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555-605 (Medium)|   Word Problems|         
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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


 


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D
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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
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­

GMAT Club Official Explanation:



In each session, 16 animals were placed into 8 pairs, so exactly 8 animals were observed as dominant and 8 as subordinate.

In the second session, 8 animals were subordinate. Of those, 5 had already been subordinate in the first session.

That means the other 3 subordinate animals in the second session must have been dominant in the first session.

So, out of the 8 animals that were dominant in the first session, 3 became subordinate in the second, leaving 8 - 3 = 5 animals that were dominant in both sessions.

Answer: D.
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(D). 5 In first session: 8 subordinate animals, of these 8, 5 were subordinate again → so 3 of them became dominant in second session. Therefore, in Second session has 8 dominant has 3 of these are from the subordinate group of session 1, so dominants who were also dominant in session 1 = 8 – 3 = 5.
Bunuel
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


 


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I THINK ANSWER IS D. SINCE 5 ANIMALS IN THE FIRST SESSION REMAINED SUBORDINATE IN THE SECOND SESSION, THEIR PAIRS REMAINED DOMINANT IN THE SECOND SESSION.
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Here we know that 5 os subordinate animals from the first session are also subordinate in the second session. Because of that, 3 dominant animals from the first session will be subordinate in the second session, to complete the 8 pairs. Since 3 dominants from the first session become subordinates in the second session, then 5 dominants from first session will remain as dominant in the second.
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Total animals: 16
In each session: 8 are dominant, 8 are subordinate.

The key information is that 5 animals were subordinate in both Session 1 and Session 2.

1. Consider the 8 animals that were subordinate in Session 1.
* We know 5 of them stayed subordinate in Session 2.
* Therefore, the other 3 must have become dominant in Session 2. (8 - 5 = 3)

2. Now consider the 8 animals that were dominant in Session 2.
* We just found that 3 of these animals were subordinate in Session 1.
* Therefore, the remaining animals must have been dominant in Session 1 as well. (8 - 3 = 5)

So, 5 animals were dominant in both sessions.

The correct answer is (D) 5.
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Since there were 5 same subordinates in the second session, the remaining 3 subordinates must have replaced any 3 dominant ones, hence leaving only 5 same dominants for both sessions
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The Answer is 5.

Can be solved by making 2 X 2 table of............ TABLE BELOW...

Total is 16 Animals..... So in 1st Session 8 Dominant and 8 Subordinate..and the same goes for Session 2..... So the outermost values are 8 each...
Now We are given that Of the animals that were subordinate in the first session, 5 were also subordinate in the second session...means the intersection of S1 and S2 will be 5......and we have to find the intersection of D1 and D2....
So if S1 -S2 is 5 then D2-S1 is 8-5=3...and D2D1 is 8-3 = 5...
table Below


D1S1TOTAL
D28
S258
8816


D1S1TOTAL
D2538
S2358
8816

Bunuel
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


 


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This is a set problem,
in first round, there are 8 dominant and 8 subordinate animals,
in second round, there are 5 subordinate animals that were subordinate in first round as well,
So it is total - (union of atleast once subordinate) = 16 - (8 + 3) = 5
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Session 1 : 8 Dominant + 8 Subordinate
Session 2 : 8 Dominant + 8 Subordinate

Its given that 5 were subordinates in both the sessions which indirectly tells us that 3 subordinate animals turned
dominant in session 2.
So, 3 dominant animals turned into subordinate for session 2.
Which directly tells us that 5 Dominant animals remained dominant in session 2 as well.
So, Answer D
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Step 1: Understanding the Setup

There are 16 animals.
In each session, they are grouped into 8 pairs.
In each pair, one is dominant, one is subordinate.
So, in each session:

8 dominant
8 subordinate


Let’s call the animals S1: subordinate in session 1 (8 animals).
Of these, 5 were also subordinate in session 2.

So, in the intersection of "subordinate in session 1" and "subordinate in session 2," there are 5 animals.

Now since 8 animals have to be subordinate in session 2 & 5 animals from session 1 are subordinate, this means that 3 animals from the dominant group in session 1 are now subordinate in session 2.

This means that there are (8-3)=5 animals in the intersection of dominant in session 1 & session 2

Hence the answer is option (D) 5
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We know that each session will have 8 dominant and 8 subordinate.
We know 5 animals were subordinate in both sessions, therefore 3 must be dominant in the second session but no in the second. Furthermore 5 must be dominant in both sessions
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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?


1st session
DominantSubordinateTotal
2nd sessionDominant8
Subordinate58
Total8816


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.
1st session
DominantSubordinateTotal
2nd sessionDominant538
Subordinate358
Total8816

5 number of animals were dominant in both sessions.

IMO D
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Bunuel
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


 


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Let the number of tagged animals be numbered as 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 and 16.

The number of tracking sessions be TWO ( A and B) and each session has 8 pairs. Which means all 16 participate in each session.

Session A and B has a DOMINANT and SUBORDINATE pair.

Let’s take session A:

Dominant : 1,2,3,4,5,6,7,8

Subordinate: 9,10,11,12,13,14,15,16.

Given that of the animals subordinate in first session, 5 animals was subordinate in session B also.

Let the five subordinate animals which are Subordinate in session B are : 9,10,11,12,13.

The Remaining three places be filled from animals present in the dominant group.

Session B :

Dominant : 1,2,3,4,5, 14,15,16

Subordinate : 9,10,11,12,13, 6,7,8

so, the number of animals which is dominant in both sessions is : 5 { 1,2,3,4,5}

Option D
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Bunuel
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


 


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Each session has 8 dominant and 8 subordinates.

Session 1 : 8 D & 8S
Session 2: 8D & 8S

Between Session 1 and Session 2, 5 are common. Hence, 3 wildlife moved from subordinate to dominant between session 1 and session 2.

Hence 8 - 3 = 5 animals were dominant in both sessions.

Option D
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Total 8

Subordinate in 2 session is 5, then dominate is 3 so in both sessions 8-3=5


Bunuel
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


 


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Two Sessions and total 16 animals were grouped into 8 pairs in each session

Session1: 8 pairs ->8 dominant and 8 subordinate (as in each pair, one is dominant and other is subordinate). Likewise we have for,
Session2: 8 pairs ->8 dominant and 8 subordinate (as in each pair, one is dominate and other is subordinate)

Now, we have been provided that of the animals that were subordinate in session1 (which was 8 as subordinate), 5animals were also subordinate in session2. So this means, of the 8 subordinate in session2, we have 5 subordinate which are also in session1 as subordinate. Also, in session1, we have left with 3 subordinates which are not subordinate in session2, thus these 3 will be dominant in session2. Therefore, we can say that in session2, of the 8 dominant, we have 3 animals who were not dominant in session1 and 5 animals who were dominant in both sessions.
Option (D)-5

Hope this helps :)

Regards,
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Answer should be D. In the first session, 8 animals were dominant and 8 were subordinate. Of the animals that were subordinate in the first session, 5 were also subordinate in the second session. This means their partners were still dominant in the second session. Hence, 5 animals were dominant in both sessions.
Bunuel
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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


 


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The answer is 5 (D)

In the first session with 8 pairs, 8 are dominant and 8 are subordinate. Out of the 8 subs, 5 remained subs in the second session so only 3 animals who were previously dominant now became subs, leaving 5 animals to be dominant twice.

Bunuel
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


 


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