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

Answer: A.
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Re: a, b, and c are integers in the set {a, b, c, 51,85,72}. [#permalink] 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] New post   21 Sep 2013, 02:38
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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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Re: a, b, and c are integers in the set {a, b, c, 51,85,72}. [#permalink] 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] 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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a, b, and c are integers in the set {a, b, c, 51,85,72}. [#permalink] New post   18 Jan 2020, 07:23
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, 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.

Answer: A.


Hi
I am not understanding how to solve this question at all. Why did we take the least values of b and c? and if a could be any value then how can we be sure?
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Re: a, b, and c are integers in the set {a, b, c, 51,85,72}. [#permalink] New post   18 Jan 2020, 07:39
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Kritisood wrote:
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, 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.

Answer: A.


Hi
I am not understanding how to solve this question at all. Why did we take the least values of b and c? and if a could be any value then how can we be sure?


The question asks whether the median of the set greater than 70? For (1) we tried to make the median as small as possible, and got that even in this case it must be more than 70.
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a, b, and c are integers in the set {a, b, c, 51,85,72}. [#permalink] New post   27 Jan 2020, 02:41
Bunuel

Hello Bunuel,

Hope you are doing well.

I have a confusion.
For option A why did you not take a as the highest number? like in option B, b is tested with both high and low.


Thanks.
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Re: a, b, and c are integers in the set {a, b, c, 51,85,72}. [#permalink] New post   27 Jan 2020, 02:48
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swadhakamal wrote:
Bunuel

Hello Bunuel,

Hope you are doing well.

I have a confusion.
For option A why did you not take a as the highest number? like in option B, b is tested with both high and low.


Thanks.


For (1) we considered the worst case scenario. So, minimized everything and got that even in this case the median turns out to be greater than 70. Naturally for all other cases, the median must be greater than 70, thus no need to consider them at all.
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Re: a, b, and c are integers in the set {a, b, c, 51,85,72}. [#permalink] New post   23 Mar 2020, 00:56
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, 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.

Answer: A.


Why do we have to make the set in ascending order ?
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Re: a, b, and c are integers in the set {a, b, c, 51,85,72}. [#permalink] New post   23 Mar 2020, 01:06
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gagan543 wrote:
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, 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.

Answer: A.


Why do we have to make the set in ascending order ?


It's according to the the definition of the median:
The median of a set with even number of terms is the average of the middle two, when arranged in ascending/descending order.
The median of a set with odd number of terms is the middle term, when arranged in ascending/descending order.
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Re: a, b, and c are integers in the set {a, b, c, 51,85,72}. [#permalink] New post   18 Mar 2023, 05:47
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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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