Of the 50 researchers in a workgroup, 40 percent will be assigned to Team A and the remaining 60 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer?

(A) 15
(B) 17
(C) 20
(D) 25
(E) 30


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This question would be tough if the wordings of the question are changed from minimum to maximum no of people.

Old Phrasing - What is the lowest possible number of researchers who will NOT be assigned to the team they prefer? = 15 people
New Phrasing - What is the highest possible number of researchers who will NOT be assigned to the team they prefer? = 45 people

I hope these phrasings will help many people to understand the concept in totality
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Team A (20) Team B (30)
Pref Team A (35), Team B (15)
20/35 => gets pref team A.
15/30 => gets pref team B
That’s 20+15 getting pref team:15 Remaining - Answer

Nice question...

what we have calculated is, atleast, 15 % people are those who has been assigned to the team which they didnt prefer, it may b more than that rite? like we dont know actually the people who has been assigned to teams are actually assigend to preferd team, it may b more than, but atleast 15% person, not less than that..

M i rite guyz??
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Even if you use a double set matrix, it will be quite irrelevant as its slightly modified. But if you draw the matrix it will be clear what the question is asking you!

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I actually solved it using a different logic and got the right answer, however I might have just gotten lucky. Please if there is a mistake in my logic, let me know.

People assigned to team A = 20
People assigned to tean B = 30

35 People wanted team A.
15 people wanted team B.

I got the answer from team B. 30 - 15= 15 since there were 30 people and only 15 wanted to be there. so the rest did not.

Assigned to A = 20

Assigned to B = 30

Preferred A = 35

Preferred B = 15

Least = 35 - 20 OR 30 - 15 = 15

Answer = A
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I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case
40 will be in team A
60 will be in team B

The larger diff is
70 want team A so diff is 70-40=30. At least 30 people will NOT get their wish, so for 50 researchers the same number is 15.
Answer choice A

[quote="Bunuel"]Of the 50 researchers in a workgroup, 40 percent will be assigned to Team A and the remaining 60 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer?

(A) 15
(B) 17
(C) 20
(D) 25
(E) 30

Here Total team =50
Allowed in A = 20
Allowed in B = 30
Want A=35
Want B=15

To find the least that don't get there preference => let us arrange them in a way that all get what they want
here B members are fully fit in B=> no left
but For A => 20 seats and 35 need them .
SO 15 will have no place to go ; hence they will be assigned to team B.
Thus => 15.
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We are given that there are a total of 50 researchers in the workgroup and that 40% will be assigned to team A and 60% assigned to team B. Thus, we know:

Assigned to team A = (0.4)(50) = 20

Assigned to team B = (0.6)(50) = 30

We are also given that 70% of the people PREFER team A and that 30% of the people PREFER team B. Thus we know:

Prefer team A = (0.7)(50) = 35

Prefer team B = (0.3)(50) = 15

We are asked to find the LOWEST POSSIBLE NUMBER of people who will NOT be assigned to the team they prefer. Let’s start with team B.

Currently we have 15 people who PREFER team B and 30 people who will be assigned to team B. Because we are looking for the lowest possible number of people who will not be assigned to the team they prefer, we must assume that all 15 people who prefer team B will indeed be assigned to team B, but this means that, of the 30 people who will be on team B, 15 of them DO NOT WANT TO BE ON THE TEAM.

Turning to team A, we know that we have 35 people who PREFER team A and 20 people who will be assigned to team A. Again we are looking for the lowest possible number of people who will not be assigned to the team they prefer, we must assume that all 20 people who will be on team A actually prefer to be on that team.

Thus the lowest number of people who do not prefer the team in which they have been assigned is 15 people.

Note that the answer is NOT 30. Don't be guilty of double-counting the disappointed people. Think instead that all 20 people assigned to team A wanted to be on it, and of the 30 people assigned to team B, exactly 15 wanted to be on it. Thus, we have 35 people who got the team they wanted, with 15 who were assigned to the team they didn't want.

Answer A.
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