This question tests your understanding of modal verbs and past necessity, specifically the difference between "didn't need to" and "needn't have."

Step 1: Understand the Context

The first sentence states a completed action: "Joe ran all the way." The second sentence provides a comment on that action: "It wasn't necessary." This tells us that the running was done, but it was not required.

Step 2: Analyze the Structure

We need to fill in the blank to combine these two ideas into one sentence that maintains the original meaning. The action (running) happened in the past, and we are commenting on its necessity.

Step 3: Evaluate the Options

• Need have: This is grammatically incorrect. The correct negative form is "needn't have."
• Didn't need: This is incomplete. It requires an infinitive ("to run") to form "didn't need to run." This phrase is used when an action was not necessary, and it typically implies that the action was not performed. For example, "I didn't need to buy milk (so I didn't)."
• Needn't have: This is the perfect construction "need not have" + past participle. It is used to say that someone did something, but that action was not necessary. It implies the action was performed. This matches our context perfectly because Joe did run.
• Doesn't need to: This is in the present tense ("does not need to"), which is incorrect because the action of running is already completed and in the past.

Step 4: Final Answer

The correct option is Needn't have. The completed sentence is: "Joe needn't have run all the way." This correctly means that Joe ran, but it was unnecessary.

Related Concept: Didn't need to vs. Needn't have

This is a key distinction in English grammar:

• Didn't need to + infinitive: Used when an action was not necessary. It often suggests that because it was unnecessary, the person did not do it.
  Example: "The meeting was canceled, so I didn't need to go." (I did not go.)
• Needn't have + past participle: Used when an action was performed but was later understood to be unnecessary. It often expresses a slight regret or wasted effort.
  Example: "I cooked a huge dinner, but then they said they'd already eaten. I needn't have bothered." (I did bother.)

Formula/Structure

The structure for expressing unnecessary past actions is:

Subject + needn't have + Past Participle

Example: She needn't have worried about the test; she passed easily.