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16 Sep 2014, 00:53
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If list S contains more than one element, how many elements are in list S?
(1) The positive difference between any two elements of list S is 2.
(2) The range of list S is 2.
(1) The positive difference between any two elements of list S is 2.
(2) The range of list S is 2.
16 Sep 2014, 00:53
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Official Solution:
If list S contains more than one element, how many elements are in list S?
(1) The positive difference between any two elements of list S is 2.
Given that the difference between ANY two elements is 2, the list cannot contain more than two elements. Otherwise, we could find a pair of elements with a difference other than 2. To illustrate, consider a list with two elements, 1 and 3. If we add a third element, say 1, then the difference between the two 1s is 0, not 2. Similarly, if the third element is 3, the difference between the two 3s is 0, not 2. This confirms the list can't have more than two elements and since the list contains more than one element, it contains exactly two elements. Sufficient.
(2) The range of list S is 2.
This is clearly insufficient. For instance, consider \(S=\{0, 2\}\) and \(S=\{0, 0, 2\}\).
Answer: A
If list S contains more than one element, how many elements are in list S?
(1) The positive difference between any two elements of list S is 2.
Given that the difference between ANY two elements is 2, the list cannot contain more than two elements. Otherwise, we could find a pair of elements with a difference other than 2. To illustrate, consider a list with two elements, 1 and 3. If we add a third element, say 1, then the difference between the two 1s is 0, not 2. Similarly, if the third element is 3, the difference between the two 3s is 0, not 2. This confirms the list can't have more than two elements and since the list contains more than one element, it contains exactly two elements. Sufficient.
(2) The range of list S is 2.
This is clearly insufficient. For instance, consider \(S=\{0, 2\}\) and \(S=\{0, 0, 2\}\).
Answer: A
01 Mar 2019, 19:37
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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.
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.
