The three integers in the set {x, y, z} are all less than 30. How many of the integers are positive?
(1) x + y + z = 67
(2) x + y = 35

This question is a little confusing. Although Statement (2) is insufficient either way, when Statement (1) and Statement (2) are taken together, z can be calculated as (35) + z = 67, or z = 32. This appears to contradict the constraint defined in the problem that all three integers must be less than 30. I'm not sure if this is a typo, but I wasted a lot of time rereading the problem to make sure I wasn't missing anything.

Don't forget that integers are positive and negative whole number, and zero. So, it is entirely possible that some of the numbers are negative.

Statement (1) alone is sufficient. Since all the numbers are less than 30, all three must be positive for their sum to be 60 or greater because there is no way to get a sum greater than or equal to 60 with just two of positive numbers less than 30