Do I need to do sth? 我需要做某事吗？

Yes，you must/have to. 是的，你必须这么做。

No, you don't have to. 不，你不必这么做。

mustn't意为“绝对不可、务必不要、千万别”，而不是“不必”。这就是为什么。

   Need I come with you ? = Do I need to come with you ? 需要我和你一起来吗 ？（摘自《麦克米伦高阶英汉双解词典》）

    所以，Do I need to leave the city by one's o'clock? No, you (  ). = Need I leave the city by one's o'clock? No, you (  ).

    张克礼编著的《英语语法与用法》指出：“对含情态动词 need 的疑问句的肯定回答用 must ，不用 need（因是非肯定词）；否定回答用 needn't”。

    don't have to = needn't （不必）。所以，问题中的答案只能选择 C :

    Do I need to leave the city by one's o'clock? No, you (  ).

    A. can't     B. mustn't     C. don't have to    D. may not 

Do I need to leave the city by one's o'clock? No, you ( don't have to).

A. can't     B. mustn't     C. don't have to    D. may not 

答案选择 C，为什么不选 B，谢谢分析。

(1)must not=mustn't 表“禁止，不许，不准”

You mustn't fire without my signal.  

没我的信号不许开枪。

We mustn't belittle her outstanding achievement.  

我们一定不能小瞧了她所取得的杰出成就。

You mustn't do that. It's wrong.  

你不能这么做。这是不对的。

That car is my property; you mustn't use it without my permission.  

这辆车是我的财产, 你必须得到我的允许才能使用.

(2)don't have to 不必

You don't have to go running upstairs every time she rings.  

用不着她一来电话你就往楼上跑。

You don't have to worry about me. I'm a good swimmer.  

你不用担心我。我水性很好。

I don't have to be a detective to figure that out.  

我不是侦探也想得出。

"You don't have to go, you know," she said worriedly.  

“你知道的，你不一定非得去。”她忧虑地说。

You don't have to get dressed up for this party.  

你没必要为这次聚会而着盛装。

(3)have to不得不，只好; 只得; 必须; 不得已;

Sometimes things have to fall apart to make way for better things.  

有时候要到达谷底，才会慢慢变好。

You have to do everything you can. You have to work your hardest. And if you do, if you stay positive, then you have a shot at a silver lining.  

你必须全力以赴，最大限度地去努力。如果你这么做，并且保持乐观，你就会看见乌云背后的幸福线。

You have to pay your outstanding bill before joining the scheme.  

在参加该项目之前必须结清余账。

You have to take capital appreciation of the property into account.  

你必须将该处房产的资本增值考虑在内。