https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=Glaydus&feedformat=atomAoPS Wiki - User contributions [en]2024-03-28T20:10:24ZUser contributionsMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=2012_AMC_10B_Problems&diff=450292012 AMC 10B Problems2012-02-24T00:58:53Z<p>Glaydus: </p>
<hr />
<div>== Problem 1 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ 48\qquad\textbf{(B)}\ 56\qquad\textbf{(C)}\ 64\qquad\textbf{(D)}\ 72\qquad\textbf{(E)}\ 80 </math><br />
<br />
[[2012 AMC 10B Problems/Problem 1|Solution]]<br />
<br />
== Problem 2 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ 50\qquad\textbf{(B)}\ 100\qquad\textbf{(C)}\ 125\qquad\textbf{(D)}\ 150\qquad\textbf{(E)}\ 200 </math><br />
<br />
[[2012 AMC 10B Problems/Problem 2|Solution]]<br />
<br />
== Problem 3 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ (998,2012)\qquad\textbf{(B)}\ (1000,1988)\qquad\textbf{(C)}\ (1000,2024)\qquad\textbf{(D)}\ (1000,4012)\qquad\textbf{(E)}\ (1012,2012) </math><br />
<br />
[[2012 AMC 10B Problems/Problem 3|Solution]]<br />
<br />
== Problem 4 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5 </math><br />
<br />
[[2012 AMC 10B Problems/Problem 4|Solution]]</div>Glaydushttps://artofproblemsolving.com/wiki/index.php?title=2012_AMC_10B_Problems&diff=450282012 AMC 10B Problems2012-02-24T00:58:35Z<p>Glaydus: </p>
<hr />
<div>== Problem 1 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ 48\qquad\textbf{(B)}\ 56\qquad\textbf{(C)}\ 64\qquad\textbf{(D)}\ 72\qquad\textbf{(E)}\ 80 </math><br />
<br />
[[2012 AMC 10B Problems/Problem 1|Solution]]<br />
<br />
== Problem 2 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ 50\qquad\textbf{(B)}\ 100\qquad\textbf{(C)}\ 125\qquad\textbf{(D)}\ 150\qquad\textbf{(E)}\ 200 </math><br />
<br />
[[2012 AMC 10B Problems/Problem 2|Solution]]<br />
<br />
== Problem 3 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ (998,2012)\qquad\textbf{(B)}\ (1000,1988)\qquad\textbf{(C)}\ (1000,2024)\qquad\textbf{(D)}\ (1000,4012)\qquad\textbf{(E)}\ (1012,2012) </math><br />
<br />
[[2012 AMC 10B Problems/Problem 3|Solution]]<br />
<br />
== Problem 4 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5 </math><br />
<br />
[[2012 AMC 10B Problems/Problem 4|Solution]]<br />
<br />
== Problem 5 ==<br />
<br />
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?<br />
<br />
</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><br />
<br />
[[2012 AMC 10B Problems/Problem 5|Solution]]</div>Glaydushttps://artofproblemsolving.com/wiki/index.php?title=2012_AMC_10B_Problems&diff=450272012 AMC 10B Problems2012-02-24T00:55:52Z<p>Glaydus: </p>
<hr />
<div>== Problem 1 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ 48\qquad\textbf{(B)}\ 56\qquad\textbf{(C)}\ 64\qquad\textbf{(D)}\ 72\qquad\textbf{(E)}\ 80 </math><br />
<br />
[[2012 AMC 10B Problems/Problem 1|Solution]]<br />
<br />
== Problem 2 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ 50\qquad\textbf{(B)}\ 100\qquad\textbf{(C)}\ 125\qquad\textbf{(D)}\ 150\qquad\textbf{(E)}\ 200 </math><br />
<br />
