GMAT Club Olympics 2025 (Day 1): At a wildlife reserve, two tracking

Based on the information given, we can form this mutually exclusive comprehensively exhaustive matrix and arrive at the answer.

	2nd S: Dominant	2nd S: Subordinate
1st S: Subordinate	3	5
1st S: Dominant	5	3

The answer is 5 as highlighted in yellow.

Out of 16 animals, 5 were subordinate in both sessions, so they were never dominant. That leaves 11 animals who filled all 16 dominant spots (8 per session). If B animals were dominant in both sessions, they contribute 2 roles each, and the other (11 − B) animals were dominant in only one session, contributing 1 each, then:

2B+(11−B)=16
⇒B=5

Answer: (D) 5

We have 16 animals that were observed in two separate sessions. In each session, the animals were randomly paired, with one animal in each pair being dominant and the other subordinate. This means in each session, exactly 8 animals were dominant and 8 were subordinate.

We know that of the 8 animals who were subordinate in the first session, 5 remained subordinate in the second session. This means 3 animals who were subordinate in the first session became dominant in the second session.

Since there are always 8 dominant animals in each session, and we've accounted for 3 of the second session's dominant animals (those who were previously subordinate), the remaining 5 dominant animals in the second session must come from those who were dominant in the first session.

Therefore, there must be 5 animals who were dominant in both the first and second sessions. These are the animals who were dominant initially and maintained their dominant status when observed again.

The right answer is D

We can solve this by using a 2 set matrix for overlapping sets:-


|--| S1 | D1 | Tot |
| S2| 5 | 3 | 8 |
| D2| 3 |5 | 8 |
| Tot| 8 | 8 | 16 |

Hence, the answer is (D)

There are 16 animals. In each session, they are grouped into 8 pairs, so 8 animals are dominant and 8 are subordinate in each session. We are told that 5 animals were subordinate in both sessions. That means of the 8 animals who were subordinate in the first session, 3 must have become dominant in the second session. Similarly, since 8 animals were subordinate in the second session and 5 were already subordinate in the first session, the remaining 3 must have been dominant in the first session. So, out of the 8 animals who were dominant in the first session, 3 became subordinate in the second session. That means 5 animals were dominant in both sessions. The answer is 5. Option D.

Given:

• Total animals = 16
• In each session, animals are grouped into 8 pairs → in each pair:
  → 1 dominant
  → 1 subordinate
• Therefore, each session has 8 dominants + 8 subordinates.

Let us define:

• D1: dominant in session 1
• S1: subordinate in session 1
• D2: dominant in session 2
• S2: subordinate in session 2

We are told:

• Of the 8 animals that were subordinate in session 1, 5 were also subordinate in session 2.

Thus, among the S1 group:

• 5 were S2
• Therefore 3 were D2 (since all animals must be either dominant or subordinate in each session)

Our goal: Find the number of animals dominant in both sessions (D1 ∩ D2).

We can set up a table:

	D2	S2	Total
D1	x	y	8
S1	3	5	8
Total	?	?	16

We know from the above:

• In S1 row: 3 D2 + 5 S2 = 8
• In total: D2 count = x + 3
• S2 count = y + 5

We also know:

• In session 2, there are 8 dominants and 8 subordinates →
  → D2 total = 8
  → S2 total = 8

Thus:

• x + 3 = 8 → x = 5
• y + 5 = 8 → y = 3

Answer:
Therefore.
5 animals were dominant in both sessions.

Correct answer D. 5

At a wildlife reserve, two tracking sessions were conducted to study 16 tagged animals. In each session, the animals were randomly grouped into 8 pairs, and in each pair, one animal was observed as dominant and the other as subordinate. Of the animals that were subordinate in the first session, 5 were also subordinate in the second session. How many animals were dominant in both sessions?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

We know:

16 animals → 8 dominant + 8 subordinate per session.

5 animals were subordinate in both sessions → overlap in subordinate group = 5.

So, 3 animals were subordinate in session 1 and dominant in session 2.

Since session 2 had 8 dominants, and 3 came from previous subordinates,
→ Remaining 5 dominants in session 2 must have also been dominant in session 1.

