( )Penny found that the designer bag she __ online was a fake.(1)will buy(2)has bought(3)buys(4)had bought?

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When two actions verb happened in the past one after another, we use the past perfect tense for the first action verb.
Note the use of "had bought"; "found"=first action verb; second action verb consecutively.
(-)Penny found "=second action" that the designer bag she (4) had bought"=first action" online was a fake="that seems genuine but is not.in order to deceive."

find和buy都是action verb，按句意的時序，buy是在find之前發生，因為主要動詞buy是「過去簡單式」，所以當其受詞的名詞子句裡的動詞buy要用「過去完成式」，以表示時間更早。

二件事情發生在過去,先發生的用過去完成式(S+had+p.p.),後發生的用過去簡單式(S+Ved),因此此題的答案為(4)

可到我的網站看看,我會不定期的分享一些文法觀念,實用英文句子及單字的用法:
https://www.facebook.com/kuan1000/

一個動作發生比另一動作早，用过去完成式had bought。但已明知其先後順序亦可用簡單式bought ，所以答案有bought 亦可。
文法也是約定成俗，其燮化會隨使用習慣而改變，就像女朋友稱馬子一樣。