HMMT 十一月 2013 · 冲刺赛 · 第 36 题

HMMT November 2013 — Guts Round — Problem 36

[ 20 ] Pick a subset of at least four of the following seven numbers, order them from least to greatest, and write down their labels (corresponding letters from A through G) in that order: (A) π ; (B) √ √ √ √ 355 1 − 1 1 − 1 e 2 + 3; (C) 10; (D) ; (E) 16 tan − 4 tan ; (F) ln(23); and (G) 2 . If the ordering of 113 5 240 the numbers you picked is correct and you picked at least 4 numbers, then your score for this problem will be ( N − 2)( N − 3), where N is the size of your subset; otherwise, your score is 0.

解析

[ 20 ] Pick a subset of at least four of the following seven numbers, order them from least to greatest, and write down their labels (corresponding letters from A through G) in that order: (A) π ; (B) √ √ √ √ 355 − 1 1 − 1 1 e 2 + 3; (C) 10; (D) ; (E) 16 tan − 4 tan ; (F) ln(23); and (G) 2 . If the ordering of 113 5 240 the numbers you picked is correct and you picked at least 4 numbers, then your score for this problem will be ( N − 2)( N − 3), where N is the size of your subset; otherwise, your score is 0. Answer: F, G, A, D, E, B, C OR F < G < A < D < E < B < C OR C > B > E > D > A > G > F √ √ √ √ 355 1 e − 1 1 − 1 We have ln(23) < 2 < π < < 16 tan − 4 tan < 2 + 3 < 10. 113 5 240