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# In a certain town, 40 percent of the residents own a car.

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Manager
Joined: 03 Mar 2018
Posts: 215
In a certain town, 40 percent of the residents own a car.  [#permalink]

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05 Mar 2018, 06:13
3
00:00

Difficulty:

85% (hard)

Question Stats:

42% (01:58) correct 58% (01:36) wrong based on 38 sessions

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In a certain town, 40 percent of the residents own a car. What percent of the residents own neither a house nor a car?

(1) Each resident who owns a house also owns a car but the vice-versa is not true

(2) 30 percent of the residents own a house

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_________________

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Joined: 21 Aug 2013
Posts: 1434
Location: India
Re: In a certain town, 40 percent of the residents own a car.  [#permalink]

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05 Mar 2018, 10:09
itisSheldon wrote:
In a certain town, 40 percent of the residents own a car. What percent of the residents own neither a house nor a car?

(1) Each resident who owns a house also owns a car but the vice-versa is not true

(2) 30 percent of the residents own a house

Statement 1
Each resident who owns a house also owns a car, that means those 'who own a house' are a subset of 'those who own a car'. Now those who own a car are 40%, and the ones with house are a subset of and less than 40%.
This means residents who lie outside this set of 40% (meaning those who dont have a car) will be our answer, because those who dont have a car cannot have a house also.
So percentage of residents who own neither a house nor a car = 100 - 40% = 60%.
Sufficient.

Statement 2
40% own a car, and 30% own a house. But we dont know how many own both a car and a house. So we will not be able to calculate those who own neither a car nor a house. Not sufficient.

Intern
Joined: 26 Oct 2016
Posts: 26
In a certain town, 40 percent of the residents own a car.  [#permalink]

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05 Mar 2018, 14:00
can someone explain with the table method? not able to solve it
DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1434
Location: India
Re: In a certain town, 40 percent of the residents own a car.  [#permalink]

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05 Mar 2018, 21:48
1
ezzo wrote:
can someone explain with the table method? not able to solve it

Hi

I have tried to explain by means of circular Venn diagram in the attached pic.

Statement 1
Since those who own a house also own a car, 'those who own house' are a subset of 'those who own car', thus 'those who own house' circle is inside the circle of 'those who own car'. So if 40% own car, that means outside the 'those who own car' circle, the remaining 60% people have no car and no house either. Sufficient.

Statement 2
We dont know how many own both car and house, and we also dont know whether one of these ('those who own car' and 'those who own house') is a subset of other or not. So we cannot deduce how many have neither a house nor a car. Not sufficient.
Attachments

IMG_20180306_110908_2.jpg [ 49.71 KiB | Viewed 346 times ]

Intern
Joined: 26 Oct 2016
Posts: 26
Re: In a certain town, 40 percent of the residents own a car.  [#permalink]

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07 Mar 2018, 09:12
Thanks. the venn diagram just made the things very much clear.

amanvermagmat wrote:
ezzo wrote:
can someone explain with the table method? not able to solve it

Hi

I have tried to explain by means of circular Venn diagram in the attached pic.

Statement 1
Since those who own a house also own a car, 'those who own house' are a subset of 'those who own car', thus 'those who own house' circle is inside the circle of 'those who own car'. So if 40% own car, that means outside the 'those who own car' circle, the remaining 60% people have no car and no house either. Sufficient.

Statement 2
We dont know how many own both car and house, and we also dont know whether one of these ('those who own car' and 'those who own house') is a subset of other or not. So we cannot deduce how many have neither a house nor a car. Not sufficient.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: In a certain town, 40 percent of the residents own a car. &nbs [#permalink] 07 Mar 2018, 09:12
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