题目

A drugstore chain can return empty lipsticks that it originally sold to the supplier for recycling. To encourage customers to return their empty lipsticks to its stores rather than throw them in the trash, the drugstore chain has instituted a new policy allowing customers to bring empty lipsticks to a store and exchange them for a new, full lipstick, as shown in the diagram.

Select from each drop-down menu the option that creates the most accurate statement based on the information provided.

Dara has 11 empty lipsticks originally purchased from this drugstore chain. If Dara exchanges these for new lipsticks under the store policy, wears the new lipsticks until they run out, and then repeats these actions (with the lipsticks that are now empty) to the fullest extent possible—without acquiring any additional lipsticks outside of the exchange program—then Dara will be able to acquire and wear

{【下拉选项标识】} new lipsticks, and will have {【下拉选项标识】}  upon reaching “End”.

解析

商店的兑换方案允许达拉(Dara)用 3 个空口红壳兑换 1 支全新的满装口红,正如第一个问题中 “yes” 的路径所示。如果一开始有 11 个空口红壳,达拉将能够进行三次这样的兑换(沿着 “yes” 的箭头方向前进并循环,共进行三次)。在这个过程中,达拉会用 9 个空壳去换 3 支满装口红 —— 这时,她将持有 3 支满装口红和 2 个空壳。


此时,达拉无法再进行兑换了。于是达拉用完其中 1 支新换的口红,用完后,她将持有 2 支满装口红和 3 个空壳,并且已经使用了 1 支口红。


达拉现在可以用这 3 个空壳再兑换 1 支满装口红 —— 最终持有 3 支满装口红(且没有空壳)。


这时,达拉会将这 3 支口红逐一用完。用完这 3 支后,达拉将只剩下 3 个空壳,此时她总共已经使用了 4 支口红。


达拉随后可以用这 3 个空壳兑换最后 1 支满装口红,然后用完这支口红 —— 这是她能使用的第 5 支,也是最后一支。用完这支口红后,达拉带着这个最后用完的口红的空壳进入 “结束” 状态。因此,达拉总共获得并使用了 5 支口红,最终持有 1 个空壳到达 “结束” 状态。

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