Question Bank: Word Problems #16

[DanielJ295]

Question Stem:

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.

The answer is only 1 alone is sufficient. I am thinking both are sufficient. We both agree that 1. is sufficient. But I believe 2. is also sufficient.

This is my thinking: If each house on Kermit Lane that has a front porch does not have a front yard, then 20 houses do not have front yards. And the total houses on Kermit must equal houses with a front yard + houses without a front yard. We know both of these amounts from the question stem and the info given in 2. So how is 2. not sufficient??

[Linh]

I think your reasoning is correct about front porches and front yard houses: (2) means there is no overlapping set between these two types of houses.

But you forgot this guy: "40 have back yards"
- If there are 20 houses having both front porches and back yards & 0 houses having both front yards and back yards , then the total houses are 60.
- If there are 10 houses having both front yards and back yards & 0 houses having both front porches and back yards, then the total houses are 70.
- If there are 0 houses having both front porches and back yards & 0 houses having both front yards and back yards , then the total houses are 100.
etc... --> insufficient.

(umm, any careless mistakes here )

[RonPurewal]

hi,
problems from MPrep materials have separate folders here -- one folder for problems from our CAT exams, and another for problems from all our other resources.

if this is from our question bank, please re-post your question in the appropriate folder. thank you.