Answer: (D) 5

Pankaj Jindal | GMAT Classic 730 | IIM Bangalore | Helping working professionals
Success story: https://gmatclub.com/forum/how-i-scored ... l#p3588949

We are told there are 16 tagged animals. In each session, the animals are split into 8 pairs: 1 dominant and 1 subordinate per pair.
So, in each session:

• \(D_1 = 8\) (dominant in Session 1)
• \(S_1 = 8\) (subordinate in Session 1)
• \(D_2 = 8\) (dominant in Session 2)
• \(S_2 = 8\) (subordinate in Session 2)

We’re told that 5 animals were subordinate in both sessions:
\(\text{S}_1 \cap \text{S}_2 = 5\)
That means 5 of the 8 animals who were subordinate in Session 1 were also subordinate in Session 2.
So, the remaining 3 animals from \(S_1\) must have been dominant in Session 2.
Let’s now figure out how many animals were dominant in both sessions:

• Total \(D_2 = 8\)
• 3 of those \(D_2\) animals came from \(S_1\)
• Therefore, the other \(8 - 3 = 5\) must have come from \(D_1\)

So, \(5\) animals were dominant in both sessions.
Final Answer: D) 5

Total tagged animals = 16

Session 1
8 Animals --> Dominant - D1 - D8
8 Animals --> Subordinate = S1 - S8

We are told that 5 subordinates in Session 1 continue to be subordinates in Session 2.

Hence 2 Subordinates from Session 1 become Dominant in Session 2
Hence 3 Dominant from Session 1 become Subordinate in Session 2

Session 2
Lets assume
5 Animals --> S4 - S8 remain Subordinate
and
3 Animals --> D6 - D7 become Subordinate

Revised numbers
8 Animals --> Dominant - D1 - D5 + S1 - S3 (Assuming D6, D7 and D8 become Subordinates in Session 2)
8 Animals --> Subordinate - S4 - S8 + D6 - D8

Hence we can see that 5 animals (D1 - D5) continue to be Dominant in the second session post the changes

IMHO Option D

Given,

• ∣S1∩S2∣=5

So, 5 animals were subordinate in both sessions.
We know:

• d=∣S1∩S2∣=5

So:

• Session 1 Subordinate: total is 8
  
  
  • So c+d=8 ⟹ c=3
• Session 2 Subordinate: total is 8
  
  
  • So b+d=8 ⟹ b+5=8 ⟹ b=3
• Session 1 Dominant: total is 8
  
  
  • So a+b=8 ⟹ a+3=8 ⟹ a=5
• Session 2 Dominant: total is 8
  
  
  • So a+c=8 ⟹ a+3=8 ⟹ a=5 ✅ Consistent.

So, the number dominant in both sessions is a = 5.

If there are 8 pairs (Total 16 animals) which can be split up as Dominant and Subordinate.
The first session will have d = 8 and s = 8

The second session has 5 of the 8 animals which were subordinate to remain subordinate. Which means that, 3 animals which were subordinate have become dominant, and 3 animals which were dominant have become subordinate.

This leaves 5 animals which were dominant in Session 1 to also be dominant in Session 2. Hence the answer is 5.

16 → (1) 8S → 5S (Given) + 3D (8subtotal - 5S) ⇒ The other group should have 3S+5D for the total to be 8S+8D

(2) 8D → 3S + 5D

Therefore, Dominant in both sessions = 5

16 Animals split into 8 pairs, with each pair having one of each category Dominant and Submissive.

If 5 were Sub in the first experiment and the second, then 3 other Animals have switched from Dom to Sub. Hence, [8-3] = 5 Remained Dom in both experiments.

Session one: 8 Dominant and 8 Subordinate, out of 8 Subordinate 5 remain subordinate in second session, That means 3 become Dominant for the first time and 5 were dominant in both sessions.

Hence, (D) 5

"in each session animals were divided into 8 pairs" and " of the animals that were subordinate in 1st session , 5 were also subordinate in the 2nd session" , that means of teh 8 animals in 1st session , 5 were still subordinate and what happened to rem 3 , they must have moved to dominant grp in 2nd session. Since in 2nd session the grp was again divided into 8 pairs, dominant grp also has 8 animals but 3 borrowed from subordinate grp and 3 send to subordinate grp. it only has 5 animals that were dominant in both the session.

I just make a table to solve this question:

	Subordinate First	Dominant First	Total
Subordinate Second	5	=3	8
Dominant Second	=3	? = 8-3 = 5	8
Total	8	8	16

All the rows and column sums will be 8, because in each round there are exactly 8 subordinates and 8 dominants. Then i fill in 5 - as the prompt said that of the 8 subordinate in round 1, 5 are subordinate in round 2.
Then I can easily calculate ? = 5 as well.

Choose d