Online Question Bank : Word Problems : #10

I had trouble with statement (2) for this example.

Of all the 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.

I can't draw a Venn diagram here - but you can look at the diagram in the official explanation if you need to visualize.

20 = front porches
20 = front yards
40 = back yards

So, at the least, there are 40 houses. A house could have 1, 2, or all 3 of the above characteristics, or it could have none of them.

(You said you had trouble with statement 2, so I'll only address that one.)
Statement 2 says that, if a house has a front porch, then it does not have a front yard. So the first two categories, above, don't overlap. I can conclude that I have at least 40 houses (20 with front porches and 20 with front yards - and these could overlap completely with the 40 that have backyards to give 40 houses total) but I could also have, say 80 houses: 20 with only front porches, 20 more with only front yards, and 40 more with only back yards. Or some other combo - but I've just found two different amounts, so I can stop here because I can't answer the question with this statement.