MOSFET Circuits: Which value of \$ V_S \$ should I choose?
You made the assumption


  Assuming saturation region operation


Which is an entirely reasonable assumption. You need to validate that your assumption was correct, and eliminate "impossible" answers. Going by the requirements for saturation, you need Vgs > Vt, and Vgs-Vt =&lt; Vds.

You'll find that one of the answers does not satisfy both conditions for saturation.