0 , so a "no" to the question asked "is wxyz < 0" but if w,x,y are all negative , then you will get wxyz < 0 , giving you a "yes" to the question asked. Also do note that this statement also tells you that z \(\neq\) 0 . Not sufficient.

Per statement 2, wx>0 ---> both w and x are of same sign (++ or - - ). Also do note that this statement also tells you that w or x \(\neq\) 0 . Again, relative signs of w and x are not sufficient to answer the question asked.

Combining the 2 statements we get, z>0 and wx>0 ---> 2 cases ( with the 3rd case not important for this question but might be for some other similar question)

Case 1: z>0, wx>0, y >0 ---> wxyz >0 , "no" to the question asked.

Case 2: z>0, wx>0 , y< 0 ---> wxyz < 0 , "yes" to the question asked.

Case 3: z>0, wx>0, y=0 ---> wxyz=0 . "no" to the question asked. Do note here that 0 is neither positive nor negative.

Thus, you still do not get a unambiguous yes or no for the question asked ---> E is thus the correct answer.

Hope this helps.
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8245
GMAT 1: 760 Q51 V42
GPA: 3.82
On the number line above, is the product of w, x, y and z negative?  [#permalink]

Show Tags

New post 25 Feb 2016, 18:25
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

On the number line above, is the product of w, x, y, and z negative?

(1) z is positive.
(2) The product of w and x is positive


In the original condition and the question, there are 4 variables(w,x,y,z), which should match with the number of equations. So you need 4 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer.
When 1) & 2), if 0 is in between x and y, it is no. If o is in between y and z, it is yes, which is not sufficient.
Therefore, the answer is E.


 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
IIMA, IIMC School Moderator
User avatar
V
Joined: 04 Sep 2016
Posts: 1370
Location: India
WE: Engineering (Other)
CAT Tests
Re: On the number line above, is the product of w, x, y and z negative?  [#permalink]

Show Tags

New post 23 May 2018, 07:47
1
Quote:
Image


On the number line above, is the product of w, x, y, and z negative?

(1) z is positive.
(2) The product of w and x is positive


niks18 gmatbusters Bunuel VeritasPrepKarishma amanvermagmat

Please validate below approach:
Clearly statements when individually taken are insufficient.

When together:
Product of w and x is positive, implies either both w and x are positive or
both are negative. Now since y lies between x and z, it can take a positive or
negative value. Hence irrespective of z being positive, we can still have final product
as positive or negative.
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1318
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: On the number line above, is the product of w, x, y and z negative?  [#permalink]

Show Tags

New post 23 May 2018, 07:57
On the number line above, is the product of w, x, y, and z negative?

(1) z is positive.
it gives no info about the nature of sign of w, x, y . hence insufficient.

(2) The product of w and x is positive
it means either :
i)both w & x are positive : now y and z should also be positive, since they are on right side of w & x. hence product is positive.

ii)or both w & x are negative.: here there are 3 cases,
a) w, x, y, z = negative. product = positive
b) w, x, y = negative, z = positive. product = negative.
c) w, x= negative, y, z = positive. product = positive.

Hence insufficient.

No even after combining St 1 & 2 , we get
w, x, y = negative, z = positive. product = negative.
OR, w, x= negative, y, z = positive. product = positive.

so it is still INSUFFICIENT.

Answer = E


adkikani wrote:
Quote:
Image


On the number line above, is the product of w, x, y, and z negative?

(1) z is positive.
it gives no info about the nature of sign of w, x, y . hence insufficient.
(2) The product of w and x is positive




Please validate below approach:
Clearly statements when individually taken are insufficient.

When together:
Product of w and x is positive, implies either both w and x are positive or
both are negative. Now since y lies between x and z, it can take a positive or
negative value. Hence irrespective of z being positive, we can still have final product
as positive or negative.

_________________
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9859
Location: Pune, India
Re: On the number line above, is the product of w, x, y and z negative?  [#permalink]

Show Tags

New post 23 May 2018, 08:45
1
adkikani wrote:
Quote:
Image


On the number line above, is the product of w, x, y, and z negative?

(1) z is positive.
(2) The product of w and x is positive


niks18 gmatbusters Bunuel VeritasPrepKarishma amanvermagmat

Please validate below approach:
Clearly statements when individually taken are insufficient.

When together:
Product of w and x is positive, implies either both w and x are positive or
both are negative. Now since y lies between x and z, it can take a positive or
negative value. Hence irrespective of z being positive, we can still have final product
as positive or negative.


Yes your logic is correct.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1318
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: On the number line above, is the product of w, x, y and z negative?  [#permalink]

Show Tags

New post 23 May 2018, 09:05
Your Query :
"When together:
Product of w and x is positive, implies either both w and x are positive or both are negative. Now since y lies between x and z, it can take a positive or negative value. Hence irrespective of z being positive, we can still have final product as positive or negative."


If Z is negative, We can conclude that w,x,y,z all are negative, or the product WXYZ is positive.

So your understanding, irrespective of z being positive, we can still have final product
as positive or negative
, doesn't seem right.

VeritasPrepKarishma, Please correct me.

adkikani wrote:
Quote:
Image


On the number line above, is the product of w, x, y, and z negative?

(1) z is positive.
(2) The product of w and x is positive




Please validate below approach:
Clearly statements when individually taken are insufficient.

When together:
Product of w and x is positive, implies either both w and x are positive or
both are negative. Now since y lies between x and z, it can take a positive or
negative value. Hence irrespective of z being positive, we can still have final product
as positive or negative.

_________________
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13734
Re: On the number line above, is the product of w, x, y and z negative?  [#permalink]

Show Tags

New post 19 Nov 2019, 16:02
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 Club Bot
Re: On the number line above, is the product of w, x, y and z negative?   [#permalink] 19 Nov 2019, 16:02
Display posts from previous: Sort by

On the number line above, is the product of w, x, y and z negative?

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





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