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In Motor City 90 percent of the population own a car, 15 percent own a motorcycle, and everybody owns one or the other or both. What is the percentage of motorcycle owners who own cars?
(A) 5%
(B) 15%
(C) 33 1/3%
(D) 50%
(E) 90%
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(A) 5%
(B) 15%
(C) 33 1/3%
(D) 50%
(E) 90%
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Total number of people = 100. Fill in:
Cars = 90
Motorcycles = 15
No Car, No Motorcycle = 0
Then:
1) Number who do not own a car: 100 - 90 = 10 (No Car)
2) Number of motorcycle owners who do not own a car MUST = 10 because 0 own neither, and the column must add up to 10 (so 10 = Motorcycle and No Car)
3) Number of car AND motorcycle owners: 15 - 10 = 5 - because row MUST add up to 15 (so 5 = Car and Motorcycle)
What is the percentage of motorcycle owners who own cars?
Motorcycle owners = 15
Motorcycle owners who own cars = 5
\(\frac{5}{15} * 100 =\) (.33 * 100) = 33 1/3 %
Answer C
II - Formula for Overlapping Sets
A + B - Both + Neither = Total number
Because we are given percentages, let the total number of people = 100
Let A = people who own cars = 90 percent = 90
Let B = people who own motorcycles = 15 percent = 15
Both?
Everyone owns a car or a motorcycle or both: "Neither" = 0
A + B - Both + Neither = Total number
90 + 15 - Both + 0 = 100
- Both = -5
Both = 5
5 people own both a motorcycle and a car.
What is the percentage of motorcycle owners who own cars?
Motorcycle owners = B, so: what percentage of B is "both"?
Or: "both" = what percentage of B?
Both = 5, B = 15
\(\frac{5}{15} * 100 =\) (.33 * 100) = 33 1/3%
Answer C
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It is a simple set theory question.
AUB = A + B - A∩B
AUB is overall: 100 (as everyone owns one or other)
A = 90 (cars)
B = 15 (bike)
A∩B is who owns both.
100 = 90 + 5 - A∩B
A∩B = 5
A.
AUB = A + B - A∩B
AUB is overall: 100 (as everyone owns one or other)
A = 90 (cars)
B = 15 (bike)
A∩B is who owns both.
100 = 90 + 5 - A∩B
A∩B = 5
A.
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Last visit: 05 Jan 2024
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Expert reply
Posts: 2,973
Bunuel
We can use the following formula:
Total = total cars + total motorcycles - both + neither
We can let the total = 100 and b = both and create the equation, noting that since everyone owns at least one vehicle, the value of neither is 0:
100 = 90 + 15 - b + 0
100 = 105 - b
b = 5
Thus, 5/15 = 1/3 = 33⅓% of the motorcycle owners also own a car.
Answer: C
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Total: Car + Motorcycle - Both
Both: 90 + 15 - 100 = 5
Motorcycle owners who own cars: \(\frac{5}{15}\) * 100 = 33 \(\frac{1}{3}\)%
Answer C
Both: 90 + 15 - 100 = 5
Motorcycle owners who own cars: \(\frac{5}{15}\) * 100 = 33 \(\frac{1}{3}\)%
Answer C
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