Question

What information would you have to know to determine the toughness of a solid?

how much kinetic energy it absorbed before it broke
its mass and volume
what materials are able to scratch it
its mass

Answer 1

You need to know 1) How much kinetic energy it absorbed before it broke.
2) What materials are able to scratch it.
3) Its mass.

Answer 2

What you need to know is How much kinetic energy it absorbed before it broke. This is the answer A.