A method

Find the error before reading the options.

Read for the error first

Read the sentence, decide what is wrong, then look for the option that fixes exactly that. Reading options first anchors you to whichever sounds smoothest.

Sounding right is unreliable: many errors are common in speech.
If nothing seems wrong, check agreement and modifiers deliberately.

Keep it minimal

The best correction changes as little as possible. An option that fixes the error and introduces wordiness is usually not the intended answer.