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4% of the population of a certain country owns both a car an

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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%

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Last edited by Bunuel on 11 Jul 2014, 12:15, edited 1 time in total.
Renamed the topic and edited the question.

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

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New post 16 Jul 2011, 09:03
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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
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Re: 4% of the population of a certain country owns both a car an [#permalink]

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New post 16 Jul 2011, 10:46
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
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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
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Re: 4% of the population of a certain country owns both a car an [#permalink]

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New post 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%

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New post 18 Jul 2011, 10:29
Good tricky question, can confuse people. I use 2x2 matrix but Karishma's approach looks quite good n quick. Will try to use that next time.

Posted from my mobile device
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New post 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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Re: 4% of the population of a certain country owns both a car an [#permalink]

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New post 07 Sep 2011, 12:18
4 = bc (boat+car)
x = b
0.2x = bc' (boat but not car)
0.8x = bc (boat+car)

0.8x = 4 ..... x = 5%
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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%


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.

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

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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.

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

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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
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New post 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.

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New post 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.

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alice7 wrote:
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.

4 = (80/100) * Total boat owners

Total boat owners = 5
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New post 20 Jan 2016, 13:24
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.

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

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alice7 wrote:
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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New post 21 Jan 2016, 05:16
20% of those who own a boat, do not own a car
-> 80% of those who own a boat, also own a car

Suppose b% of country's population owns a boat
-> 80% of b own both a car and a boat

But it's given that

80% of b = 4
-> b = 400/80 = 5

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

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New post 12 Sep 2016, 13:58
0.2(A+B) = A

This gives us B=4A

Also, according to the question B = 4x (Let total population be 100x. 4% is 4x)
Therefore, 4A = 4x

That implies, A=x
A + B = 5x, which is equal to 5 percent of total population.

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

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New post 12 Sep 2016, 18:37
PareshGmat wrote:
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

This clarify a lot of doubts. Pictorial representation helps and the same can be use in real exam too.
Thanks for the good explanation.

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