IPMAT Indore 2025 · Quantitative Ability · Question 6

IPMAT Indore 2025 previous year question on Deductive Reasoning, with the answer and a step-by-step solution.

Deductive ReasoningLogical Reasoning - Cat Set TypesType in the answer (TITA)Hard

Set 1: Five expedition teams – biologists, geologists and explorers — this question belongs to a set. Read the full set with all 3 questions →

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 is equal.

The following additional information is available:

Every team has at least 2 members from each skill set.

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 ______
Answer & solution

Answer: 2


Five teams of 15 members each, every member a biologist, a geologist or an explorer.

Team

Biologists

Geologists

Explorers

Row total

A

?

6

?

15

B

?

?

?

15

C

6

?

?

15

D

6

?

?

15

E

?

?

?

15

Total

?

?

?

75

Four rules stay on the board throughout:

Every cell is at least 2

The three skills are shared equally across all 75 members

Explorer counts are all different and strictly decrease from A to E

Teams B, C, D and E each have more biologists than explorers

Step 1 — each column totals 25

75 members shared equally among 3 skills gives 75 ÷ 3 = 25 per column.

Team

Biologists

Geologists

Explorers

Row total

A

?

6

?

15

B

?

?

?

15

C

6

?

?

15

D

6

?

?

15

E

?

?

?

15

Total

25

25

25

75

Step 2 — Team A caps the explorers at 7

Row A totals 15 and 6 of them are geologists, so biologists + explorers = 9. Since biologists must be at least 2, Team A can hold at most 7 explorers.

Team

Biologists

Geologists

Explorers

Row total

A

≥ 2

6

≤ 7

15

B

?

?

?

15

C

6

?

?

15

D

6

?

?

15

E

?

?

?

15

Total

25

25

25

75

Team A holds the largest explorer count, so this cap is really a cap on the whole explorer column.

Step 3 — the explorer column is forced

We need five different values, decreasing, smallest at least 2, largest at most 7, adding to 25. Only {2, 3, 4, 5, 6, 7} are available and they add to 27, so exactly one of them is dropped — and dropping the 2 is the only way to land on 25.

Candidate set

Sum

Verdict

6, 5, 4, 3, 2

20

too small

7, 5, 4, 3, 2

21

too small

7, 6, 4, 3, 2

22

too small

7, 6, 5, 3, 2

23

too small

7, 6, 5, 4, 2

24

too small

7, 6, 5, 4, 3

25

only fit

Team A's biologists come free here: 9 − 7 = 2.

Team

Biologists

Geologists

Explorers

Row total

A

2

6

7

15

B

?

?

6

15

C

6

?

5

15

D

6

?

4

15

E

?

?

3

15

Total

25

25

25

75

Step 4 — Team B is squeezed from both sides

Two separate rules push Team B's biologists to the same number from opposite directions.

Pressure from

Reasoning

Result

Biologists > explorers

explorers = 6

at least 7

Geologists ≥ 2

biologists + geologists = 15 − 6 = 9

at most 7

Both arrows point at 7, so Team B has 7 biologists and 2 geologists.

Team

Biologists

Geologists

Explorers

Row total

A

2

6

7

15

B

7

2

6

15

C

6

?

5

15

D

6

?

4

15

E

?

?

3

15

Total

25

25

25

75

Step 5 — Team E's biologists by subtraction

The biologist column must reach 25, and four of its five entries are now known: 2 + 7 + 6 + 6 = 21, leaving 4 for Team E.

Check the rule: 4 biologists beats 3 explorers, so Team E still satisfies the biologists > explorers condition.

Team

Biologists

Geologists

Explorers

Row total

A

2

6

7

15

B

7

2

6

15

C

6

?

5

15

D

6

?

4

15

E

4

?

3

15

Total

25

25

25

75

Step 6 — the last geologists

Each remaining geologist cell is whatever the row needs to reach 15.

Team

15 − biologists − explorers

Geologists

C

15 − 6 − 5

4

D

15 − 6 − 4

5

E

15 − 4 − 3

8

Final table and answer

Team E has 4 biologists.

Team

Biologists

Geologists

Explorers

Row total

A

2

6

7

15

B

7

2

6

15

C

6

4

5

15

D

6

5

4

15

E

4

8

3

15

Total

25

25

25

75

Verification sweep:

Every cell is at least 2

All three columns total 25

Explorers run 7, 6, 5, 4, 3 — distinct and strictly decreasing

B, C, D and E each have more biologists than explorers: 7 > 6, 6 > 5, 6 > 4, 4 > 3

IMPORTANT NOTE — 3 moves

In the exam, only three moves actually matter. Everything else is arithmetic.

Move

What it uses

What it gives

1

Columns are 25 each. In Team A, biologists + explorers = 9, and biologists ≥ 2, so explorers ≤ 7. Five distinct values, each ≥ 2, largest ≤ 7, summing to 25

Explorers = 7, 6, 5, 4, 3 and Team A has 2 biologists

2

Team B has 6 explorers, so biologists ≥ 7; but geologists ≥ 2 forces biologists ≤ 7

Team B has 7 biologists

3

Biologist column: 25 − (2 + 7 + 6 + 6)

Team E has 4 biologists

Move 1 is the whole puzzle. Teach students to hunt for the row with a given value (Team A's 6 geologists) and turn it into a cap on the constrained column.

Answer: 2

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