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Every high school in the city of Euclid sent a team of 3 students to a

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Every high school in the city of Euclid sent a team of 3 students to a  [#permalink]

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New post 31 Mar 2019, 20:56
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Question Stats:

55% (02:12) correct 45% (02:55) wrong based on 29 sessions

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Every high school in the city of Euclid sent a team of 3 students to a math contest. Each participant in the contest received a different score. Andrea's score was the median among all students, and hers was the highest score on her team. Andrea's teammates Beth and Carla placed 37th and 64th, respectively. How many schools are in the city?

A. 22
B. 23
C. 24
D. 25
E. 26

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Re: Every high school in the city of Euclid sent a team of 3 students to a  [#permalink]

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New post 31 Mar 2019, 21:33
If Andrea’s score is the highest among her teammates, then being the median of the whole group her position can least be 65th.

So we get the total no of student in the whole group as 129

As 65=n+1/2
So no of schools participated = 129/3= 43.

What am i doing wrong here.

Posted from my mobile device
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Re: Every high school in the city of Euclid sent a team of 3 students to a  [#permalink]

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New post 31 Mar 2019, 22:01
Bunuel wrote:
Every high school in the city of Euclid sent a team of 3 students to a math contest. Each participant in the contest received a different score. Andrea's score was the median among all students, and hers was the highest score on her team. Andrea's teammates Beth and Carla placed 37th and 64th, respectively. How many schools are in the city?

A. 22
B. 23
C. 24
D. 25
E. 26


Total number of students who participate = 3 * number of schools

Since Andreas score is the median score we can assume that the total number of students will be odd otherwise we will have two students with the median score.
Hence A-C-E can be eliminated as they are even.

So we are left with B & D.

if we look at D, then the total number of students = 3 * 25 = 75 and the median score would belong to the 37th student. But in the question stem, we have clearly told that Ben is the 37th students and Andreas has a score better than that. So we can eliminate D.

Hence B is the correct answer.
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Re: Every high school in the city of Euclid sent a team of 3 students to a  [#permalink]

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New post 01 Apr 2019, 02:51
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Bunuel wrote:
Every high school in the city of Euclid sent a team of 3 students to a math contest. Each participant in the contest received a different score. Andrea's score was the median among all students, and hers was the highest score on her team. Andrea's teammates Beth and Carla placed 37th and 64th, respectively. How many schools are in the city?

A. 22
B. 23
C. 24
D. 25
E. 26


solve the question with logic using answer options
since 3 students per school are participating so in total 3* no of school ; are the ranks of students and no 2 students can get same rank
Andrea score is highest in her group so her rank will also be< 37
the answer has to be odd count of schools because only with an odd * 3 ; we shall get count of equal no of schools around the median
in this case 23 & 25 are options with
25*3 ; 75 ranks , but median ; 75/2 ; 37.5 not possible for Andrea rank as her rank has to be <37 , where as here its coming 38
23*3 ; 69 ranks , median ; 69/2 ; 34.5 , possible for Andrea her rank would 35 possible
IMO B
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Re: Every high school in the city of Euclid sent a team of 3 students to a  [#permalink]

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New post 02 Apr 2019, 06:56
Given Andrea's was median among all students , So total no of students should be a odd number , 2n+1 --Statement 1

Beth and Carla ranked 37 and 64th , also given Andrea's rank is greater then these 2 ranks ---Statement 2

Also given each school sent 3 kids to participate - So total of students should be a multiple of 3 --Statement 3 .

Answer choice should suffice these statement , Only Options B and D are odd .

Option B - 23 - 23*3 = No of Students = 69 , median of 69 is 34 which > 37,64
Option D - 25 - 25*3 = 75 , Median is 37 , which <37 , False from Statement 2 .
So Option B ,23 is Answer
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Re: Every high school in the city of Euclid sent a team of 3 students to a  [#permalink]

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New post 28 Apr 2019, 01:43
Tusharwyvern wrote:
If Andrea’s score is the highest among her teammates, then being the median of the whole group her position can least be 65th.

So we get the total no of student in the whole group as 129

As 65=n+1/2
So no of schools participated = 129/3= 43.

What am i doing wrong here.

Posted from my mobile device


the only problem of your reasoning is that you are taking a look at the ranking the other way round.
try to think as 1st ranked is the best and 100th rank is the worst :)

rgds,
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Re: Every high school in the city of Euclid sent a team of 3 students to a   [#permalink] 28 Apr 2019, 01:43
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