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Set S is comprised of six distinct positive integers less
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29 Oct 2017, 04:03
29 Oct 2017, 04:03
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61% (01:10) correct
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Set S is comprised of six distinct positive integers less than 10. Which of the following must be true?
I: The median is an integer
II: The median is less than the average
III: The range of digits in Set S is less than 8
(A) I only
(B) I & II
(C) II & III
(D) III only
(E) None of the above.
Kudos for correct solution.
I: The median is an integer
II: The median is less than the average
III: The range of digits in Set S is less than 8
(A) I only
(B) I & II
(C) II & III
(D) III only
(E) None of the above.
Kudos for correct solution.
Re: Set S is comprised of six distinct positive integers less
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30 Oct 2017, 09:43
30 Oct 2017, 09:43
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Let's check each choice one by one:
I. Since there are six integers, the median is the mean of the two central values which may be both an integer (if the two numbers are equal) or a fraction (if the numbers are different)
II. To know if the median is less than the average we should know the numbers in the set. Indeed, it can be the case but also the opposite or they can even be equal
III. The range could be 8 is the lowest number is 0 and the largest is 8, thus it is not necessarily less than 8
Answer E
I. Since there are six integers, the median is the mean of the two central values which may be both an integer (if the two numbers are equal) or a fraction (if the numbers are different)
II. To know if the median is less than the average we should know the numbers in the set. Indeed, it can be the case but also the opposite or they can even be equal
III. The range could be 8 is the lowest number is 0 and the largest is 8, thus it is not necessarily less than 8
Answer E
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Re: Set S is comprised of six distinct positive integers less
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23 Mar 2022, 12:11
23 Mar 2022, 12:11
Bunuel wrote:
Set S is comprised of six distinct positive integers less than 10. Which of the following must be true?
I: The median is an integer
II: The median is less than the average
III: The range of digits in Set S is less than 8
(A) I only
(B) I & II
(C) II & III
(D) III only
(E) None of the above.
Kudos for correct solution.
I: The median is an integer
II: The median is less than the average
III: The range of digits in Set S is less than 8
(A) I only
(B) I & II
(C) II & III
(D) III only
(E) None of the above.
Kudos for correct solution.
It could be the case that set S is {1, 2, 4, 5, 8, 9}
In this case, the median = (4 + 5)/2 = 4.5
Since 4.5 is not an integer, we can eliminate answer choices A and B since they state that the median must be an integer.
Also, in the set above, the range = 9 - 1 = 8
Since the range is NOT less than 8, we can eliminate answer choices C and D since they state that the range must be less than 8.
By the process of elimination, the correct answer is E.
