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If S is a set of Four numbers w,x,y, and z, is the range of [#permalink]
24 Aug 2010, 18:33

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

74% (02:42) correct
26% (00:45) wrong based on 35 sessions

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?

Re: variables for a set [#permalink]
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.

Re: variables for a set [#permalink]
25 Aug 2010, 03:12

Expert's post

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.