2006 AMC 8 Problem 4

Attempt Problem 4 of the 2006 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2006 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

4.

Initially, a spinner points west. Chenille moves it clockwise 214 2 \frac{1}{4} revolutions and then counterclockwise 334 3 \frac{3}{4} revolutions. In what direction does the spinner point after the two moves?

North

East

South

West

Northwest

Answer: B
Concepts:fractiontransformation
Difficulty rating: 660
Solution:

If the spinner goes 2142 \frac{1}{4} revolutions clockwise and 3343 \frac{3}{4} revolutions counterclockwise, it goes 1121 \frac{1}{2} revolutions counterclockwise.

This means that the spinner will be pointing east.

Thus, B is the correct answer.

← Problem 3#3
Full Exam

Problem 4 in Other Years

1985 AMC 8 · 1986 AMC 8 · 1987 AMC 8 · 1988 AMC 8 · 1989 AMC 8 · 1990 AMC 8 · 1991 AMC 8 · 1992 AMC 8 · 1993 AMC 8 · 1994 AMC 8 · 1995 AMC 8 · 1996 AMC 8 · 1997 AMC 8 · 1998 AMC 8 · 1999 AMC 8 · 2000 AMC 8 · 2001 AMC 8 · 2002 AMC 8 · 2003 AMC 8 · 2004 AMC 8 · 2005 AMC 8 · 2007 AMC 8 · 2008 AMC 8 · 2009 AMC 8 · 2010 AMC 8 · 2011 AMC 8 · 2012 AMC 8 · 2013 AMC 8 · 2014 AMC 8 · 2015 AMC 8 · 2016 AMC 8 · 2017 AMC 8 · 2018 AMC 8 · 2019 AMC 8 · 2020 AMC 8 · 2022 AMC 8 · 2023 AMC 8 · 2024 AMC 8 · 2025 AMC 8 · 2026 AMC 8