Problem Solving

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

pullagurla 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

is the answer for this PS A
because A=40% and B=60% assigned to each team respectively
since we have to find the lowest possible.. we suppose that 70% who like team A is assigned 40%
thus 30% left will be settled in team B. so the lowest can be only 30%*50=15

if we find the maximum number of people who settled to team they dislike , we suppose 30% people settled to team B like team A thus that 30% percent of people is assigned to team they dislike and 70 percent like team A is settled only 40% thus there is also 30 % left dislike the team they were assigned , so totally there;s 60 percent to dislike their team
60%*50=30
does it help you a bit?

Hi!
This question is interesting.
if all the researchers, who prefer Team A, were assigned to Team A, the wanted number would be:
[spoiler](70% - 40%)*50 = 30% * 50 = 15

IMO A[/spoiler]

hope it helps!
Best,
Maciek

pullagurla 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

The more complicated the problem, the more time you should spend thinking about it before diving in. Hence:

Step 1 of the Kaplan Method for Problem Solving: Analyze the Problem

We have a percent word problem and we're given enough information to calculate actual numbers as well. We also have a minimum question, phrased negatively, so we need to translate it very carefully (if you misinterpret the question, you're dead before you even get started).

We also note that the answers are numbers that are fairly close together, making estimation tough but adding backsolving as a possible strategy.

Step 2 of the Kaplan Method for Problem Solving: State the Task

We want "the lowest possible number of researchers who will NOT be assigned to the team they prefer". To minimize the unhappy researchers, we want to maximize the happy ones. So, we can first address the question "what's the maximum number of researchers who DO get their preference", then subtract that from 50, the total number of researchers.

Step 3 of the Kaplan Method for Problem Solving: Approach Strategically

Now that we know what we want to calculate, we have to actually do so.

50 workers total

20 on team A, 30 on team B

35 WANT to be on team A, 15 WANT to be on team B.

Well, team A only has 20 spots, so we can make 20 of the "wanna be A" people happy; team B has 15 slots, so we can make all 15 of the"wanna be B" happy.

20 + 15 = 35 happy people.

50 - 35 = 15 unhappy people.

Accordingly, the minimum number of unhappy people is 15.

Step 4 of the Kaplan Method for Problem Solving: Confirm your Answer

We solved for the minimum number of unhappy people; double checking, we interpreted the question correctly: choose (A).

Maybe I'm missing something, but why can't the answer be 5?

If 20 must be on team A 30 on team B; and 35 WANT to be on team A and 15 WANT to be on team B...

then why can't you put 30 of those that want to be on Team A on Team B?

That makes 30 unhappy researchers on Team B with 5 remaining who will end up on Team A with the other 15 that wanted to be on Team B. That means you have 45 unhappy researchers and only 5 happy ones.

35 (want to be on A) - 30 (spots on B) = 5 (want to be on Team A and end up on Team A)

Maybe, I'm misreading the question?

quiimari wrote:Maybe I'm missing something, but why can't the answer be 5?

...
Maybe, I'm misreading the question?

Quiimari,

Absolutely you misread the question. it asks you to find the lowest number of unhappy researchers not the lowest number of happy ones.