IPMAT Indore 2025
DILR
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 number of teams having more geologists than biologists is ______
The number of teams having more geologists than biologists is ______
Entered answer:
✅ Correct Answer: 2
Slide 1/7
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:
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 | Explorers |
|---|---|---|---|
| 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: .Whenever points like these are mentioned, don't get lazy, just start adding
| 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 (point 3) and (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 |
Only teams A and E have more geologists than biologists, hence, answer is 2.
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