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Of all houses on Kermit Lane, 20 have front porches, 20 have

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Of all houses on Kermit Lane, 20 have front porches, 20 have

by BTGmoderatorLU » Tue May 28, 2019 5:51 pm

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Source: Manhattan Prep

Of all houses on Kermit Lane, 20 have front porches, 20 have front yards, and 40 have back yards. How many houses are on Kermit Lane?

1) No house on Kermit Lane is without a back yard.
2) Each house on Kermit Lane that has a front porch does not have a front yard.

The OA is A
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Source: — Data Sufficiency |

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by Ian Stewart » Sat Jun 01, 2019 6:00 am

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If every house has a back yard, and, as Statement 1 tells us, 40 houses have a back yard, there are 40 houses in total, so Statement 1 is sufficient.

From Statement 2, if a house has a front porch, it does not have a front yard. So if a house has a front yard, it cannot have a front porch. So we have 20 houses with only the porch, and 20 with only the yard, for a minimum of 40 houses in total. But some houses might have neither a porch nor a yard, so we don't know how many houses we have in total, and the answer is A.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by deloitte247 » Fri Jun 07, 2019 12:50 pm

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How many houses are on kermit Lane?
Statement 1
No house on kermit lane is without back yard
This means that all house on kermit lane have a backyard since number of houses with backyard = 40
Therefore, 40 houses are on kermit lane.
Statement 1 is SUFFICIENT.

Statement 2
Each house on kermit lane that have a front porch does not have a front yard
This means that houses with front porch and front yard are disjoint set with no intersection, but there is no information relating to the number f houses with backyards, so it is difficult to arrive at a definite conclusion for the number of houses on kermit lane.
Hence statement 2 is INSUFFICIENT.
Since statement 1 alone is SUFFICIENT,

$$Answer\ is\ Option\ A$$
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