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# M14-18

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:53
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55% (hard)

Question Stats:

47% (00:28) correct 53% (00:46) wrong based on 89 sessions

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If set $$S$$ contain more than 1 element, how many elements does set $$S$$ contain?

(1) The difference between any two elements of set $$S$$ is 2.

(2) The range of set $$S$$ is 2.
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:53
Official Solution:

(1) The difference between any two elements of set $$S$$ is 2. Since the difference between ANY two elements is 2 then there cannot be more than 2 elements in the set, else we could select some particular two elements whose difference wouldn't be 2. Sufficient.

(2) The range of set $$S$$ is 2. Clearly insufficient, consider: $$S=\{0, 2\}$$ and $$S=\{0, 0, 2\}$$.

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29 Nov 2014, 12:52
Dear Math God Bunuel,
is there a way of solving this problem using algebra?
I tried solving the equations for statement (1) : x-y=2 and y-x=2 but I could not find any solution.
What would be a pair of numbers, which could be in set S ?
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Joined: 20 Jul 2012
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02 Mar 2017, 00:59
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Bunuel wrote:
If set $$S$$ contain more than 1 element, how many elements does set $$S$$ contain?

(1) The difference between any two elements of set $$S$$ is 2.

(2) The range of set $$S$$ is 2.

Dear Bunuel,
One questions, here....... Stmt 1 says : - The difference between any two elements of set S is 2
Now, if the set elements are {0,2} difference between first element and the second element is not 2 its -2 i.e 0-2 = -2

i could not construct a set where the difference between ANY 2 ELEMENTS is 2;
Perhaps, it could be that the +ve difference or mod of the difference of the 2 elements ....is a more accurate statement.

Please correct my understanding above.
Math Expert
Joined: 02 Sep 2009
Posts: 43789

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07 Mar 2017, 00:35
grsm wrote:
Bunuel wrote:
If set $$S$$ contain more than 1 element, how many elements does set $$S$$ contain?

(1) The difference between any two elements of set $$S$$ is 2.

(2) The range of set $$S$$ is 2.

Dear Bunuel,
One questions, here....... Stmt 1 says : - The difference between any two elements of set S is 2
Now, if the set elements are {0,2} difference between first element and the second element is not 2 its -2 i.e 0-2 = -2

i could not construct a set where the difference between ANY 2 ELEMENTS is 2;
Perhaps, it could be that the +ve difference or mod of the difference of the 2 elements ....is a more accurate statement.

Please correct my understanding above.

You are right. Edited as suggested. Thank you.
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Re: M14-18   [#permalink] 07 Mar 2017, 00:35
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# M14-18

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