Let's only look at statement 2.
The dishwasher has 55 minutes remaining in its cycle.
Statement 2 says: Putting away the dishes will take Patrick 7 minutes.
Patrick needs to put away the dishes after the dishwasher completes its cycle.
So completing the cycle and putting away the dishes will take 62 minutes, which is more than exactly an hour. Therefore, given only statement 2, Patrick can't even complete the one task of putting away the dishes, let alone completing all his tasks. Statement 2 alone is sufficient to tell whether or not Patrick will complete his tasks on time.
With this in mind, let's look at statement 1 alone.
He can vacuum the floors and fold the laundry while the dishwasher is running, all within an hour. After the dishwasher completes the cycle, he needs to start putting away the dishes. Since it'll take another 55 minutes for the dishwasher to complete the cycle, and guests arrive in exactly 60 minutes, the question becomes how long it takes Patrick to put away the dishes. If he can do it within 5 minutes, then yes, he can complete all his tasks before his guests arrive. On the other hand, if it takes him more than 5 minutes to put away the dishes, then no, he cannot complete all his tasks on time. Statement 1 does not tell you how long it takes him to put away the dishes, and therefore statement 1 alone is not sufficient.
The answer is B - statement 2 alone is sufficient, but statement 1 alone is not sufficient.
