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If S is a set of four numbers w, x, y, and z, is the range o
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17 Jan 2014, 02:27
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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!
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Re: If S is a set of four numbers w, x, y, and z, is the range o
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Re: If S is a set of four numbers w, x, y, and z, is the range o
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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)
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Re: If S is a set of four numbers w, x, y, and z, is the range o
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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.



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Re: If S is a set of four numbers w, x, y, and z, is the range o
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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
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Re: If S is a set of four numbers w, x, y, and z, is the range o
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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?
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Re: If S is a set of four numbers w, x, y, and z, is the range o
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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
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