Of the 75 houses, 48 have a patio. How many have a swimming

[Guest]

Of the 75 houses, 48 have a patio. How many have a swimming pool?

1. 38 of the houses have a patio but don't have a swimming pool.
2. The number of houses that have a patio and a swimming pool equals the number that have neither a patio nor a swimming pool.


My question is:
Is the answer A insufficient only because it doesn't tell us if any of the houses have neither a swimming pool nor a patio?

Thanks

[RA]

Is the OA (C)?

To calculate houses with swimming pools we need to know 2 pieces of information
-- the number of houses with swimming pool and patio and
-- the number of houses with swimming pool but no patio

Choice (A) helps us calculate the first piece of information (48 - 38 = 10) but doesn't tell us anything about the second piece of information. Hence choice (A) is insufficient.

[Guest]

No. The answer is B.

[san]

Is the OA (C)?

To calculate houses with swimming pools we need to know 2 pieces of information
-- the number of houses with swimming pool and patio and
-- the number of houses with swimming pool but no patio

Choice (A) helps us calculate the first piece of information (48 - 38 = 10) but doesn't tell us anything about the second piece of information. Hence choice (A) is insufficient.

Of the 75 houses, 48 have a patio. How many have a swimming pool?

1. 38 of the houses have a patio but don't have a swimming pool.
2. The number of houses that have a patio and a swimming pool equals the number that have neither a patio nor a swimming pool.

I will say the answer is B.
the total number of p+s=75, and p itself has 48 (the total number of p), so it give us (75-48)=27 (the total number not P)
in statement 1, p=38, but don't have s (48-38)=10. however, it does not tell us anything about not p or not s. it is not sufficient to answer the question.

statement 2: the number of (total number of p)+(total number of s)=total number of not p+ total number of not s, since we know the total num. of p=48, and total num. of not p=27, now you can figure out the answer. so it is sufficient to answer the question.

[RonPurewal]

this is an overlapping sets problem featuring 2 sets.

like any other such problem, it can be tackled efficiently with the use of the double-set matrix.

i have posted such a solution here.

[abedinbhuiyan]

Ron,

U r solution is not there. Pls respond.

BR

[atul.prasad]

Let there be n houses that have neither P nor S

a = Only P (no S)
x = Both P and S
b = Only S

Therefore a+x+b = 75-n
and a+x = 48 (houses which have P)
(The number of house who have either P or S or both = total number of houses - houses who have neither)

from statement 1 , we know a= 38
but we need to find out b+x , which cant be evaluated using this
INSUFFICIENT

from statement 2
n = x
so
a+x + b+x = 75
We already know what a+x is, so b+x = 27
Hence SUFFICIENT and answer should be B

[jnelson0612]

atul's logic is correct.

Also, please see this link which demonstrates the use of the double set matrix to solve this problem: of-the-75-houses-in-a-certain-community-48-have-a-patio-t3491.html

Thank you,