Grouping researchers

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 116
Joined: Tue Mar 31, 2009 10:50 am
Followed by:1 members

Grouping researchers

by LulaBrazilia » Sun Mar 09, 2014 6:34 pm
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

User avatar
GMAT Instructor
Posts: 1052
Joined: Fri May 21, 2010 1:30 am
Thanked: 335 times
Followed by:98 members

by Patrick_GMATFix » Sun Mar 09, 2014 6:44 pm
Cool question. The answer is A. I go through the question in detail in the full solution below (taken from the GMATFix App).

Image

-Patrick
  • Ask me about tutoring.

Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Sun Mar 09, 2014 5:50 pm
Thanked: 1 times

by vinaycfc » Sun Mar 09, 2014 6:48 pm
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?

Total number of researchers=50
40% of researchers put in group A=4/10*50=20 persons
remaining 60% are put in group B=50-20=30 persons

however,

70% of researchers prefer group A =7/10*50=35 persons
30% of researchers prefer group B =3/10*50=15 persons

Given group B can accommodate 30 persons. Let us put all researchers who prefer to be in group B into group B itself so 30-15. There are 15 spaces left in group B. However it is given that the remaining 35 do prefer group A. The maximum capacity of group A is 20 so if we fill the group with people who prefer group A we have 35-20 15 persons left and 15 vacant spaces in group B. therefore 15 persons who prefer group A will have to join Group B.

User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pm
Thanked: 448 times
Followed by:34 members
GMAT Score:650

by theCodeToGMAT » Sun Mar 09, 2014 7:01 pm
Team A = 40/100 * 50 = 20
Team B = 30

Preference
Team A = 70*50/100 = 35
Team B = 15

Maximum Intake by Team A = 20
Delta people = 35 - 20 = 15 People

[spoiler]{A}[/spoiler]
R A H U L

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Mon Mar 10, 2014 3:59 am
LulaBrazilia wrote: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

B:
30% prefer B.
60% will be assigned to B.
Thus, every researcher who prefers B can be assigned to B.

A:
70% prefer A.
Only 40% will be assigned to A.
Thus, at least 30% of the 50 researchers will be disappointed:
30% of 50 = 15.

The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

User avatar
Master | Next Rank: 500 Posts
Posts: 359
Joined: Wed Mar 11, 2009 4:37 am
Location: Kolkata, India
Thanked: 50 times
Followed by:2 members

by Abhishek009 » Mon Mar 10, 2014 8:29 am
LulaBrazilia wrote:Of the 50 researchers in a workgroup, 40 percent will be assigned to team A
Team A = 20
LulaBrazilia wrote: the remaining 60 percent to team B.
Team B = 30
LulaBrazilia wrote:However, 70 percent of the researchers prefer team A and 30 percent prefer team B.
According to Preference ,

Team A = 35

Team B = 15
LulaBrazilia wrote:What is the lowest possible number of researchers who will NOT be assigned to the team they prefer?

We find that actually members of Team B = 30 , however only 15 people prefer to be in team B

Thus 15 people who are actually in team B will feel disappointed since they never wanted to be in Team B.

Hence IMO [spoiler](A)[/spoiler]
Abhishek

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7223
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Mon May 18, 2015 5:39 am
LulaBrazilia wrote: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
Solution:

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.

The answer is A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage

Junior | Next Rank: 30 Posts
Posts: 25
Joined: Tue Jul 16, 2019 4:10 am

by rishab0507 » Sat Sep 07, 2019 9:36 am
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?

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

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

Now 2nd case :
Prefer team A = (0.7)(50) = 35

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

Considering team B first : Total assigned are 30, and 15 people wanted to be on it . So it got more than people wanted, Means all people who desired would be in it, This part we have to assume.
Consider A: Total people in A is 20 but 35 people desired, so 15 people are left.
15 : A is answer:

We cannot add both because in B already has more than what desired by people