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# Of the 50 researchers in a workgroup, 40 percent will be

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Of the 50 researchers in a workgroup, 40 percent will be [#permalink]

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20 Aug 2012, 02:11
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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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Re: Of the 50 researchers in a workgroup, 40 percent will be [#permalink]

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20 Aug 2012, 02:12
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SOLUTION

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

The number of researchers assigned to Team A will be 0.40*50 = 20;
The number of researchers assigned to Team B will be 0.60*50 = 30.

The number of researchers who prefer Team A will be 0.70*50 = 35;
The number of researchers who prefer Team B will be 0.30*50 = 15.

Now, if ALL 20 spots in Team A, will be filled by the researchers who prefer Team A, then the remaining 15 researchers who prefer Tam A will be assigned to Team B (along with 15 researchers who DO prefer Team B).

Hence, the minimum number of researchers who will NOT be assigned to the team they prefer is 15.

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Re: Of the 50 researchers in a workgroup, 40 percent will be [#permalink]

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06 Feb 2013, 05:12
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A great way to solve this is to use the Double-Matrix Chart

------------Team A|Team B
prefer A|______|__________=.7 * 50 = 35
prefer B|______|__________=.3 * 50 = 15
________________________________
----------.4*50=20 + .6*50=30-----------= 50

Columns:
20 people should be assigned to A.
30 people should be assigned to B.

Rows:
35 prefer Team A.
15 prefer Team B.

All totaling to 50.

In order to get the lowest number who will not get what they want,
we give the assignment to those who wants it as much as we can.

For example:
If 35 wants Team A... assign as much as we can to Team A.
If 15 wants Team B... assign as much as we can to Team B.

(See table below)

------------Team A|Team B
prefer A|___20_|___?_______=.7 * 50 = 35
prefer B|___?__|__15_______=.3 * 50 = 15
________________________________
---------------20---+----30--------= 50

Now we calculate the balance of those who did not get the slot...

------------Team A|Team B
prefer A|___20_|___15_______=.7 * 50 = 35
prefer B|___0__|__15_______=.3 * 50 = 15
________________________________
---------------20---+----30--------= 50

Note that the row of "prefer A" should always tally to 35. That is why we know the balance is 15.
Note that the row of "prefer B" should always tally to 15. That is why we know the balance is 0.

Now we sum up those who did not get what they want:

15 on those who prefer A did not get it
0 on those who prefer B did not get it.

This chart works on all overlapping set problems...
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Re: Of the 50 researchers in a workgroup, 40 percent will be [#permalink]

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21 Aug 2012, 15:29
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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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Re: Of the 50 researchers in a workgroup, 40 percent will be [#permalink]

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14 Nov 2012, 05:03
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Hi Bunuel,

How to solve this using Double set Matrix?

Regards,
Sachin
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Re: Of the 50 researchers in a workgroup, 40 percent will be [#permalink]

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23 Dec 2012, 05:59
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Sachin9 wrote:
Hi Bunuel,

How to solve this using Double set Matrix?

Regards,
Sachin

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!
Attachments

File comment: matrix diagram

Og_prob.jpg [ 31.25 KiB | Viewed 17619 times ]

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Re: Of the 50 researchers in a workgroup, 40 percent will be [#permalink]

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19 Jul 2014, 19:04
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Sachin9 wrote:
Hi Bunuel,

How to solve this using Double set Matrix?

Regards,
Sachin

Matrix based on the question:
Attachment:

matrix.png [ 2.6 KiB | Viewed 13583 times ]

The question is asking us to make x+y minimum.

If you make y=0, x will become 15
So, x+y = 15
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Re: Of the 50 researchers in a workgroup, 40 percent will be [#permalink]

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20 Aug 2012, 05:33
IMO A

15 person prefer B and 30 will be assigned to Team B. All preference for Team B are fulfilled.
35 Person prefer A and only 20 will be assigned to Team A and rest 15 person will be forced to join team B.
So (35-20)=15 will not get their preference.
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Re: Of the 50 researchers in a workgroup, 40 percent will be [#permalink]

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22 Aug 2012, 06:19
fameatop wrote:
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

Could you please explain how to work on the second question?
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Re: Of the 50 researchers in a workgroup, 40 percent will be [#permalink]

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23 Aug 2012, 08:48
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
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Re: Of the 50 researchers in a workgroup, 40 percent will be [#permalink]

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24 Aug 2012, 05:25
SOLUTION

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

The number of researchers assigned to Team A will be 0.40*50 = 20;
The number of researchers assigned to Team B will be 0.60*50 = 30.

The number of researchers who prefer Team A will be 0.70*50 = 35;
The number of researchers who prefer Team B will be 0.30*50 = 15.

Now, if ALL 20 spots in Team A, will be filled by the researchers who prefer Team A, then the remaining 15 researchers who prefer Tam A will be assigned to Team B (along with 15 researchers who DO prefer Team B).

Hence, the minimum number of researchers who will NOT be assigned to the team they prefer is 15.

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Re: Of the 50 researchers in a workgroup, 40 percent will be [#permalink]

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10 Sep 2012, 19:43
I think I sort of understand this one. Why does the question ask for "lowest#?"
Will there be a big difference between lowest and highest?
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Re: Of the 50 researchers in a workgroup, 40 percent will be [#permalink]

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11 Sep 2012, 10:46
grignard wrote:
I think I sort of understand this one. Why does the question ask for "lowest#?"
Will there be a big difference between lowest and highest?

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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Re: Of the 50 researchers in a workgroup, 40 percent will be [#permalink]

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02 Feb 2013, 01:20
A B
prefer oneself 35 15
assigned workers 20 30
______________________________________________
15 -15
so remained the 15 worker who forced to go to B

The correct is A
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Re: Of the 50 researchers in a workgroup, 40 percent will be [#permalink]

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20 Feb 2014, 12:23
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.
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Re: Of the 50 researchers in a workgroup, 40 percent will be [#permalink]

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23 Jul 2014, 22:02
Assigned to A = 20

Assigned to B = 30

Preferred A = 35

Preferred B = 15

Least = 35 - 20 OR 30 - 15 = 15

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Re: Of the 50 researchers in a workgroup, 40 percent will be [#permalink]

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10 Sep 2014, 01:27
Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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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Page: 155
Difficulty: 600

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Team A..40% of 50 = 20
Team B..60% of 50 = remaining 30.
but 70% of researcher prefer A i.e 35

so out of 35 only 20 ppl got allocated to preferred one hence 15 hasn't
it would be the same story for ppl who preferred Team B as well.

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Re: Of the 50 researchers in a workgroup, 40 percent will be [#permalink]

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16 Nov 2014, 06:55
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.
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Re: Of the 50 researchers in a workgroup, 40 percent will be [#permalink]

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11 Jan 2015, 06:20
I did the same with the matrix.

However, in the end I just said:

(assigned to B) - preferred B = 30 - 15 = 15
(preferred A - assigned to A) = 35 - 20 = 15

So, in every case, at least 15 people will be assigned to a group they don't like.
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