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Yesterday ,my sister gave me a book she.....reading the day before.
a- finished b- had finished
c- has finished d- was finishing

The answer given by the exam setter is (b). Why is (a) wrong?

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Yesterday is in the past. "the day before" is further back in the past. "further back in the past" indicates the past perfect, i.e. (b).

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I would choose A.

We often just use Simple Past when the sequence of events is clear. The word 'before' makes it clear.

Clive