This is another not very good question in my view. The correct answer - I presume - is B. This suggests that you hurried, but in the end this turned out to have been unnecessary. However, option D is not quite 'wrong enough' to be ruled out entirely. 'We didn't need to hurry' makes sense. You hurried, but in fact you didn't need to. A native speaker would be likely to say this in this situation. Whoever wrote this question is being rather unfair to you.

b maintains the had....have not tense which both of your questions have been using.

Sorry, I made a mistake in my example sentence... but I NEEDN'T HAVE COOKED so much food...

Just to be clear, the auxiliary verbs "have" and "has" are used with the present perfect tense, and the auxiliary verb "had" is used with the past perfect tense.

The three forms of the verb "need" are: need (infinitive or present tense) / needed (simple past tense) / needed (used with the present and past perfect tenses, and includes the auxiliary verbs: have, has or had). The past perfect verb is usually accompanied by a verb in the simple past tense, e.g., "reached". The correct answer is B. For example: I COOKED enough food for three people, but I NEEDED HAVE COOKED so much food because no one came and I was the only one who ate the food I cooked.