The manager promised to keep us of how our business was going on.
informed B. informing C. to inform D. havinginformed
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解析：考查动词短语。固定词组:inform sb of sth通知某人某事；本题是其变化形式，keep sb informed of sth让某人知道某事。因为sb与inform之间构成被动关系，故使用过去分词的形式。句意：经理答应让我知道我们的生意进展的情况。故选A。