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
GET READY FOR THE AMC 10 WITH AoPS
Learn with outstanding instructors and top-scoring students from around the world in our AMC 10 Problem Series online course.
CHECK SCHEDULE

Difference between revisions of "2012 AMC 10B Problems"
Line 22: Line 22:
  
 
[[2012 AMC 10B Problems/Problem 3|Solution]]
 
[[2012 AMC 10B Problems/Problem 3|Solution]]
 +
 +
== Problem 4 ==
 +
 +
When Ringo places his marbles into bags with 6 marbles per bag, he has 4 marbles left over.  When Paul does the same with his marbles, he has 3 marbles left over.  Ringo and Paul pool their marbles and place them into as many bags as possible, with 6 marbles per bag.  How many marbles will be left over?
 +
 +
<math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5 </math>
 +
 +
[[2012 AMC 10B Problems/Problem 4|Solution]]
 +
 +
== Problem 5 ==
 +
 +
Anna enjoys dinner at a restaurant in Washington, D.C., where the sales tax on the meals is 10%.  She leaves a 15% tip on the price of her meal before the sales tax is added, and the tax is calculated on the pre-tip amount.  She spends a total of <math>27.50 for dinner.  What is the cost of her dinner without tax or tip?
 +
 +
</math> \textbf{(A)}\ <math>18\qquad\textbf{(B)}\ </math>20\qquad\textbf{(C)}\ <math>21\qquad\textbf{(D)}\ </math>22\qquad\textbf{(E)}\ <math>24 </math>
 +
 +
[[2012 AMC 10B Problems/Problem 5|Solution]]

Revision as of 19:55, 23 February 2012

Problem 1

Each third-grade classroom at Pearl Creek Elementary has 18 students and 2 pet rabbits. How many more students than rabbits are there in all 4 of the third-grade classrooms?

$\textbf{(A)}\ 48\qquad\textbf{(B)}\ 56\qquad\textbf{(C)}\ 64\qquad\textbf{(D)}\ 72\qquad\textbf{(E)}\ 80$

Solution

Problem 2

A circle of radius 5 is inscribed in a rectangle as shown. The ratio of the length of the rectangle to its width is 2:1. What is the area of the rectangle?

$\textbf{(A)}\ 50\qquad\textbf{(B)}\ 100\qquad\textbf{(C)}\ 125\qquad\textbf{(D)}\ 150\qquad\textbf{(E)}\ 200$

Solution

Problem 3

The point in the xy-plane with coordinates (1000, 2012) is reflected across the line y=2000. What are the coordinates of the reflected point?

$\textbf{(A)}\ (998,2012)\qquad\textbf{(B)}\ (1000,1988)\qquad\textbf{(C)}\ (1000,2024)\qquad\textbf{(D)}\ (1000,4012)\qquad\textbf{(E)}\ (1012,2012)$

Solution

Problem 4

When Ringo places his marbles into bags with 6 marbles per bag, he has 4 marbles left over. When Paul does the same with his marbles, he has 3 marbles left over. Ringo and Paul pool their marbles and place them into as many bags as possible, with 6 marbles per bag. How many marbles will be left over?

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5$

Solution

Problem 5

Anna enjoys dinner at a restaurant in Washington, D.C., where the sales tax on the meals is 10%. She leaves a 15% tip on the price of her meal before the sales tax is added, and the tax is calculated on the pre-tip amount. She spends a total of $27.50 for dinner. What is the cost of her dinner without tax or tip?$ \textbf{(A)}\ $18\qquad\textbf{(B)}$20\qquad\textbf{(C)}\ $21\qquad\textbf{(D)}$22\qquad\textbf{(E)}\ $24$

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2012_AMC_10B_Problems&oldid=45027"