"The boss had me checking / check ..."

have 本來就有這些用法。第一題單純的選項A,C不應該同時出現(第2題沒有check這選項，所以還好)。V-ing 這用法字典裡頭就有了:

http://oaadonline.oxfordlearnersdictionaries.com/dictionary/have
26 .... 第2個句型用法

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The boss had me_____all of last month's sales figures.
(A) to check (b) checked (c) checking (d) checks

答案是 (c)

https://groups.google.com/forum/#!original/tw.bbs.lang.english/Ugd6CAyLPBk/oPVX8P2yYlIJ
(回答的人是程度不錯的美國人)

https://groups.google.com/forum/#!original/tw.bbs.lang.english/Ugd6CAyLPBk/0X5eJZkV0QEJ