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a, b, and c are integers in the set {a, b, c, 51,85,72}.

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a, b, and c are integers in the set {a, b, c, 51,85,72}.  [#permalink]

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New post 20 Sep 2013, 16:39
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a, b, and c are integers in the set {a, b, c, 51,85,72}. Is the median of the set greater than 70?

(1) b>c>69
(2) a<c<71
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Re: a, b, and c are integers in the set {a, b, c, 51,85,72}.  [#permalink]

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New post 20 Sep 2013, 17:56
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a, b, and c are integers in the set {a, b, c, 51, 85, 72}. Is the median of the set greater than 70?

The median of 6 integers is the average of the middle two, when arranged in ascending/descending order.

(1) b > c > 69 --> the least values of c and b are 70 and 71, respectively. Even if a is the smallest of the numbers the median = (70 + 71)/2>70 (the set in this case is{a, 51, 70, 71, 72, 85}). Sufficient.

(2) a < c < 71. If a=69, b=70, and c is the smallest number, then the set is {c, 51, 69, 70, 72, 85} and the median is less than 70 but if a=69, b=70, and c is the largest number, then the set is {51, 69, 70, 72, 85, c} and the median is greater than 70. Not sufficient.

Answer: A.
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Re: a, b, and c are integers in the set {a, b, c, 51,85,72}.  [#permalink]

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New post 21 Sep 2013, 01:51
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Well, Bunnel i have a question over here - As the question does not specify whether the integers are different or not - in that case if we take 70 and 70 in the first statement than in that case answer will be different - am i right?
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Re: a, b, and c are integers in the set {a, b, c, 51,85,72}.  [#permalink]

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New post 21 Sep 2013, 02:38
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Re: a, b, and c are integers in the set {a, b, c, 51,85,72}.  [#permalink]

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New post 21 Sep 2013, 02:41
Yeah !!! Missed that one :) One has to be greater than 69.

Well, thanks.
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Re: a, b, and c are integers in the set {a, b, c, 51,85,72}.  [#permalink]

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New post 02 Nov 2013, 19:31
nikhilsehgal wrote:
Yeah !!! Missed that one :) One has to be greater than 69.

Well, thanks.


came here to post about that very question. Sloppiness kills on this test! It got me too on this question
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Re: a, b, and c are integers in the set {a, b, c, 51,85,72}.  [#permalink]

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New post 28 May 2019, 13:42
Bunuel wrote:
a, b, and c are integers in the set {a, b, c, 51, 85, 72}. Is the median of the set greater than 70?

The median of 6 integers is the average of the middle two, when arranged in ascending/descending order.

(1) b > c > 69 --> the least values of c and b are 70 and 71, respectively. Even if a is the smallest of the numbers the median = (70 + 71)/2>70 (the set in this case is{a, 51, 70, 71, 72, 85}). Sufficient.

(2) a < c < 71. If a=69, b=70, and c is the smallest number, then the set is {c, 51, 69, 70, 72, 85} and the median is less than 70 but if a=69, b=70, and c is the largest number, then the set is {51, 69, 70, 72, 85, c} and the median is greater than 70. Not sufficient.

Answer: A.



Explanation for statement 2 is a little off track Bunuel. Statement 2 does not say anything about the value of 'b'. b can surely take the values which you have suggested but by reading your logic,
i am assuming that you intended the reasoning mentioned below:-

(2) a < c < 71. If a=69, c=70, and b is the smallest number, then the set is {b, 51, 69, 70, 72, 85} and the median is less than 70 but if a=69, c=70, and b is the largest number, then the set is {51, 69, 70, 72, 85, b} and the median is greater than 70. Not sufficient.

Again, its a minor fix, but helps to make this explanation crystal clr..
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Re: a, b, and c are integers in the set {a, b, c, 51,85,72}.   [#permalink] 28 May 2019, 13:42
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