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4% of the population of a certain country owns both a car an [#permalink]

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16 Jul 2011, 08:55

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4% of the population of a certain country owns both a car and a boat. If 20% of those who own a boat, do not own a car, what percentage of the country's population owns a boat?

4% of the population of a country, , owns a car and a boat. If 20% of those who own a boat, do not own a car, what percentage of the country's population owns a boat?

5% 7.5% 10% 12.5% 15%

When I read, "If 20% of those who own a boat, do not own a car", I say to myself, "Ok, then 80% of those who own a boat, do own a car too." But this number (people who own a boat and a car) is given as 4% of Population. So 80% of Boat owners = 4% of Population Boat owners = 1/20 of Population = 5% of Population
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Re: 4% of the population of a certain country owns both a car an [#permalink]

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17 Jul 2011, 22:28

Assume there are 1000 people, 40 owns both car & boat. 20% of those who owns a boat do not own a car i.e. 80% of boat owners, own cars. i.e. 0.8 B = 40 ==> B = 50 % of boat owners = 50/1000 = 5%

Re: 4% of the population of a certain country owns both a car an [#permalink]

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18 Jul 2011, 12:40

VeritasPrepKarishma wrote:

AnkitK wrote:

4% of the population of a country, , owns a car and a boat. If 20% of those who own a boat, do not own a car, what percentage of the country's population owns a boat?

5% 7.5% 10% 12.5% 15%

When I read, "If 20% of those who own a boat, do not own a car", I say to myself, "Ok, then 80% of those who own a boat, do own a car too." But this number (people who own a boat and a car) is given as 4% of Population. So 80% of Boat owners = 4% of Population Boat owners = 1/20 of Population = 5% of Population

Perfect approach - I also used the same approach. .

20% of those who own boat -> own no Car So 80% of those who own boat -> own a car This is 4% of population So 80% of those who own boat = 4% of population ==> 100% of those who own boat = (4/80)100 = 5%

Hope this makes sense...Give kudos to Karishma because she posted this solution first
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4% of the population of a certain country owns both a car and a boat. If 20% of those who own a boat, do not own a car, what percentage of the country's population owns a boat?

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

Say total population of the country is 100. Then # of people who owns both a car and a boat is 0.04*100=4.

Now, since 20% of those who own a boat, do not own a car, then 80% of those who own a boat, do own a car, so own both a car and a boat. So, we have that if # of people who owns a boat is B, then # of people who owns both a car and a boat is 0.8B. On the other hand we know that # of people who owns both a car and a boat is 4, hence 0.8B=4 --> B=5. Which means that 5% of the population owns a boat.

Re: 4% of the population of a certain country owns both a car [#permalink]

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27 Dec 2012, 21:44

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monir6000 wrote:

4% of the population of a certain country owns both a car and a boat. If 20% of those who own a boat, do not own 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 “x” be the total number of people with a boat. Let “y” be the total population. 4% own both a boat and a car -> 0.04y ------- 1 20% of those who own a boat do not own a car So 80% of those who own a boat own a car -> 0.8x ------2 Since 1 and 2 represent the number of people with both car and boat 0.04y = 0.8x x= 0.05y -> 5% of entire population.

Re: 4% of the population of a certain country owns both a car an [#permalink]

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19 Jan 2016, 21:44

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.

Re: 4% of the population of a certain country owns both a car an [#permalink]

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19 Jan 2016, 21:44

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.

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.

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.

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.

"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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Re: 4% of the population of a certain country owns both a car an [#permalink]

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14 Oct 2017, 21:28

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