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# M14-18

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Math Expert
Joined: 02 Sep 2009
Posts: 55631

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16 Sep 2014, 00:53
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Difficulty:

55% (hard)

Question Stats:

47% (01:07) correct 53% (01:06) wrong based on 59 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.

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:53
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, 13:52
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: 29 Jan 2018
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01 Mar 2019, 19:37
Hi Bunuel,
I think there is some gap in the question.
S1: states "Positive difference between any two elements of set S is 2." Eg: if set S={2,4,6,8} or{1,3,5,7}or any other combination with a difference 2, then the no. of elements cannot be determined since difference between any 2 elements is 2, however number of elements are varying.
S2: states "Range is 2". this is also inconsistent because if S={1,1,2,2,3,3,3}or{1,3}or {2,2,4,4} in such a case range 2 but number of elements are varying!!

combining both the inferences we say S={1,3} or {2,4} or....... as range is 2 and positive difference is also 2. Hence I think the correct choice is C.
Kindly correct me if I am wrong.
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Joined: 02 Sep 2009
Posts: 55631

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02 Mar 2019, 04:24
keerthisagarch wrote:
Hi Bunuel,
I think there is some gap in the question.
S1: states "Positive difference between any two elements of set S is 2." Eg: if set S={2,4,6,8} or{1,3,5,7}or any other combination with a difference 2, then the no. of elements cannot be determined since difference between any 2 elements is 2, however number of elements are varying.
S2: states "Range is 2". this is also inconsistent because if S={1,1,2,2,3,3,3}or{1,3}or {2,2,4,4} in such a case range 2 but number of elements are varying!!

combining both the inferences we say S={1,3} or {2,4} or....... as range is 2 and positive difference is also 2. Hence I think the correct choice is C.
Kindly correct me if I am wrong.

The difference between ANY two elements of set S is 2.

S cannot be {2, 4, 6, 8} or {1, 3, 5, 7}. Are the difference between ANY two elements of set S 2? No. For example, 8 - 2 = 6 and 7-3 = 4.
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Re: M14-18   [#permalink] 02 Mar 2019, 04:24
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# M14-18

Moderators: chetan2u, Bunuel