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Of the 75 houses in a certain community, 48 have a patio.

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by BTGmoderatorLU » Fri Jul 19, 2019 2:35 pm

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Source: GMAT Prep

Of the 75 houses in a certain community, 48 have a patio. How many of the houses in the community have a swimming pool?

1) 38 of the houses in the community have a patio but do not have a swimming pool.
2) The number of houses in the community that have a patio and a swimming pool is equal to the number of houses in the community that have neither a swimming pool nor a patio.

The OA is B
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Sat Jul 20, 2019 12:35 am
BTGmoderatorLU wrote:Source: GMAT Prep

Of the 75 houses in a certain community, 48 have a patio. How many of the houses in the community have a swimming pool?

1) 38 of the houses in the community have a patio but do not have a swimming pool.
2) The number of houses in the community that have a patio and a swimming pool is equal to the number of houses in the community that have neither a swimming pool nor a patio.

The OA is B
Given: Total number of houses = 75;

Say,

# of houses that have ONLY swimming pool = s;
# of houses that have ONLY patio = p;
# of houses that have both swimming pool and patio= b;

Thus, we have p + b = 48 (given)

# of houses that have neither swimming pool nor patio= n

=> 75 = s + b + p + n = s + n = 48
s + n = 27

We have to find out the value of s + b.

Let's take each statement one by one.

1) 38 of the houses in the community have a patio but do not have a swimming pool.

=> p = 38. Thus, b = 48 - 10 = 38. But we can't get the value of s + b. Insufficient.

2) The number of houses in the community that have a patio and a swimming pool is equal to the number of houses in the community that have neither a swimming pool nor a patio.

=> n = b

Thus, s + b = s + b = s + 10

From s + n = 27, we have s + 10 = 27 => s = 17

Thus, s + b = 17 + 10 = 27. Sussicient.

The correct answer: B

Hope this helps!

-Jay
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by deloitte247 » Sat Jul 20, 2019 11:13 am
Let houses with patio only = P
Let houses with pool only = Q
Let houses with patio & pool = R
Let houses with no patio & pool = S
Given that P + Q + R + S = 75
Where P + R = 48
Find Q + R
Q + S + 48 = 75
Q + S = 75 - 48 = 27

Statement 1 => 35 of the houses have patio but no swimming pool. This means P = 58 but no information about R or S.
Hence, statement is NOT SUFFICIENT

Statement 2 => The number of houses with a patio and a pool is equal to number of houses with no pool and patio
This means R = S
Q + R where R = S will be Q + S which is 27
Statement 2 alone is SUFFICIENT
Answer = option B
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