Question

Of the $50$ researchers in a work group, $40$ 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?
$A)15$
$B)17$
$C)20$
$D)25$
$E)30$

Answer 1

Hint: First, there are a total of fifty researchers in the workgroup.
There are two kinds of teams, which are team A and team B. $40$ the percent will be assigned to Team A, but $70$ the percent of the researchers prefer Team A.
Likewise, $60$ the percent is assigned to Team B but $30$ the percent only prefer Team B.
We need to find the lowest possible number of the given fifty researchers who are not assigned to their liked team.

Complete step by step answer:
We need to use the percentage formula to solve this question further to simplify the teams.
From the given that, $40$ percent will be assigned to Team A, which means $\dfrac{{40}}{{100}} \times 50$(the fourth percentage is written in the fraction form into times of the given persons fifty)
Hence, we get Team A assigned with $\dfrac{{40}}{{100}} \times 50 \Rightarrow 20$
Similarly for team B, we have $60$ percent is assigned; thus, we get $\dfrac{{60}}{{100}} \times 50 \Rightarrow 30$
If we add the team A and B we get the overall person, $20 + 30 = 50$which is the assigned calculation.
Now we will calculate the refer teams A and B which are $\dfrac{{70}}{{100}} \times 50 \Rightarrow 35$and $\dfrac{{30}}{{100}} \times 50 \Rightarrow 15$ prefer person in the total fifty counts.
If all of the $15$people in team B are assigned to the team B that they prefer, then which is to have$30$researchers, then $15$ who will prefer team A will be needed to assign team B.
Hence the given question is to find the lowest possible; which is $20$spots on team A.
Hence, we get $35 - 20 = 15$(where thirty-five is the team A possible and twenty is the alternative way in team A to fill the spot to team B)

So, the correct answer is “Option A”.

Note: We are simply able to solve those problems after finding the total preferred members like in team A $35$ and team B $15$. Thus, to get the lowest possible who will not be assigned to their preferred team is $\min (15,35) = 15$
If the question is about the greatest possible of the not assigned we get $35$, we are also able to solve this using the above formula or using the help of maximum concept.