问个Prep的数学题目，百思不得其解

prep1- of the 75 houses in a certain community, 48 have a patio, how many of the houses have a swimming pool?

(1)38 of the houses in the community have a patio but don't 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.

我认为两个条件一起才充分，prep上给出的答案是（2）本身充分

谁知道是怎么回事啊，多谢多谢！

Let x=the number of houses that have both patio and sp; y=the number of houses that only have sp; z= the number of houses that have neither patio and sp.

Then, the number of houses that only have patio is (48-x). And 48+y+z=75. We want to know what is (x+y), i.e. the number of houses that have sp.

From (2), x=z. So x+y=z+y=75-48=27. (2) is sufficient.

If it's hard to understand for you, then drawing a picture might help a lot.