Bunuel wrote:

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%

Attachment:

matrix.png [ 8.03 KiB | Viewed 2199 times ]
I - Double Matrix (see Diagram) 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 SetsA + 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 = -5Both = 55 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

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"