What does the inability of seismic S-waves to pass through Earth's outer core indicate about the outer core?

Correct answer: It is in a liquid state

S-waves are shear waves, and their particles vibrate perpendicular to the direction of propagation. Such waves require a medium with rigidity, so they travel through solids but cannot propagate through liquids. Since observations show that S-waves do not pass through Earth’s outer core, the outer core is inferred to be liquid. P-waves can pass through both solids and liquids, so their behaviour alone would not establish this conclusion.