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Difference between revisions of "2011 AMC 12A Problems"

m (Deleted the slash between dollar signs in Problem 1.)
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== Problem 1 ==
 
== Problem 1 ==
 +
A cell phone plan costs <math>20</math> dollars each month, plus <math>5</math> cents per text message sent, plus <math>10</math> cents for each minute used over <math>30</math> hours. In January Michelle sent <math>100</math> text messages and talked for <math>30.5</math> hours. How much did she have to pay?
 +
 +
<math>
 +
\textbf{(A)}\ 24.00 \qquad
 +
\textbf{(B)}\ 24.50 \qquad
 +
\textbf{(C)}\ 25.50 \qquad
 +
\textbf{(D)}\ 28.00 \qquad
 +
\textbf{(E)}\ 30.00 </math>
 +
 
[[2011 AMC 12A Problems/Problem 1|Solution]]
 
[[2011 AMC 12A Problems/Problem 1|Solution]]
−
A cell phone plan costs <math>\</math>20 dollars each month, plus <math>5</math> cents per text message sent, plus <math>10</math> cents for each minute used over <math>30</math> hours. In January Michelle sent <math>100</math> text messages and talked for <math>30.5</math> hours. How much did she have to pay?
 
−
 
−
<math> \textbf{(A)}\ </math> <math> 24.00 \qquad
 
−
\textbf{(B)}\ </math> <math> 24.50\qquad
 
−
\textbf{(C)}\ </math> <math> 25.50\qquad
 
−
\textbf{(D)}\ </math> <math> 28.00\qquad
 
−
\textbf{(E)}\ </math> <math> 30.00</math>
 
  
 
== Problem 2 ==
 
== Problem 2 ==
−
[[2011 AMC 12A Problems/Problem 2|Solution]]
+
There are <math>5</math> coins placed flat on a table according to the figure. What is the order of the coins from top to bottom?
−
There are 5 coins placed flat on a table according to the figure. What is the order of the coins from top to bottom?
 
  
−
<math> \textbf{(A)}\ (C, A, E, D, B) \qquad
+
<math>
 +
\textbf{(A)}\ (C, A, E, D, B) \qquad
 
\textbf{(B)}\ (C, A, D, E, B) \qquad
 
\textbf{(B)}\ (C, A, D, E, B) \qquad
−
\textbf{(C)}\ (C, D, E, A, B) </math>
+
\textbf{(C)}\ (C, D, E, A, B) \qquad
−
<math>
+
\textbf{(D)}\ (C, E, A, D, B) \qquad
−
\textbf{(D)}\ (C, E, A, D, B) \qquad
+
\textbf{(E)}\ (C, E, D, A, B) </math>
−
\textbf{(E)}\ (C, E, D, A, B)</math>
+
 
 +
[[2011 AMC 12A Problems/Problem 2|Solution]]
  
 
== Problem 3 ==
 
== Problem 3 ==
−
[[2011 AMC 12A Problems/Problem 3|Solution]]
+
A small bottle of shampoo can hold <math>35</math> milliliters of shampoo, whereas a large bottle can hold <math>500</math> milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy?
−
A small bottle of shampoo can hold 35 milliliters of shampoo, whereas a large bottle can hold 500 milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy?
 
  
−
<math> \textbf{(A)}\ 11 \qquad
+
<math>
 +
\textbf{(A)}\ 11 \qquad
 
\textbf{(B)}\ 12 \qquad
 
\textbf{(B)}\ 12 \qquad
−
\textbf{(C)}\ 13 \qquad
+
\textbf{(C)}\ 13 \qquad
−
\textbf{(D)}\ 14 \qquad
+
\textbf{(D)}\ 14 \qquad
−
\textbf{(E)}\ 15</math>
+
\textbf{(E)}\ 15 </math>
 +
 
 +
[[2011 AMC 12A Problems/Problem 3|Solution]]
  
 
== Problem 4 ==
 
== Problem 4 ==
−
[[2011 AMC 12A Problems/Problem 4|Solution]]
+
At an elementary school, the students in third grade, fourth grade, and fifth grade run an average of <math>12</math>, <math>15</math>, and <math>10</math> minutes per day, respectively. There are twice as many third graders as fourth graders, and twice as many fourth graders as fifth graders. What is the average number of minutes run per day by these students?
−
At an elementary school, the students in third grade, fourth grade, and fifth grade run an average of 12, 15, and 10 minutes per day, respectively. There are twice as many third graders as fourth graders, and twice as many fourth graders as fifth graders. What is the average number of minutes run per day by these students?
 
