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# m14 q18

Author Message
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 $$(0, 2)$$ .

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: 2021
Followers: 157

Kudos [?]: 1560 [0], given: 376

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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 $$(0, 2)$$ .

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
_________________
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

### Show Tags

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

Moderator: Bunuel

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