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).
