Five teams-A, B, C, D, and E — each consisting of 15 members, are going on expeditions to five different locations. Each team includes members from three different skill sets: biologists,…
Question and options
Five teams-A, B, C, D, and E — each consisting of 15 members, are going on expeditions to five different locations. Each team includes members from three different skill sets: biologists, geologists, and explorers. However, the number of members from each skill set varies by team and each member has only one speciality. The total number of biologists, geologists, and explorers are equal.
The following additional information is available
- Every team has at least 2 members from each of the three skill sets.
- Teams C and D have 6 biologists each, and Team A has 6 geologists.
- Every team except A has more biologists than explorers.
- The number of explorers in each team is distinct and decreases in the order A, B, C, D, and E.
The median number of biologists across five teams is
The following additional information is available
- Every team has at least 2 members from each of the three skill sets.
- Teams C and D have 6 biologists each, and Team A has 6 geologists.
- Every team except A has more biologists than explorers.
- The number of explorers in each team is distinct and decreases in the order A, B, C, D, and E.
The median number of biologists across five teams is
- 5
- 6
- 7
- 4
Answer and explanation
Correct answer: B - 6
The median is . Team A has at most seven explorers, so the descending counts are bounded by , all of which are attained because their sum is the required . Subtracting A's geologists and explorers from its team size gives two biologists, B must have seven to outnumber its six explorers and leave room for two geologists, and E needs four to bring the total to , giving the sorted counts . Dividing the total by five gives the mean .
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