In a country, 4% of the population owns both a car and a boat. If 20%

Question

In a country, 4% of the population owns both a car and a boat. If 20% of boat owners do not have a car, what percentage of the country's population owns a boat?

A. 5% 
 B. 7.5% 
 C. 10% 
 D. 12.5% 
 E. 15%

M05-12

Bunuel · Accepted Answer

In a country, 4% of the population owns both a car and a boat. If 20% of boat owners do not have a car, what percentage of the country's population owns a boat?

A. 5% 
 B. 7.5% 
 C. 10% 
 D. 12.5% 
 E. 15%

Let's assume the total population of the country is 100. In this case, the number of people who own both a car and a boat is  0.04*100 = 4 .
 
Since 20% of boat owners do not own a car, it follows that 80% of boat owners do own a car, and therefore own both a car and a boat. If we denote the number of people who own a boat as B, then the number of people who own both a car and a boat is 0.8B. We know that there are 4 people who own both a car and a boat, so  0.8B = 4 . From this, we can calculate that  B = 5 . This means that 5% of the population owns a boat.

Answer: A

subhashghosh · Answer

0.04x has B+C ( x is total population)

Let # of people who own a boat = y

20% of those who own a boat, do not own a car

=> 0.2y do not have a car

=> 80% of those who own a boat own a car

=> 0.8y = 0.04x

=> y/x = 4/80

So %age = 4/80 * 100 = 5%

Answer - A

yogesh1984 · Answer

for such Q's visualization may be tricky sometimes, I would recommend to use 2 * matrix here (this method is quite useful- just give it a shot)

lets say X is the % of population with a boat then you would get the equation-

4+ 0.2 * X = X -> solving this results X= 5% (here visualization is the important point!)

Hope it helps

PareshGmat · Answer

Refer diagram below:

4% has both boat & car

20% of those who own a boat, do not own a car; it also means 80% of those who own a boat also own a car

\frac{80}{100} b = 4

b = 5

alice7 · Answer

hi paresh gmat, I used the same venn diagram but I got 76 people who owned car but not boat. but as 20 is the number of people who only owns boat but not car, then 20/100 should be 20%? Am I missing something.

KarishmaB · Answer

How did you get the underlined part? 
You are given that 20% of those who owned a boat did not own a car. So 80% of total boat owners were also car owners. This is the overlap region which has 4 people. The 4 people account for 80% of total boat owners.

4 = (80/100) * Total boat owners

Total boat owners = 5

alice7 · Answer

SO If you assume total as 100. And 4 is the no which has both and 20 is only car. then 100-20-4 = 76 people who has only boat.

KarishmaB · Answer

"If 20% of those who own a boat, do not own a car," 
does not imply that 20 people own only boat. It implies that 20% of people who own a boat do not have a car. So if 10 people own a boat, 2 of them do not have a car. If 50 people own a boat, 10 of them do not have a car. If 100 people own a boat, 20 of them do not have a car etc.

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In a country, 4% of the population owns both a car and a boat. If 20%

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In a country, 4% of the population owns both a car and a boat. If 20%

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