这个题目，B 和 D 两个答案都正确，属于命题失误。分别为：

Good at putting on a show, corrupt officials can often manage to deceive their seniors into believing their feigned

innocence.

Being good at putting on a show, corrupt officials can often manage to deceive their seniors into believing their feigned

innocence.

【翻译】（因为）贪官污吏善于作秀，往往能骗得老前辈相信他们虚伪的清白。

【理由】 当形容词作原因状语时，单个的形容词须加 being（加 being 后变成现在分词）；当形容词词组作原因状语时，being 可加可不加，都正确，本题便是。

如果形容词词组做其他状语时，例如 “伴随、方式” 等，一般不加 being。

此外，详情可参考：http://ask.yygrammar.com/q-41366.html

例句：

1. 当形容词作原因状语时，单个的形容词须加 being：

Being hungry, they had to look for food.

2. 如果形容词词组做其他状语时，例如 “伴随、方式” 等，一般不加 being：

They went to bed, cold and hungry.