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If S is a set of Four numbers w,x,y, and z, is the range of

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Intern
Joined: 17 Jun 2010
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If S is a set of Four numbers w,x,y, and z, is the range of  [#permalink]

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24 Aug 2010, 18:33
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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.

If a problem says "S is a set of four numbers w,x,y,z...."
Must one assume that w,x,y,z are 4 distinct numbers?
Meaning w,x,y,z cannot be 3,3,3, and 3?

Thank you!

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-s-is-a-set-of-four-numbers-w-x-y-and-z-is-the-range-o-166184.html
Manager
Joined: 02 Apr 2010
Posts: 100
Re: If S is a set of Four numbers w,x,y, and z, is the range of  [#permalink]

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25 Aug 2010, 02:25
Statement 1:

The range is defined as the difference between the largest and the smallest number of a set. Since the difference between w and z is greater than 2, the range must exceed 2. => Sufficient

Statement 2:

Doesn't tell us anything about the other numbers in the set except for z. => Inusufficient

Hence, choice A is correct.

To answer your question, unless it is explicitly stated otherwise, different variables (such as w,x,z, etc.) can represent the same numbers. If this were not the case, the solution to the above problem would be D (i.e. both statements alone sufficient), not A.
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Joined: 02 Sep 2009
Posts: 50613
Re: If S is a set of Four numbers w,x,y, and z, is the range of  [#permalink]

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25 Aug 2010, 03:12
vachir wrote:
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.

If a problem says "S is a set of four numbers w,x,y,z...."
Must one assume that w,x,y,z are 4 distinct numbers?
Meaning w,x,y,z cannot be 3,3,3, and 3?

Thank you!
stanford2012 wrote:
Statement 1:

The range is defined as the difference between the largest and the smallest number of a set. Since the difference between w and z is greater than 2, the range must exceed 2. => Sufficient

Statement 2:

Doesn't tell us anything about the other numbers in the set except for z. => Inusufficient

Hence, choice A is correct.

To answer your question, unless it is explicitly stated otherwise, different variables (such as w,x,z, etc.) can represent the same numbers. If this were not the case, the solution to the above problem would be D (i.e. both statements alone sufficient), not A.

Above reasoning is correct and answer is A. Though I have little correction: even if it were stated that w, x, y, and z represent distinct numbers answer still would be A, as statement (2) would just tell us that from those four distinct unknowns z is the smallest one (obviously one of unknowns would be the smallest one, what difference it makes to know that it's z?).

If it were stated that w, x, y, and z are distinct integers then yes answer would be D, but in this case question does not makes any sense as stem would be enough to answer the question: any set with 4 distinct integers has a range more than or equal to 3.

Hope it's clear.
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Re: If S is a set of Four numbers w,x,y, and z, is the range of  [#permalink]

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25 Aug 2010, 05:19
makes sense, thank you everyone.
Manager
Joined: 14 Jun 2010
Posts: 211
Re: If S is a set of Four numbers w,x,y, and z, is the range of  [#permalink]

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27 Aug 2010, 09:32
Intern
Joined: 23 Oct 2014
Posts: 11
Re: If S is a set of Four numbers w,x,y, and z, is the range of  [#permalink]

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23 Oct 2014, 10:42
Hi,
I still am not convinced with the answer as "A" since it is not mentioned the set A has consecutive numbers
the set may have A =(w,x,y,z) = (2,100,25,0)

in this case W=2 is not the largest number.

do we assume that W is the largest number? Please help me understand if i am going wrong.
Math Expert
Joined: 02 Sep 2009
Posts: 50613
Re: If S is a set of Four numbers w,x,y, and z, is the range of  [#permalink]

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24 Oct 2014, 02:06
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Nab77 wrote:
Hi,
I still am not convinced with the answer as "A" since it is not mentioned the set A has consecutive numbers
the set may have A =(w,x,y,z) = (2,100,25,0)

in this case W=2 is not the largest number.

do we assume that W is the largest number? Please help me understand if i am going wrong.

It's not necessary w to be the largest number. Check complete solution below.

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-s-is-a-set-of-four-numbers-w-x-y-and-z-is-the-range-o-166184.html
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Re: If S is a set of Four numbers w,x,y, and z, is the range of  [#permalink]

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02 Nov 2018, 15:07
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Re: If S is a set of Four numbers w,x,y, and z, is the range of &nbs [#permalink] 02 Nov 2018, 15:07
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