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