Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49960

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:
60% (00:46) correct 40% (00:56) wrong based on 737 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.
_________________
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? Extrahard Quant Tests with Brilliant Analytics




Math Expert
Joined: 02 Sep 2009
Posts: 49960

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




Director
Joined: 03 Feb 2013
Posts: 862
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)
_________________
Thanks, Kinjal My Debrief : http://gmatclub.com/forum/hardworknevergetsunrewardedforever189267.html#p1449379 My Application Experience : http://gmatclub.com/forum/hardworknevergetsunrewardedforever18926740.html#p1516961 Linkedin : https://www.linkedin.com/in/kinjaldas/
Please click on Kudos, if you think the post is helpful



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: 12660
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
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



Manager
Joined: 12 Jun 2016
Posts: 217
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?
_________________
My Best is yet to come!



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12660
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
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



NonHuman User
Joined: 09 Sep 2013
Posts: 8429

Re: If S is a set of four numbers w, x, y, and z, is the range o
[#permalink]
Show Tags
27 Sep 2018, 08:38
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




Re: If S is a set of four numbers w, x, y, and z, is the range o &nbs
[#permalink]
27 Sep 2018, 08:38