[[2012 AMC 10B Problems/Problem 2|Solution]]<br />
<br />
== Problem 3 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ (998,2012)\qquad\textbf{(B)}\ (1000,1988)\qquad\textbf{(C)}\ (1000,2024)\qquad\textbf{(D)}\ (1000,4012)\qquad\textbf{(E)}\ (1012,2012) </math><br />
<br />
[[2012 AMC 10B Problems/Problem 3|Solution]]<br />
<br />
== Problem 4 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5 </math><br />
<br />
[[2012 AMC 10B Problems/Problem 4|Solution]]<br />
<br />
== Problem 5 ==<br />
<br />
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?<br />
<br />
</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><br />
<br />
[[2012 AMC 10B Problems/Problem 5|Solution]]</div>Glaydushttps://artofproblemsolving.com/wiki/index.php?title=2012_AMC_10B_Problems&diff=450262012 AMC 10B Problems2012-02-24T00:51:04Z<p>Glaydus: </p>
<hr />
<div>== Problem 1 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ 48\qquad\textbf{(B)}\ 56\qquad\textbf{(C)}\ 64\qquad\textbf{(D)}\ 72\qquad\textbf{(E)}\ 80 </math><br />
<br />
[[2012 AMC 10B Problems/Problem 1|Solution]]<br />
<br />
== Problem 2 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ 50\qquad\textbf{(B)}\ 100\qquad\textbf{(C)}\ 125\qquad\textbf{(D)}\ 150\qquad\textbf{(E)}\ 200 </math><br />
<br />
[[2012 AMC 10B Problems/Problem 2|Solution]]<br />
<br />
== Problem 3 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ (998,2012)\qquad\textbf{(B)}\ (1000,1988)\qquad\textbf{(C)}\ (1000,2024)\qquad\textbf{(D)}\ (1000,4012)\qquad\textbf{(E)}\ (1012,2012) </math><br />
<br />
[[2012 AMC 10B Problems/Problem 3|Solution]]</div>Glaydushttps://artofproblemsolving.com/wiki/index.php?title=2012_AMC_10B_Problems&diff=450252012 AMC 10B Problems2012-02-24T00:50:22Z<p>Glaydus: </p>
<hr />
<div>== Problem 1 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ 48\qquad\textbf{(B)}\ 56\qquad\textbf{(C)}\ 64\qquad\textbf{(D)}\ 72\qquad\textbf{(E)}\ 80 </math><br />
<br />
[[2012 AMC 10B Problems/Problem 1|Solution]]<br />
<br />
== Problem 2 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ 50\qquad\textbf{(B)}\ 100\ qquad\textbf{(C)}\ 125\qquad\textbf{(D)}\ 150\qquad\textbf{(E)}\ 200 </math><br />
<br />
[[2012 AMC 10B Problems/Problem 2|Solution]]<br />
<br />
== Problem 3 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ (998,2012)\qquad\textbf{(B)}\ (1000,1988)\qquad\textbf{(C)}\ (1000,2024)\qquad\textbf{(D)}\ (1000,4012)\qquad\textbf{(E)}\ (1012,2012) </math><br />
<br />
[[2012 AMC 10B Problems/Problem 3|Solution]]</div>Glaydushttps://artofproblemsolving.com/wiki/index.php?title=2012_AMC_10B_Problems&diff=450242012 AMC 10B Problems2012-02-24T00:49:16Z<p>Glaydus: </p>
<hr />
<div>== Problem 1 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ 48\qquad\textbf{(B)}\ 56\qquad\textbf{(C)}\ 64\qquad\textbf{(D)}\ 72\qquad\textbf{(E)}\ 80 </math><br />
<br />
[[2012 AMC 10B Problems/Problem 1|Solution]]<br />
<br />
== Problem 2 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ 50\qquad\textbf{(B)}\ \100\ qquad\textbf{(C)}\ 125\qquad\textbf{(D)}\ 150\qquad\textbf{(E)}\ 200 </math><br />
