Re: Of the 214 cars at a car dealership, 113 have leather seats,
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09 Feb 2022, 10:06
We can solve this using the overlapping sets formula for two which is Total = Group1 + Group2 - Those in Both Groups + Neither.
So, for the first case, Total = 214, Group 1(Having leather seats) = 113, Group2(Having power windows) = 145, Neither = 30 (Here neither is minimum).
According to the formula, we get 214 = 113 + 145 + Both - 30 = 74.
Now, consider the second case in which all those in Group 1 are already in Group 2, so Total = 214, Group 1(Having leather seats) = 113, Group2(Having power windows) = 145 - 113 = 32(As Group 1 is already in Group 2), Neither = 214 - 145 = 69(Here neither is maximum).
According to the formula, we get 214 = 113 + 145 + Both - 69 = 113.
So the range of Both is 74 < Both < 113. Hence the only options that satisfy this condition is option 3 and option 4.