根据英语的搭配习惯，有些名词通常要后接 to doing sth，而不接 to do sth，因为其中的 to 是介词，而不是不定式符号，你的试题中的 key 就属于这类词。下面略举几例：

1. alternative  选择，可供选择的办法，替换

Unfortunately, there’s no practical alternative to driving. 遗憾的是，除了开车没有其他可行的方案。

Amalgamation was the only alternative to going bankrupt. 要想不破产，唯一的选择就是联合起来。

2. aversion 讨厌，憎恶

He had an aversion to getting up early. 他十分讨厌早起。

I have an aversion to traveling during the heat of August. 我讨厌在8月份的热浪中出去旅行。

3. dislike 不喜爱，厌恶

Most of my friends feel a dislike to gambling. 我的大部分朋友都厌恶赌博。

I have a strong dislike to wearing such clothes in public. 我非常不喜欢在公共场合穿那样的衣服。

4. hindrance 妨碍

Noise is a hindrance to studying. 噪音妨碍学习。

Poor health is a hindrance to finding a job. 身体不好对于找工作是一个妨碍。

5. key 答案，秘诀，关键

The humble potato may be the key to feeding the world’s population. 　这不起眼的土豆有可能是解决全世界人口温饱的关键。

A chemical has been discovered that may be the key to unlocking the mysteries of Parkinson’s disease. 已经发现一种化学物质，可能是揭开帕金森氏病奥秘的关键。

6. objection 反对，异议

He had no objection to getting up early. 他对早起没有反对意见。

I have no objection to hearing your story again. 再听一遍你的故事，我没有异议。

7. opposition反对，抵抗，对抗

There will be considerable opposition to increasing the budget. 对增加预算有大量的反对意见。

There continues to be overwhelming opposition to cutting school funding. 削减学校资金一事，一直为绝大多数人所反对。

8. priority 优先，优先权

The Government gave priority to reforming the legal system. 政府将改革法制列为工作的重点。

The government should give top priority to rebuilding the inner cities. 政府应该优先重建城内中心区。

9. resistance 阻力，抵抗，反抗

There is still much resistance to carrying out this plan. 要执行这一计划仍有很大阻力。