How can a mixture of nails and sawdust be most efficiently separated into its component parts? a: by cooling it b: by filtering it c: by using a magnet d: by using a catalyst

The answer is C. By using a magnet.

you could filter out the nails, but using the magnet is more efficient

A physical change can happen without changing any of the characteristics, for example if you have an ice cube which is frozen H2O and you let it sit it will melt only changing the physical appearance and the molecules in the substance. A physical change doesn't change the physical composition.