which of these would not produce a representative sample that determines the favorite food of the students…

Brief Explanations:

A representative sample should be unbiased and reflect the entire population (students at the local middle - school). Asking students at a pizzeria, cafeteria, or mall food court may attract students with a particular food preference (e.g., those who like pizza or frequent the mall food court). Asking from the student directory is more likely to be random and representative.

Answer:

ask every tenth student who enters a pizzeria on Thursday, ask every tenth student who enters the cafeteria on Tuesday, ask every tenth student who enters the food court at the mall