KapTeacherEli wrote:Though you do not need to have this memorized, it's actually an important mathematical rule called the pigeonhole principle. It is rarely tested, but it can show up. For instance, one Kaplan practice question reads, "If there are 10 white sox, 8 black socks, and 12 blue socks in a drawer, what is the smallest number of socks that can be selected at random that guarantees a pair of the same color is selected?"

[spoiler]Well, here, the "pigeonholes" are the colors. Three socks could be one of each color. But once we have four, we have more socks than colors, and therefore at least once color has to have two socks.[/spoiler]

mehaksal wrote:If there are more oak trees in Oregon than there are leaves on any one Oregon oak tree, and if every Oregon oak tree has at least one leaf, then ______.

Which of the following most logically completes the passage?

(A) the average number of oak tree leaves per Oregon oak tree must be less than half the number of Oregon oak trees.

(B) there are fewer leaves on at least one Oregon oak tree than half the number of those trees.

(C) there must be at least two oak trees in Oregon with the same number of leaves.

(D) there must be at least as many Oregon oak trees with half as many leaves as the Oregon tree with the most leaves, as there are Oregon oak trees with twice as many leaves as the Oregon oak tree with the fewest leaves.

(E) there must be more oak trees than any other type of tree in Oregon.