What is the Length of Line segment AB ?
Triangle XZY is similar to Triangle BZA and Triangle CYZ is similar to Triangle BYA
$$Ratio=\frac{XZ}{BZ}=\frac{ZY}{ZA}=\frac{XY}{AB}=\frac{CY}{BY}=\frac{YZ}{YA}=\frac{CZ}{BA}$$

Statement 1
Line segment XY=4, Using
$$\frac{ZY}{ZA}=\frac{XY}{AB}\ and\ \ \frac{YZ}{YA}=\frac{CZ}{AB}$$
$$ZY=YA+YZ\ \ XY=4\ CZ=6$$
$$\frac{YA+AZ}{AZ}=\frac{4}{AB}------------eqn\left(i\right)$$
$$\frac{YA+AZ}{YA}=\frac{6}{AB}------------eqn\left(ii\right)$$
eqn i divided by eqn ii
$$\frac{YA+AZ}{AZ}\cdot\frac{AZ\ AY}{\frac{YA}{AZ}}=\frac{4}{AB}\cdot\frac{AB}{6}$$
$$\frac{AY}{AZ}=\frac{4}{6}=\frac{2}{3}$$
$$\frac{YA+AZ}{AZ}=\frac{4}{AB}$$
$$\frac{AY}{AZ}+\frac{AZ}{AZ}=\frac{4}{AB}$$
N.B AY/AZ = 2/3 , hence AY = 2 and AZ = 3
$$\frac{2}{3}+\frac{3}{3}=\frac{4}{AB}$$
$$\frac{5}{3}=\frac{4}{AB}$$

Statement 2
Line segment AZ > line segment AY, the exact value is not given in this statement here. Hence it is INSUFFICIENT.
$$Answer\ is\ Option\ A\ $$

Statement 1 alone is SUFFICIENT.