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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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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If 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


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Re: If S is a set of four numbers w, x, y, and z, is the range o [#permalink]

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SOLUTION

If 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.
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Re: If S is a set of four numbers w, x, y, and z, is the range o [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If 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) w-z > 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 [#permalink]

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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 [#permalink]

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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.

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Re: If S is a set of four numbers w, x, y, and z, is the range o [#permalink]

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New post 07 Aug 2017, 07:03
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 [#permalink]

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Hi susheelh,

Yes - if you know 2 (or more) of the values in a set, then you know the MINIMUM value of the RANGE.

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Re: If S is a set of four numbers w, x, y, and z, is the range o   [#permalink] 07 Aug 2017, 11:16
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