<br />
[[2012 AMC 10B Problems/Problem 2|Solution]]<br />
<br />
== Problem 3 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ (998,2012)qquad\textbf{(B)}\ (1000,1988)\qquad\textbf{(C)}\ (1000,2024)\qquad\textbf{(D)}\ (1000,4012)\qquad\textbf{(E)}\ (1012,2012) </math><br />
<br />
[[2012 AMC 10B Problems/Problem 3|Solution]]</div>Glaydushttps://artofproblemsolving.com/wiki/index.php?title=2012_AMC_10B_Problems&diff=450232012 AMC 10B Problems2012-02-24T00:48:16Z<p>Glaydus: 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..."</p>
<hr />
<div>== Problem 1 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ 48\qquad\textbf{(B)}\ 56\qquad\textbf{(C)}\ 64\qquad\textbf{(D)}\ 72\qquad\textbf{(E)}\ 80 </math><br />
<br />
[[2012 AMC 10B Problems/Problem 1|Solution]]<br />
<br />
== Problem 2 ==<br />
<br />
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?<br />
<br />
<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><br />
<br />
[[2012 AMC 10B Problems/Problem 2|Solution]]<br />
<br />
== Problem 3 ==<br />
<br />
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?<br />
<br />
<math> \textbf{(A)}\ (998,2012)qquad\textbf{(B)}\ (1000,1988)\qquad\textbf{(C)}\ (1000,2024)\qquad\textbf{(D)}\ (1000,4012)\qquad\textbf{(E)}\ (1012,2012) </math><br />
<br />
[[2012 AMC 10B Problems/Problem 3|Solution]]</div>Glaydushttps://artofproblemsolving.com/wiki/index.php?title=2012_AMC_10B&diff=450222012 AMC 10B2012-02-24T00:39:10Z<p>Glaydus: </p>
<hr />
<div>'''2012 AMC 10B''' problems and solutions. The test was held on February 22, 2012. <br />
<br />
*[[2012 AMC 10B Problems]]<br />
*[[2012 AMC 10B Bnswer Key]]<br />
**[[2012 AMC 10B Problems/Problem 1|Problem 1]]<br />
**[[2012 AMC 10B Problems/Problem 2|Problem 2]]<br />
**[[2012 AMC 10B Problems/Problem 3|Problem 3]]<br />
**[[2012 AMC 10B Problems/Problem 4|Problem 4]]<br />
**[[2012 AMC 10B Problems/Problem 5|Problem 5]]<br />
**[[2012 AMC 10B Problems/Problem 6|Problem 6]]<br />
**[[2012 AMC 10B Problems/Problem 7|Problem 7]]<br />
**[[2012 AMC 10B Problems/Problem 8|Problem 8]]<br />
**[[2012 AMC 10B Problems/Problem 9|Problem 9]]<br />
**[[2012 AMC 10B Problems/Problem 10|Problem 10]]<br />
**[[2012 AMC 10B Problems/Problem 11|Problem 11]]<br />
**[[2012 AMC 10B Problems/Problem 12|Problem 12]]<br />
**[[2012 AMC 10B Problems/Problem 13|Problem 13]]<br />
**[[2012 AMC 10B Problems/Problem 14|Problem 14]]<br />
**[[2012 AMC 10B Problems/Problem 15|Problem 15]]<br />
**[[2012 AMC 10B Problems/Problem 16|Problem 16]]<br />
**[[2012 AMC 10B Problems/Problem 17|Problem 17]]<br />
**[[2012 AMC 10B Problems/Problem 18|Problem 18]]<br />
**[[2012 AMC 10B Problems/Problem 19|Problem 19]]<br />
**[[2012 AMC 10B Problems/Problem 20|Problem 20]]<br />
**[[2012 AMC 10B Problems/Problem 21|Problem 21]]<br />
**[[2012 AMC 10B Problems/Problem 22|Problem 22]]<br />
**[[2012 AMC 10B Problems/Problem 23|Problem 23]]<br />
**[[2012 AMC 10B Problems/Problem 24|Problem 24]]<br />
**[[2012 AMC 10B Problems/Problem 25|Problem 25]]</div>Glaydus