Choice (C) is correct.
The stem doesn't give us much information to work with, so we can go directly to the statements. They will be sufficient only if y must be less than z or cannot be less than z.
Statement (1): insufficient. This tells us the sum of y and z, but it says nothing about their relative values. It is possible that y and z are equal (if each is 0.5), or that either variable is greater (e.g., y = 1 and z = 0, or vice versa). Eliminate (A) and (D).
Statement (2): insufficient. Let's say that y2 = 9 and that z2 = 25. Then y = 3 or -3 and z = 5 or -5. If y = 3 and z = 5, then z is greater. However, if y = -3 and z = -5, then y is greater. The question cannot be answered definitively, so the statement is insufficient. Eliminate (B).
Statements (1) and (2): sufficient. Picking numbers may be difficult, since there are many possibilities for y and z. Instead, try to work with the equations. Since y + z = 1, it follows that y = 1 - z. Replace y with 1 - z in the equation y2 < z2 to get (1 - z)2 < z2. Using FOIL to expand the left side, you get z2 - 2z + 1 < z2. Subtracting z2 from both sides you have -2z + 1 < 0, or 1 < 2z. Dividing both sides by 2 you are left with 
< z. Since z must be greater than and y + z = 1, y must be less than . Therefore, y must be less than z. The statements combined are sufficient, so choice (C) is correct.
