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SVP  Joined: 06 Sep 2013
Posts: 1570
Concentration: Finance
a, b, and c are integers in the set {a, b, c, 51,85,72}.  [#permalink]

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 58453
Re: a, b, and c are integers in the set {a, b, c, 51,85,72}.  [#permalink]

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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.

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Intern  Joined: 15 Oct 2012
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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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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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nikhilsehgal wrote:
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?

(1) says that b>c>69.
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Intern  Joined: 15 Oct 2012
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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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Yeah !!! Missed that one One has to be greater than 69.

Well, thanks.
Manager  Joined: 26 Sep 2013
Posts: 184
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41 Re: a, b, and c are integers in the set {a, b, c, 51,85,72}.  [#permalink]

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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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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.

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

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