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# m14 q18

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Intern
Joined: 25 Jan 2011
Posts: 15
Concentration: Marketing, Entrepreneurship
Schools: Foster (M)
GPA: 3.62
WE: Design (Other)
Followers: 0

Kudos [?]: 7 [0], given: 2

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31 Oct 2011, 12:44
I'm pretty confused on the question below...

If set $$S$$ consists of distinct numbers such that the difference between any two different elements of set $$S$$ is an integer, how many elements does set $$S$$ contain?

1 The difference between any two different elements of set $$S$$ is 2.
2 The range of set $$S$$ is 2.

Statement (1) by itself is sufficient. S1 says that there are only two different elements in the set. As all elements in the set are distinct, we can conclude that set $$S$$ contains 2 elements.

Statement (2) by itself is insufficient. Consider $$(-1, 0, 1)$$ and $$(0, 2)$$ .
The correct answer is A.

Am I missing something here? Where on earth does it say in S1 that there are only two elements in the set? To me, it says that the difference between ANY two elements is 2. Which means that the set could be (0,2,4,6,8,12) or just (2,4).

Can anyone please offer an explanation?
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2013
Followers: 163

Kudos [?]: 1822 [0], given: 376

Re: m14 q18 [#permalink]

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31 Oct 2011, 13:30
ModRos wrote:
I'm pretty confused on the question below...

If set $$S$$ consists of distinct numbers such that the difference between any two different elements of set $$S$$ is an integer, how many elements does set $$S$$ contain?

1 The difference between any two different elements of set $$S$$ is 2.
2 The range of set $$S$$ is 2.

Statement (1) by itself is sufficient. S1 says that there are only two different elements in the set. As all elements in the set are distinct, we can conclude that set $$S$$ contains 2 elements.

Statement (2) by itself is insufficient. Consider $$(-1, 0, 1)$$ and $$(0, 2)$$ .
The correct answer is A.

Am I missing something here? Where on earth does it say in S1 that there are only two elements in the set? To me, it says that the difference between ANY two elements is 2. Which means that the set could be (0,2,4,6,8,12) or just (2,4).

Can anyone please offer an explanation?

ANY two means ANY two, not just the consecutive two:
(0,2,4,6,8,12)
0-2=2
2-4=2
4-6=2
OKAY
how about 0-8=8{:Falsifies the statement.}
_________________
Intern
Joined: 25 Jan 2011
Posts: 15
Concentration: Marketing, Entrepreneurship
Schools: Foster (M)
GPA: 3.62
WE: Design (Other)
Followers: 0

Kudos [?]: 7 [0], given: 2

Re: m14 q18 [#permalink]

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31 Oct 2011, 13:48
Oh geez. That was so obvious, my brain just didn't "see" it for some reason. Thank you!
Re: m14 q18   [#permalink] 31 Oct 2011, 13:48
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# m14 q18

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