Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59590

If S is a set of four numbers w, x, y, and z, is the range o
[#permalink]
Show Tags
17 Jan 2014, 02:27
Question Stats:
56% (01:02) correct 44% (01:06) wrong based on 1113 sessions
HideShow timer Statistics
The Official Guide For GMAT® Quantitative Review, 2ND EditionIf S is a set of four numbers w, x, y, and z, is the range of the numbers in S greater than 2 ? (1) w  z > 2 (2) z is the least number in S. Data Sufficiency Question: 41 Category: Arithmetic Statistics Page: 156 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.
_________________




Math Expert
Joined: 02 Sep 2009
Posts: 59590

Re: If S is a set of four numbers w, x, y, and z, is the range o
[#permalink]
Show Tags
17 Jan 2014, 02:27
SOLUTIONIf S is a set of four numbers w, x, y, and z, is the range of the numbers in S greater than 2 ?(1) w  z > 2. The range of a set is the difference between the largest and the smallest elements of the set, since the difference of some particular two numbers are already more than 2 then the the range must also be more than 2. Sufficient. (2) z is the least number in S > just says that from four unknowns z is the smallest one (obviously one of the unknowns would be the smallest one, what difference does it make to know that it's z?). Not sufficient. Answer: A.
_________________




Director
Joined: 03 Feb 2013
Posts: 835
Location: India
Concentration: Operations, Strategy
GPA: 3.88
WE: Engineering (Computer Software)

Re: If S is a set of four numbers w, x, y, and z, is the range o
[#permalink]
Show Tags
17 Jan 2014, 12:00
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIf S is a set of four numbers w, x, y, and z, is the range of the numbers in S greater than 2 ? (1) w  z > 2 (2) z is the least number in S. The Range of a set is defined as highest element of the set  lowest element of the set. Statement 1) wz > 2. We don't know if w is the highest or z is lowest elements of the set. But we don't require that information. As if w is not the highest element and z is not the lowest element, then the highest  lowest will be more than 2. Sufficient. Statement 2) z is the least number in S. we don't know the value of z and also we don't know the value of highest element of the set. We cannot determine if the range of the set > 2 Not Sufficient. Hence Option A)



Intern
Joined: 22 Jun 2015
Posts: 1

Re: If S is a set of four numbers w, x, y, and z, is the range o
[#permalink]
Show Tags
01 Aug 2015, 12:39
I got this one wrong and had difficulty fully understanding Bunuel's explanation. Here's how I reasoned through it:
(1) Range is max  min. There are various possibilities for the values of w and z: (a) If W is max and Z is not min, then the range must be >2 (because a number smaller than Z will be subtracted from W). (b) If W is not max and Z is min, the range must also be >2 (because Z will be subtracted from a number larger than W). (c) If W is not max and Z is not min, the range must be >2 (because a number smaller than Z will be subtracted from a number larger than W).
Statement 1 is sufficient.
(2) Doesn't tell us about the values of w, x or y. Therefore, there is no way to determine if the range is >2.
Statement 2 is not sufficient.
Answer: A
I think my reasoning for Statement 1 is right but it took me a bit of time to get to it. Not sure if there is a shortcut to reaching the above conclusion.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15669
Location: United States (CA)

Re: If S is a set of four numbers w, x, y, and z, is the range o
[#permalink]
Show Tags
01 Aug 2015, 20:26
Hi wongylo, From your explanation, it looks like you considered all three possible 'relationships' between W and Z (from the information provided in Fact 1). By focusing on the specifics of what the given question asked, you could have combined all of those ideas into one big idea and saved some time... We're told that there are 4 numbers. We're asked if the RANGE of those 4 numbers is greater than 2. Notice that '2' is a relatively small range for 4 values. For example, if the 4 values were consecutive integers, then the range would be 3. To end up with a range that is 2 or less, we'd need duplicate numbers or 4 numbers that included decimal points and were close together. From Fact 1, we're told that W and Z differ by MORE than 2...so who cares what the other two numbers are. The range MUST be greater than 2. Fact 1 is SUFFICIENT. GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Manager
Joined: 12 Jun 2016
Posts: 205
Location: India
Concentration: Technology, Leadership
WE: Sales (Telecommunications)

Re: If S is a set of four numbers w, x, y, and z, is the range o
[#permalink]
Show Tags
07 Aug 2017, 08:03
Hello Bunuel and EMPOWERgmatRichC, After going through S1/Fact1 in this question, would I be wrong if I generalize as follows  For ANY given set the Range is always greater than or equal to the difference between any two elements of the set?
_________________



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15669
Location: United States (CA)

Re: If S is a set of four numbers w, x, y, and z, is the range o
[#permalink]
Show Tags
07 Aug 2017, 12:16
Hi susheelh, Yes  if you know 2 (or more) of the values in a set, then you know the MINIMUM value of the RANGE. GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Intern
Joined: 11 Feb 2019
Posts: 12

Re: If S is a set of four numbers w, x, y, and z, is the range o
[#permalink]
Show Tags
01 May 2019, 01:41
What is the range of a singleton? For example {5}



Manager
Joined: 15 Jul 2016
Posts: 105
Location: India

If S is a set of four numbers w, x, y, and z, is the range o
[#permalink]
Show Tags
Updated on: 29 Jul 2019, 06:57
Important property : Range of a subset is lesser or equal to that of main set.
Here (w,z) is a subset and its range is greater than 2 > The range of the main set will also be greater than 2.
Originally posted by Hanzel101 on 29 Jul 2019, 06:54.
Last edited by Hanzel101 on 29 Jul 2019, 06:57, edited 1 time in total.



NonHuman User
Joined: 09 Sep 2013
Posts: 13726

Re: If S is a set of four numbers w,x,y and z, is the range of
[#permalink]
Show Tags
26 Sep 2019, 03:53
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.
_________________




Re: If S is a set of four numbers w,x,y and z, is the range of
[#permalink]
26 Sep 2019, 03:53






