utkalnayak wrote:At a certain dealership, every car on the lot has at least one of the three modest options: windows, brakes and radio. 40 cars have windows, 30 have brakes, and 50 have a radio. 21 cars have brakes and radio, 13 have windows and brakes. 17 have windows and radio. If 11 cars have all 3 options, what is the total number of cars on the lot ?
A. 69
B. 70
C. 80
D. 91
E. 120
Draw a VENN DIAGRAM representing the following:
40 cars have windows.
30 cars have brakes.
50 cars have radios.
Complete the Venn diagram by working from the INSIDE OUT.
11 cars have all 3 options.
21 cars have brakes and radio.
13 have windows and brakes.
17 have windows and radio.
Subtracting from these figures the 11 cars with all 3 options, we get:
Subtracting the values in the diagram from W=40, B=30, and R=50, we get:
What is the total number of cars on the lot?
Adding together the values in the Venn Diagram, we get:
T = 21+2+7+6+11+10+23 = 80.
The correct answer is
C.
Why can we not apply the following formula on the above problem? Are the numbers given in the problem statement not calculated accurately ?
(A + B + C ) = A + B + C - (AB + BC + CA) - 2(ABC)
In this formula:
AB = the elements in ONLY A AND B.
BC = the elements in ONLY B AND C.
CA = the elements in ONLY C AND A.
The prompt does not provide these values.
In the prompt:
The 21 cars with brakes and radio include both the cars with ONLY brakes and radio AND the cars will ALL 3 OPTIONS.
The 13 cars with windows and brakes include both the cars with ONLY windows and brakes AND the cars will ALL 3 OPTIONS.
The 17 cars with windows and radio include both the cars with ONLY windows and radio AND the cars will ALL 3 OPTIONS.
For this reason, I would solve with a Venn Diagram, as shown above.
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