Eli has arranged all his books on two shelves such that the upper and lower shelves each hold the same number of books

题目

Eli has arranged all his books on two shelves such that the upper and lower shelves each hold the same number of books. Exactly half of the books in the collection are children’s books, all of which have illustrations. All the children’s books have illustrations only on the right (IOR)—that is, on odd-numbered pages only. Do the majority of the books on the lower shelf have IOR?

(1) A majority of the children’s books are on the lower shelf.

(2) A majority of the books that have IOR are on the upper shelf.

选项

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

解析

埃利将他所有的书都放在两个书架上，使得上层和下层书架上的书数量相同。这个收藏中正好有一半是儿童书籍，所有儿童书籍都有插图。所有儿童书籍的插图只在右侧（IOR）——即仅在奇数页。下层书架上的书大多数有IOR吗？

假设总共有16本书，儿童书籍的数量为8本，且全部都有IOR。每个书架上有8本书，我们需要确定下层书架上是否有超过4本书有IOR。

（1）大多数儿童书籍在下层书架上。

这意味着下层书架上有5本或更多的儿童书籍。由于所有儿童书籍都有IOR，而下层书架共有8本书，所以下层书架上的书大多数有IOR。充分。

（2）大多数有IOR的书在上层书架上。

如果只有儿童书籍（共8本）有IOR，且所有儿童书籍都在上层书架上，那么下层书架上没有书有IOR，问题的答案是否定的。然而，如果有11本书有IOR，其中6本在上层书架上，那么下层书架上仍有5本有IOR，此时答案是肯定的。不充分。

答案：A。

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