Step 1: Understand the analogy.
The progression in the first set, [dry \( \rightarrow \) arid \( \rightarrow \) parched], represents an increase in the severity or intensity of dryness.
Similarly, in the second set, [diet \( \rightarrow \) fast \( \rightarrow \) \(\_\_\_\_\_\_\_\_\)], the words should represent an increase in the intensity of food restriction.
Step 2: Analyze the options.
Option (A): starve — This indicates extreme food deprivation, making it the most intense stage of food restriction.
Option (B): reject — This does not relate to the concept of food restriction.
Option (C): feast — This is the opposite of food restriction and does not fit the analogy.
Option (D): deny — While this relates to refusal, it does not specifically convey the intensity of food restriction as required in the analogy.
Conclusion:
The correct word to complete the analogy is \( \mathbf{starve} \), corresponding to option \( \mathbf{(A)} \).