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BMAT 2022 · Question 19 · Logic

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There were 60 episodes of my favourite TV show. After it finished, 20 DVDs were released, each containing 3 episodes. DVD 1 contained episodes 1, 2 and 3, DVD 2 contained episodes 4, 5 and 6, etc. I bought all 20 DVDs, but I have since lost DVDs 7, 16 and 19. The collection has recently been reissued, this time as 12 DVDs, with DVD 1 containing episodes 1, 2, 3, 4 and 5, DVD 2 containing episodes 6, 7, 8, 9 and 10, etc. I am keen to make sure that I have all the missing episodes, but I don’t want to buy more of the new DVDs than necessary.

How many of the new DVDs will I buy?