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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, 07:55
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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? A. 5% B. 7.5% C. 10% D. 12.5% E. 15% M0512
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Last edited by Bunuel on 11 Jul 2014, 11:15, edited 1 time in total.
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Re: 4% of the population of a certain country owns both a car an [#permalink]
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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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16 Jul 2011, 09:46
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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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Re: 4% of the population of a certain country owns both a car an [#permalink]
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17 Jul 2011, 21:10
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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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17 Jul 2011, 21:28
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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Re: 4% of the population of a certain country owns both a car an [#permalink]
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18 Jul 2011, 09:29
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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Re: 4% of the population of a certain country owns both a car an [#permalink]
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18 Jul 2011, 11:40
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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07 Sep 2011, 11:18
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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Re: 4% of the population of a certain country owns both a car [#permalink]
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29 Apr 2012, 02:59
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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27 Dec 2012, 20:44
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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.



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Re: 4% of the population of a certain country owns both a car an [#permalink]
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24 Jul 2014, 00:32
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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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Re: 4% of the population of a certain country owns both a car an [#permalink]
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19 Jan 2016, 20:44
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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Re: 4% of the population of a certain country owns both a car an [#permalink]
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19 Jan 2016, 20:44
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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Re: 4% of the population of a certain country owns both a car an [#permalink]
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19 Jan 2016, 22:02
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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Re: 4% of the population of a certain country owns both a car an [#permalink]
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20 Jan 2016, 12:24
SO If you assume total as 100. And 4 is the no which has both and 20 is only car. then 100204 = 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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20 Jan 2016, 22:33
alice7 wrote: SO If you assume total as 100. And 4 is the no which has both and 20 is only car. then 100204 = 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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21 Jan 2016, 04:16
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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12 Sep 2016, 12:58
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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12 Sep 2016, 17:37
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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