  
−
  <math> \textbf{(A)}\ 12 \qquad
+
  <math>
 +
\textbf{(A)}\ 1 \qquad
 
\textbf{(B)}\ \frac{37}{3} \qquad
 
\textbf{(B)}\ \frac{37}{3} \qquad
−
\textbf{(C)}\ \frac{88}{7}\qquad
+
\textbf{(C)}\ \frac{88}{7} \qquad
−
\textbf{(D)}\ 13 \qquad
+
\textbf{(D)}\ 13 \qquad
−
\textbf{(E)}\ 14</math>
+
\textbf{(E)}\ 14 </math>
 +
 
 +
[[2011 AMC 12A Problems/Problem 4|Solution]]
  
 
== Problem 5 ==
 
== Problem 5 ==
−
[[2011 AMC 12A Problems/Problem 5|Solution]]
+
Last summer <math>30%</math> of the birds living on Town Lake were geese, <math>25%</math> were swans, <math>10%</math> were herons, and <math>35%</math> were ducks. What percent of the birds that were not swans were geese?
−
Last summer 30% of the birds living on Town Lake were geese, 25% were swans, 10% were herons, and 35% were ducks. What percent of the birds that were not swans were geese?
 
 
   
 
   
−
<math> \textbf{(A)}\ 20 \qquad
+
<math>
 +
\textbf{(A)}\ 20 \qquad
 
\textbf{(B)}\ 30 \qquad
 
\textbf{(B)}\ 30 \qquad
−
\textbf{(C)}\ 40 \qquad
+
\textbf{(C)}\ 40 \qquad
 
\textbf{(D)}\ 50 \qquad
 
\textbf{(D)}\ 50 \qquad
−
\textbf{(E)}\ 60
+
\textbf{(E)}\ 60</math>
−
</math>
+
 
 +
[[2011 AMC 12A Problems/Problem 5|Solution]]
  
 
== Problem 6 ==
 
== Problem 6 ==
 
[[2011 AMC 12A Problems/Problem 6|Solution]]
 
[[2011 AMC 12A Problems/Problem 6|Solution]]
−
The players on a basketball team made some three-point shots, some two-point shots, and some one-point free throws. They scored as many points with two-point shots as with three-point shots. Their number of successful free throws was one more than their number of successful two-point shots. The team's total score was 61 points. How many free throws did they make?
+
The players on a basketball team made some three-point shots, some two-point shots, and some one-point free throws. They scored as many points with two-point shots as with three-point shots. Their number of successful free throws was one more than their number of successful two-point shots. The team's total score was <math>61</math> points. How many free throws did they make?
 
   
 
   
−
<math> \textbf{(A)}\ 13 \qquad
+
<math>
 +
\textbf{(A)}\ 13 \qquad
 
\textbf{(B)}\ 14 \qquad
 
\textbf{(B)}\ 14 \qquad
 
\textbf{(C)}\ 15 \qquad
 
\textbf{(C)}\ 15 \qquad
 
\textbf{(D)}\ 16 \qquad
 
\textbf{(D)}\ 16 \qquad
−
\textbf{(E)}\ 17
+
\textbf{(E)}\ 17 </math>
−
</math>
 
  
 
== Problem 7 ==
 
== Problem 7 ==
 +
A majority of the <math>30</math> students in Ms. Demeanor's class bought pencils at the school bookstore. Each of these students bought the same number of pencils, and this number was greater than <math>1</math>. The cost of a pencil in cents was greater than the number of pencils each student bought, and the total cost of all the pencils was <math>17.71</math>. What was the cost of a pencil in cents?
 +
 +
<math>
 +
\textbf{(A)}\ 7 \qquad
 +
\textbf{(B)}\ 11 \qquad
 +
\textbf{(C)}\ 17 \qquad
 +
\textbf{(D)}\ 23 \qquad
 +
\textbf{(E)}\ 77 </math>
 +
 
[[2011 AMC 12A Problems/Problem 7|Solution]]
 
[[2011 AMC 12A Problems/Problem 7|Solution]]
  
 
== Problem 8 ==
 
== Problem 8 ==
 +
In the eight term sequence <math>A</math>, <math>B</math>, <math>C</math>, <math>D</math>, <math>E</math>, <math>F</math>, <math>G</math>, <math>H</math>, the value of <math>C</math> is <math>5</math> and the sum of any three consecutive terms is <math>30</math>. What is <math>A+H</math>?
 +
 +
<math>
 +
\textbf{(A)}\ 17 \qquad
 +
\textbf{(B)}\ 18 \qquad
 +
\textbf{(C)}\ 25 \qquad
 +
\textbf{(D)}\ 26 \qquad
 +
\textbf{(E)}\ 43 </math>
 +
 
[[2011 AMC 12A Problems/Problem 8|Solution]]
 
[[2011 AMC 12A Problems/Problem 8|Solution]]
  

Revision as of 20:16, 9 February 2011

Problem 1

A cell phone plan costs $20$ dollars each month, plus $5$ cents per text message sent, plus $10$ cents for each minute used over $30$ hours. In January Michelle sent $100$ text messages and talked for $30.5$ hours. How much did she have to pay?

