Of the 50 researchers in a work group, 40% will be assigned to Team A and the remaining 60% to Team B. However, 70% of the researchers prefer team A and 30% prefer Team B. What is the least possible number of researchers who will not be assigned to the team they prefer ?

Number of researchers who prefer Team A = 70% of 50 = 35
Number of researchers who prefer Team B = (50 - 35) = 15
Number of researchers assigned to Team A = 40% of 50 = 20
Number of researchers assigned to Team B = (50 - 20) = 30
To find the least possible number of researchers who will not be assigned to the team they prefer, we assume that the maximum number of researchers get the team they prefer.
So,Number of researchers who are assigned to the team they prefer = 20 (Team A) + 15 (Team B) = 35
∴ Required number = (50 - 35) = 15