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# There are many houses in city X. Out of all the houses, 20 have unc

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There are many houses in city X. Out of all the houses, 20 have unc  [#permalink]

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14 Mar 2020, 17:56
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GMATBusters’ Quant Quiz Question -1

There are many houses in city X. Out of all the houses, 20 have uncovered parking space, 20 have covered parking space, and 40 have central garden. How many houses are in city X?
1) No house in city X is without a central garden.
2) Each house in city X that has a covered parking space does not have uncovered parking space.

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Re: There are many houses in city X. Out of all the houses, 20 have unc  [#permalink]

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14 Mar 2020, 17:57

Official Solution :

1) No house in city X is without a central garden.
it means each house is having a central garden.There is not even a single house which doesn't have central garden.
From question stem, we know that the number of houses having central garden is 40.
Hence, number of houses in the city is 40.
SUFFICIENT.

2) Each house in city X that has a covered parking space does not have uncovered parking space.
It means no house is having both covered parking space and uncovered parking space, but there might be some houses which is having no parking space.
Hence, we cannot find the number of houses in the city.
NOT SUFFICIENT.

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Re: There are many houses in city X. Out of all the houses, 20 have unc  [#permalink]

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14 Mar 2020, 18:14
There are many houses in city X. Out of all the houses, 20 have uncovered parking space, 20 have covered parking space, and 40 have central garden. How many houses are in city X?
1) No house in city X is without a central garden.
2) Each house in city X that has a covered parking space does not have uncovered parking space.

Ven diagram approach:
Subset 1: houses having only uncovered parking space = 20
Subset 2: houses having only covered parking space = 20
Subset 3: houses having only central garden = 40

1) No house in city X is without a central garden means all subset 3 is part of subset 1 and subset 2. However, we don't know the no. of houses that do not have uncover and covered parking space. So, total can't be determined. Insufficient.

2) Each house in city X that has a covered parking space does not have uncovered parking space.
No more details about common parts of subset 1, 2 and 3. So insufficient.

1) +2) No information about no. of houses that do not have uncover and covered parking space. So, total can't be determined. Insufficient.

Imo. Ans. E
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Re: There are many houses in city X. Out of all the houses, 20 have unc  [#permalink]

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14 Mar 2020, 18:23
1) Sufficient. If no house in city X is without a central garden, it means that since there only 40 houses with central garden in city X, those are exactly the number of total houses in city X. If city X had more houses, there would be some of them WITH central garden, violating the statement.

2) Not sufficient. We know that each house in city X that has a covered parking space does not have uncovered parking space, which means that in city X, there are at least 40 houses: 20 houses with uncovered parking and 20 with covered parking. It could be the case that each one of these houses has a central garden as well, so the total number of houses would tally up to 40 (assuming only houses with uncovered parking, covered parking and central garden exist). Conversely, none of those houses could have central garden, so the total would add up to 80 (again same assumption as above).

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Re: There are many houses in city X. Out of all the houses, 20 have unc  [#permalink]

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14 Mar 2020, 18:59
Many houses in city X

Uncovered Parking space - 20
Covered Parking Space - 20
Central garden - 40

Need: How many houses in City X

Option 1: No houses in the City X is without central garden.

We already know that there are 40 houses with city X and from option 1 we know that there is no house without central garden. So there are 40 houses in the city

Option 1 alone is Sufficient

Option 2: Each house in city X that has a covered parking space does not have uncovered parking space.

This option says that house that has covered parking space does not have uncovered parking space and this applies to vice-versa as well. No house has both Covered and uncovered parking space.

Is there any house without parking space at all ? - This is not give.

Option 2 alone is Insufficient.

Ans: A
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Re: There are many houses in city X. Out of all the houses, 20 have unc  [#permalink]

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14 Mar 2020, 19:56
Quote:
There are many houses in city X. Out of all the houses, 20 have uncovered parking space, 20 have covered parking space, and 40 have central garden. How many houses are in city X?
1) No house in city X is without a central garden.
2) Each house in city X that has a covered parking space does not have uncovered parking space.

Given Information :
Number of houses with uncovered parking spaces = 20
Number of houses with covered parking spaces = 20
Number of houses with Central garden = 40

Asked : Number of houses = ?
Type : Specific Value
Quote:
1) No house in city X is without a central garden.

If there is no house without a central garden that means the total number of houses are the houses that have central garden. This directly gives us the answer as 40.

Quote:
2) Each house in city X that has a covered parking space does not have uncovered parking space.

While this statement does look sufficient when we come from Statement 1 but actually that is not the case.
Yes This does tell us that there is no overlap between covered parking houses and uncovered parking houses but doesn't talk about where do the houses with central garden count.

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Re: There are many houses in city X. Out of all the houses, 20 have unc  [#permalink]

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14 Mar 2020, 20:32
OA is A
Statement 1 is sufficient enough to explain the no. Of houses present in the city.
As per the statement no house in city x is without central garden and it's already given 40 houses have central garden (sufficient)
Statement 2: The one having covered parking space doesn't have uncovered parking space. But nothing is mentioned about central garden (insufficient)
So OA is A

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Re: There are many houses in city X. Out of all the houses, 20 have unc  [#permalink]

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15 Mar 2020, 01:15
Given: There are many houses in city X. Out of all the houses, 20 have uncovered parking space, 20 have covered parking space, and 40 have central garden.

Asked: How many houses are in city X?

1) No house in city X is without a central garden.
All houses in city X have central garden
There are 40 houses with central garden
There are 40 houses in city X
SUFFICIENT

2) Each house in city X that has a covered parking space does not have uncovered parking space.
There are minimum 40 houses in city X since (20 + 20 = 40)
But exact number can not be ascertained.
NOT SUFFICIENT

IMO A
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Re: There are many houses in city X. Out of all the houses, 20 have unc  [#permalink]

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15 Mar 2020, 02:50
statement 1- sufficient
No house in city x is without central garden=40
That implies total house =40
statement 2-insufficient
It does not tell about relation among houses with central garden,covered n uncovered parking
Re: There are many houses in city X. Out of all the houses, 20 have unc   [#permalink] 15 Mar 2020, 02:50