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

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

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20 Sep 2013, 15:39
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54% (02:06) correct 46% (02:27) wrong based on 261 sessions

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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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Joined: 02 Sep 2009
Posts: 61403
a, b, and c are integers in the set {a, b, c, 51,85,72}.  [#permalink]

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20 Sep 2013, 16:56
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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.

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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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21 Sep 2013, 00:51
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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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21 Sep 2013, 01:38
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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]

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21 Sep 2013, 01:41
Yeah !!! Missed that one One has to be greater than 69.

Well, thanks.
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Joined: 26 Sep 2013
Posts: 182
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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02 Nov 2013, 18:31
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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Joined: 21 Feb 2017
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a, b, and c are integers in the set {a, b, c, 51,85,72}.  [#permalink]

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18 Jan 2020, 06:23
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.

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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Joined: 02 Sep 2009
Posts: 61403
Re: a, b, and c are integers in the set {a, b, c, 51,85,72}.  [#permalink]

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18 Jan 2020, 06:39
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.

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]

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27 Jan 2020, 01:41
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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Joined: 02 Sep 2009
Posts: 61403
Re: a, b, and c are integers in the set {a, b, c, 51,85,72}.  [#permalink]

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27 Jan 2020, 01:48
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] 27 Jan 2020, 01:48
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