Logical Reasoning

Arrangements

Medium

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

Entered answer:

✅ Correct Answer: 6

Slide 1/6

5 teams $×$ 15 members (in each team) $=$ 75 total members.

Equal distribution across skill sets $=$ 25 biologists, 25 geologists, 25 explorers.

Step 1. Create your data-structure (table). If this is properly done, half of the headache is solved:

Team	Biologists	Geologists	Explorers	Total
A				15
B				15
C				15
D				15
E				15
Total	25	25	25	75

Step 2. From “Teams C and D have 6 biologists each, Team A has 6 geologists” (point 2):

Team	Biologists	Geologists
A		6
B
C	6
D	6
E

Step 3. Explorers are all distinct, decreasing A → E, summing to 25 with each ≥2 (points 4 & 1).

The only fit is: $E_A,E_B,E_C,E_D,E_E=7,6,5,4,3$ .

Whenever points like these are mentioned, don't get lazy, just start adding $(3+4+5+6+7 = 25)$

Team	Biologists	Geologists	Explorers
A		6	7
B			6
C	6		5
D	6		4
E			3

Step 4. Now each team total is 15. Find the remaining value for A, C and D:

Team	Biologists	Geologists	Explorers
A	2	6	7
B			6
C	6	4	5
D	6	5	4
E			3

Step 5. For B, we need $B_B>E_B=6$ (point 3) and $G_B\ge2$ (point 1).

So, biologists need to be 7 or more:

If we have 7 biologists, we can have 2 geologists ✅
If we have 8 biologists, we can have only 1 geologist ❌ -> At least 2 are required (point 1).

Team	Biologists	Geologists	Explorers
A	2	6	7
B	7	2	6
C	6	4	5
D	6	5	4
E			3

Step 6. Finally, for E, every column (biologists, geologists, explorers must sum to 25):

Team	Biologists	Geologists	Explorers
A	2	6	7
B	7	2	6
C	6	4	5
D	6	5	4
E	4	8	3

The biologists (in ascending order) are: 2, 4, 6, 6, 7.

The middle most value (median) is 6.

Question 2

The number of biologists in team E is _____

Question 8

The number of teams having more geologists than biologists is ______

The median number of biologists across five teams is

Solution

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