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

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Manager
Joined: 11 Feb 2011
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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%

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Last edited by Bunuel on 11 Jul 2014, 11:15, 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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16 Jul 2011, 08:03
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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%

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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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Senior Manager Joined: 24 Mar 2011 Posts: 428 Location: Texas Re: 4% of the population of a certain country owns both a car an [#permalink] ### Show Tags 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% Manager Joined: 14 Apr 2011 Posts: 192 Re: 4% of the population of a certain country owns both a car an [#permalink] ### Show Tags 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 _________________ Looking for Kudos Manager Status: On... Joined: 16 Jan 2011 Posts: 181 Re: 4% of the population of a certain country owns both a car an [#permalink] ### Show Tags 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 _________________ Labor cost for typing this post >= Labor cost for pushing the Kudos Button http://gmatclub.com/forum/kudos-what-are-they-and-why-we-have-them-94812.html Senior Manager Status: mba here i come! Joined: 07 Aug 2011 Posts: 260 Re: 4% of the population of a certain country owns both a car an [#permalink] ### Show Tags 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% _________________ press +1 Kudos to appreciate posts Math Expert Joined: 02 Sep 2009 Posts: 43831 Re: 4% of the population of a certain country owns both a car [#permalink] ### Show Tags 29 Apr 2012, 02:59 Expert's post 3 This post was BOOKMARKED 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. _________________ Current Student Joined: 12 Jan 2012 Posts: 26 GMAT 1: 720 Q49 V39 Re: 4% of the population of a certain country owns both a car [#permalink] ### Show Tags 27 Dec 2012, 20:44 1 This post received KUDOS 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. SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1839 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Re: 4% of the population of a certain country owns both a car an [#permalink] ### Show Tags 24 Jul 2014, 00:32 1 This post received KUDOS 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 Attachments car.png [ 4.42 KiB | Viewed 3344 times ] _________________ Kindly press "+1 Kudos" to appreciate Intern Joined: 12 Nov 2014 Posts: 21 Re: 4% of the population of a certain country owns both a car an [#permalink] ### Show Tags 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. Intern Joined: 12 Nov 2014 Posts: 21 Re: 4% of the population of a certain country owns both a car an [#permalink] ### Show Tags 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. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7942 Location: Pune, India Re: 4% of the population of a certain country owns both a car an [#permalink] ### Show Tags 19 Jan 2016, 22:02 1 This post received KUDOS Expert's post 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 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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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 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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20 Jan 2016, 22:33
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Expert's post
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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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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Re: 4% of the population of a certain country owns both a car an [#permalink]

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Re: 4% of the population of a certain country owns both a car an   [#permalink] 14 Oct 2017, 20:28
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