Đề thi học sinh giỏi Toán Hoa Kì lần thứ 24 dành cho Khối 10 (AMC-10B)

Trích dẫn Đề thi học sinh giỏi Toán Hoa Kì lần thứ 24 dành cho Khối 10 (AMC-10B)

Problem 1: Define $x\diamond y$ to be $|x-y|$ for all real numbers x and y. What is the value of $(1\circ(2\circ3))-((1\circ2)\diamond3)?$ $(A)-2(B)-1(C)0(D)1$ (D) 1 (E) 2 Problem 2: In rhombus ABCD, point P lies on segment $\overline{AD}$ so that $\overline{BP}\bot\overline{AD}.$ $AP=3.and~PD=2.$ $AP=3,$ and $PD=2.$ What is the area of ABCD? (Note: The figure is not drawn to scale.) $(A)3\sqrt5$ (B) 10 $(C)6\sqrt5$ (D) 20 (E) 25 Problem 3: How many three-digit positive integers have an odd number of even digits? (A) 150 (B) 250 (C) 350 (D) 450 (E) 550 Problem 4: A donkey suffers an attack of hiccups and the first hiccup happens at 4:00 one afternoon. Suppose that the donkey hiccups regularly every 5 seconds. AAt what time does the donkey's 700th hiccup ocuur? (A) 15 seconds after 4:58 (B) 20 seconds after 4:58 (C) 25 seconds after 4:58 (D) 30 seconds after 4:58 (E) 35 seconds after 4:58