**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 *y*^{2} = 9 and that *z*^{2} = 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 *y*^{2} < *z*^{2} to get (1 -* z*)^{2} < *z*^{2}. Using FOIL to expand the left side, you get *z*^{2 }- 2*z* + 1 < *z*^{2}. Subtracting *z*^{2} from both sides you have -2*z* + 1 < 0, or 1 < 2*z*. 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.