Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 18 Apr 2013
Posts: 34

On the number line, there are 4 points w,x,y and z, in an ascending
[#permalink]
Show Tags
05 Jul 2017, 09:31
Question Stats:
63% (01:22) correct 37% (01:38) wrong based on 164 sessions
HideShow timer Statistics
On the number line, there are 4 points w,x,y and z, in an ascending order. If wxyz<0, which of the following must be positive? 1) wx 2) xy 3) yz A) 1 only B) 2 only C) 3 only D) 1 and 3 only E) 2 and 3 only
Official Answer and Stats are available only to registered users. Register/ Login.



Director
Joined: 05 Mar 2015
Posts: 986

Re: On the number line, there are 4 points w,x,y and z, in an ascending
[#permalink]
Show Tags
05 Jul 2017, 10:14
roastedchips wrote: On the number line, there are 4 points w,x,y and z, in an ascending order. If wxyz<0, which of the following must be positive?
1) wx 2) xy 3) yz
A) 1 only B) 2 only C) 3 only D) 1 and 3 only E) 2 and 3 only for wxyz<0 two cases on number line is possible case 1 : w<0 & z>y>x>0 case 2: w<x<y<0 & z>0 A) wx wx results >0 with case 2 & wx<0 with case 1.........Discard B)xy both cases we have xy>0.........Keep it C) yz yz results >0 with case 1 & yz<0 with case 2.........Discard Only B satiesfies Ans B



SC Moderator
Joined: 22 May 2016
Posts: 1903

On the number line, there are 4 points w,x,y and z, in an ascending
[#permalink]
Show Tags
05 Jul 2017, 11:47
roastedchips wrote: On the number line, there are 4 points w,x,y and z, in an ascending order. If wxyz<0, which of the following must be positive?
1) wx 2) xy 3) yz
A) 1 only B) 2 only C) 3 only D) 1 and 3 only E) 2 and 3 only For the product of two or more numbers to be negative, there must be an odd number of negative factors. Here there are four numbers. Either only one is negative, or three are negative. I assigned values. Ascending order, smallest to greatest, is w<x<y<z. Case A: if only one factor is negative, we have: w<x<y<z ==> 1 < 2 < 3 < 4 Here, w is the one negative factor, and x, y, and z are positive Case B: If there are three negative factors, we have w<x<y<z ==> 4 < 3 < 2 < 1 Here, w,x, and y are negative, and z is positive. Assess options for "must be positive." I. wx  In Case A, wx is negative. Reject. II. xy  In both Case A and B, xy is positive because x and y have the same sign. Keep. III. yz  In Case B, yz is negative. Reject. Only II is true. Answer B.
_________________
In the depths of winter, I finally learned that within me there lay an invincible summer.  Albert Camus, "Return to Tipasa"



Intern
Joined: 11 Aug 2016
Posts: 47
Location: India
Concentration: Operations, General Management
GPA: 3.95
WE: Design (Manufacturing)

Re: On the number line, there are 4 points w,x,y and z, in an ascending
[#permalink]
Show Tags
05 Jul 2017, 11:52
roastedchips wrote: On the number line, there are 4 points w,x,y and z, in an ascending order. If wxyz<0, which of the following must be positive?
1) wx 2) xy 3) yz
A) 1 only B) 2 only C) 3 only D) 1 and 3 only E) 2 and 3 only w,x,y and z are on the number line in ascending order. Since wxyz is <0, none of w,x,y,z can be 0. 0 can take 5 different places but we need to find cases when wxyz <0 Case 1 w<x<y<z<0 => wxyz>0 => discard case Case 2 w<x<y<0<z => wxyz<0 => wx is +ve, xy is +ve yz is ve Case 3 w<x<0<y<z => wxyz>0 => discard case Case 4: w<0<x<y<z => wxyz<0 => wx is ve, xy is +ve, yz is +ve Case 5 0<w<x<y<z => wxyz>0 => Discard Only for cases 2 and 4, wxyz<0. Now we will check the signs of wx, xy and yz wx ve for case 4 => Not always +ve => 1) must not be true xy +ve for both cases => xy is always +ve => 2) must be true yz ve for case 2 => not always +ve => 3) must not be true. Only 2) must be true Answer B



Manager
Joined: 23 May 2017
Posts: 243
Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)

Re: On the number line, there are 4 points w,x,y and z, in an ascending
[#permalink]
Show Tags
05 Jul 2017, 13:33
Attachment:
FullSizeRender (7).jpg [ 61.7 KiB  Viewed 1537 times ]
+B
_________________
If you like the post, please award me Kudos!! It motivates me



Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 1167
Location: India
WE: Engineering (Other)

On the number line, there are 4 points w,x,y and z, in an ascending
[#permalink]
Show Tags
11 Jul 2018, 18:40
chetan2u pikolo2510 VeritasPrepKarishma Bunuel pushpitkc niks18Any other option than testing cases?
_________________
It's the journey that brings us happiness not the destination.



PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1201
Location: India
GPA: 3.82

Re: On the number line, there are 4 points w,x,y and z, in an ascending
[#permalink]
Show Tags
11 Jul 2018, 22:36
adkikani wrote: hi adkikaniYou will have to work through case based scenarios as \(wxyz<0\) so \(z>0\) and a situation where \(x<0\) and \(y>0\) is not possible. because in that case \(wxyz>0\) So Now only two cases remain Case 1: \(w,x,y<0\) & \(z>0\) This case will give Option 1 & Option 2 as positive solutions. Case 2: \(w<0\) & \(x,y,z>0\) This case will give Option 2 as the only Solution. As this is a Must be true question, so only Option 2 holds in all the scenarios.



BSchool Forum Moderator
Joined: 05 Jul 2017
Posts: 471
Location: India
GPA: 4

Re: On the number line, there are 4 points w,x,y and z, in an ascending
[#permalink]
Show Tags
12 Jul 2018, 00:52
I did it in this way Only two possible cases satisfy the above condition w x y z 1)    + 2)  + + + In the both the above cases, only xy is positive. Hence answer is B
_________________
My journey From 410 to 700 Here's my experience when I faced a glitch in my GMAT Exam Don't do this mistake when you give your GMATPrep Mock! NEW GMATPrep software analysis by Bunuel




Re: On the number line, there are 4 points w,x,y and z, in an ascending &nbs
[#permalink]
12 Jul 2018, 00:52






