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Difference between revisions of "2012 AMC 10B Problems"

(Created page with "== 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-grad...")
 
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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?
 
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?
  
<math> \textbf{(A)}\ 50\ \text{by}\ 4\qquad\textbf{(B)}\ \ 100\ \text{by}\ 6\qquad\textbf{(C)}\ \ 125\ \text{by}\ 8\qquad\textbf{(D)}\ 150\ \text{by}\ 4\qquad\textbf{(E)}\ 200\ \text{by}\ 8 </math>
+
<math> \textbf{(A)}\ 50\qquad\textbf{(B)}\ \100\ qquad\textbf{(C)}\ 125\qquad\textbf{(D)}\ 150\qquad\textbf{(E)}\ 200 </math>
  
 
[[2012 AMC 10B Problems/Problem 2|Solution]]
 
[[2012 AMC 10B Problems/Problem 2|Solution]]

Revision as of 19:49, 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?

$\textbf{(A)}\ 50\qquad\textbf{(B)}\ \100\ qquad\textbf{(C)}\ 125\qquad\textbf{(D)}\ 150\qquad\textbf{(E)}\ 200$ (Error compiling LaTeX. Unknown error_msg)

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