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M05-12

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Bunuel
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M05-12 [#permalink] New post   16 Sep 2014, 00:25
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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%
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Bunuel
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Re M05-12 [#permalink] New post   16 Sep 2014, 00:25
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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
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gmatminator
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Re: M05-12 [#permalink] New post   28 Aug 2015, 13:19
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Solved with a table, setting TOT to 100:

---------Boat----NOT Boat----TOT-
Car------- 4 ---------------------
NOT Car-- 0.2x -------------------
TOT------- x ----------------100 -

4+0.2x=x
x=5
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Re: M05-12 [#permalink] New post   29 Aug 2019, 08:18
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Bunuel 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's say N=100.
Imagine a 2D Venn diagram, showing Boat, Car and Both.
4% Own both. So the Common area gets a value of 4.
Let's assume the people who own boat but not both to be x.

0.2(x+4)=x (20% of those who own a boat which is nothing but (x+4) is nothing but the people who do not own a car which is people who own only a boat which is x)
0.2x+0.8=x
0.8=0.8x
x=1

So 4+1 is 5%
Hence A.
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Re: M05-12 [#permalink] New post   29 Aug 2019, 10:00
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I used the table method to help me visualize:

_________________Own A Car_____Don't Own A Car___Total
Own A Boat___________4%____________.2x_____________x__
Don't Own A Boat______________________________________
Total_____________________________________________100%

Looking at this, one can clearly see that 4% of the total is equal to 80% of those who own a boat:
4=.8x
x=5

The correct answer is answer choice A.


Please give kudos if this was helpful in any way!
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Re: M05-12 [#permalink] New post   20 May 2020, 11:59
chetan2u Bunuel

If the same question stem was a part of DS, then was the data sufficient?
We are assuming that 80% is 4%(population), but what if there is definite % of null sample, who don't own anything?
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Re: M05-12 [#permalink] New post   20 May 2020, 13:28
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ankitthapar83 wrote:
chetan2u Bunuel

If the same question stem was a part of DS, then was the data sufficient?
We are assuming that 80% is 4%(population), but what if there is definite % of null sample, who don't own anything?

No unnecessary assumptions are made here.

Population does not own a car = Population does not own a car but owns a boat + population does not own a car and does not own a boat
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Re: M05-12 [#permalink] New post   29 Apr 2023, 10:26
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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M05-12 [#permalink] New post   14 Jun 2023, 19:38
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this is more like a fun word problem which can be solved without pen and paper. but it ain't easy though! nice question!

20% of boat owners do not have car => 80% boat owners have both boat and car. only 4% of entire population have both boat and car.

Now, 80% of boat owners = 4% of population => 100% boat owners will be 5% of populatio
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M05-12 [#permalink]
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