Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2005 AMC 8 Problems/Problem 1"

(→‎Solution)
(→‎Solution)
 
(5 intermediate revisions by 5 users not shown)
Line 1: Line 1:
−
==Problem 1==
+
==Problem==
−
Jamie counted the number of edges of a cube, Jimmy counted the numbers of corners, and Judy counted the number of faces. They then added the three numbers. What was the resulting sum?  
+
Connie multiplies a number by <math>2</math> and gets <math>60</math> as her answer. However, she should have divided the number by <math>2</math> to get the correct answer. What is the correct answer?
  
−
<math>\mathrm{(A)}\ 12 \qquad\mathrm{(B)}\ 16 \qquad\mathrm{(C)}\ 20 \qquad\mathrm{(D)}\ 22 \qquad\mathrm{(E)}\ 26</math>
+
<math> \textbf{(A)}\ 7.5\qquad\textbf{(B)}\ 15\qquad\textbf{(C)}\ 30\qquad\textbf{(D)}\ 120\qquad\textbf{(E)}\ 240 </math>
  
 
==Solution==
 
==Solution==
−
On a cube, there are <math> 12 </math> edges, <math> 8 </math> corners, and <math> 6 </math> faces. Adding them up gets <math> 12+8+6= \boxed{\mathrm{(E)}\ 26} </math>.
+
If <math>x</math> is the number, then <math>2x=60</math> and <math>x=30</math>. Dividing the number by <math>2</math> yields <math>\dfrac{30}{2} = \boxed{\textbf{(B)}\ 15}</math>.
 +
 
 +
A second way to do it is to divide the number by <math>4</math>, as you multiplied by <math>2</math> when you were supposed to divide by <math>2</math>. So, <math>\dfrac{60}{4} = \boxed{\textbf{(B)}\ 15}</math>.
 +
 
 +
==See Also==
 +
{{AMC8 box|year=2005|before=First <br/> Question|num-a=2}}
 +
{{MAA Notice}}

Latest revision as of 08:10, 8 January 2024

Problem

Connie multiplies a number by $2$ and gets $60$ as her answer. However, she should have divided the number by $2$ to get the correct answer. What is the correct answer?

$\textbf{(A)}\ 7.5\qquad\textbf{(B)}\ 15\qquad\textbf{(C)}\ 30\qquad\textbf{(D)}\ 120\qquad\textbf{(E)}\ 240$

Solution

If $x$ is the number, then $2x=60$ and $x=30$. Dividing the number by $2$ yields $\dfrac{30}{2} = \boxed{\textbf{(B)}\ 15}$.

A second way to do it is to divide the number by $4$, as you multiplied by $2$ when you were supposed to divide by $2$. So, $\dfrac{60}{4} = \boxed{\textbf{(B)}\ 15}$.

See Also

2005 AMC 8 (Problems • Answer Key • Resources)
Preceded by
First
Question 		Followed by
Problem 2
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2005_AMC_8_Problems/Problem_1&oldid=210171"