$\textbf{(A)}\ 24.00 \qquad \textbf{(B)}\ 24.50 \qquad \textbf{(C)}\ 25.50 \qquad \textbf{(D)}\ 28.00 \qquad \textbf{(E)}\ 30.00$

Solution

Problem 2

There are $5$ coins placed flat on a table according to the figure. What is the order of the coins from top to bottom?

$\textbf{(A)}\ (C, A, E, D, B) \qquad \textbf{(B)}\ (C, A, D, E, B) \qquad \textbf{(C)}\ (C, D, E, A, B) \qquad \textbf{(D)}\ (C, E, A, D, B) \qquad \textbf{(E)}\ (C, E, D, A, B)$

Solution

Problem 3

A small bottle of shampoo can hold $35$ milliliters of shampoo, whereas a large bottle can hold $500$ milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy?

$\textbf{(A)}\ 11 \qquad \textbf{(B)}\ 12 \qquad \textbf{(C)}\ 13 \qquad \textbf{(D)}\ 14 \qquad \textbf{(E)}\ 15$

Solution

Problem 4

At an elementary school, the students in third grade, fourth grade, and fifth grade run an average of $12$, $15$, and $10$ minutes per day, respectively. There are twice as many third graders as fourth graders, and twice as many fourth graders as fifth graders. What is the average number of minutes run per day by these students? 

$\textbf{(A)}\ 1 \qquad \textbf{(B)}\ \frac{37}{3} \qquad \textbf{(C)}\ \frac{88}{7} \qquad \textbf{(D)}\ 13 \qquad \textbf{(E)}\ 14$

Solution

Problem 5

Last summer $30%$ (Error compiling LaTeX. Unknown error_msg) of the birds living on Town Lake were geese, $25%$ (Error compiling LaTeX. Unknown error_msg) were swans, $10%$ (Error compiling LaTeX. Unknown error_msg) were herons, and $35%$ (Error compiling LaTeX. Unknown error_msg) were ducks. What percent of the birds that were not swans were geese?

$\textbf{(A)}\ 20 \qquad \textbf{(B)}\ 30 \qquad \textbf{(C)}\ 40 \qquad \textbf{(D)}\ 50 \qquad \textbf{(E)}\ 60$

Solution

Problem 6

Solution The players on a basketball team made some three-point shots, some two-point shots, and some one-point free throws. They scored as many points with two-point shots as with three-point shots. Their number of successful free throws was one more than their number of successful two-point shots. The team's total score was $61$ points. How many free throws did they make?

$\textbf{(A)}\ 13 \qquad \textbf{(B)}\ 14 \qquad \textbf{(C)}\ 15 \qquad \textbf{(D)}\ 16 \qquad \textbf{(E)}\ 17$

Problem 7

A majority of the $30$ students in Ms. Demeanor's class bought pencils at the school bookstore. Each of these students bought the same number of pencils, and this number was greater than $1$. The cost of a pencil in cents was greater than the number of pencils each student bought, and the total cost of all the pencils was $17.71$. What was the cost of a pencil in cents?

$\textbf{(A)}\ 7 \qquad \textbf{(B)}\ 11 \qquad \textbf{(C)}\ 17 \qquad \textbf{(D)}\ 23 \qquad \textbf{(E)}\ 77$

Solution

Problem 8

In the eight term sequence $A$, $B$, $C$, $D$, $E$, $F$, $G$, $H$, the value of $C$ is $5$ and the sum of any three consecutive terms is $30$. What is $A+H$?

$\textbf{(A)}\ 17 \qquad \textbf{(B)}\ 18 \qquad \textbf{(C)}\ 25 \qquad \textbf{(D)}\ 26 \qquad \textbf{(E)}\ 43$

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

Problem 16

Solution

Problem 17

Solution

Problem 18

Solution

Problem 19

Solution

Problem 20

Solution

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution

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