From Kaplan 800 - Please confirm answers

Two problems: I do not have OAs. So, please confirm answers.

1. x, y, z -> All positive integers.
0<x<y<z.
x: Even, y: Odd, Z: Prime.
What is the possible value of x+y+z?
Options: A. 4
B. 5
C. 11
D. 15
E. 18.

[spoiler]My Approach: Even + Odd + Odd (Since z is greater than 2) = Even. 4 is not possible. Hence Ans is E[/spoiler]

2. a and b are integers such that 1 + b = 5. Which of the following is true?
I. a*b is odd
II. If a is off, b is even
III. If a is negative, b is positive.

Options: A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

[spoiler]
My approach: since the sum is odd, either of them can be even or odd but not both. So, the product will be even. So, I is not true
If one is odd, then other is even. So, II must be true.
If one is negative, then other must be bigger and hence positive to make sure that the sum is positive. Hence the correct answer is D[/spoiler]