View source for 2015 AMC 8 Problems

==Problem 1==

How many square yards of carpet are required to cover a rectangular floor that is <math>12</math> feet long and <math>9</math> feet wide? (There are 3 feet in a yard.)

<math>\textbf{(A) }12\qquad\textbf{(B) }36\qquad\textbf{(C) }108\qquad\textbf{(D) }324\qquad \textbf{(E) }972</math>

[[2015 AMC 8 Problems/Problem 1|Solution]]

==Problem 2==

Point <math>O</math> is the center of the regular octagon <math>ABCDEFGH</math>, and <math>X</math> is the midpoint of the side <math>\overline{AB}.</math> What fraction of the area of the octagon is shaded?

<math>\textbf{(A) }\frac{11}{32} \quad\textbf{(B) }\frac{3}{8} \quad\textbf{(C) }\frac{13}{32} \quad\textbf{(D) }\frac{7}{16}\quad \textbf{(E) }\frac{15}{32}</math>

<asy>
pair A,B,C,D,E,F,G,H,O,X;
A=dir(45);
B=dir(90);
C=dir(135);
D=dir(180);
E=dir(-135);
F=dir(-90);
G=dir(-45);
H=dir(0);
O=(0,0);
X=midpoint(A--B);

fill(X--B--C--D--E--O--cycle,rgb(0.75,0.75,0.75));
draw(A--B--C--D--E--F--G--H--cycle);

dot("$A$",A,dir(45));
dot("$B$",B,dir(90));
dot("$C$",C,dir(135));
dot("$D$",D,dir(180));
dot("$E$",E,dir(-135));
dot("$F$",F,dir(-90));
dot("$G$",G,dir(-45));
dot("$H$",H,dir(0));
dot("$X$",X,dir(135/2));
dot("$O$",O,dir(0));
draw(E--O--X);
</asy>
[[2015 AMC 8 Problems/Problem 2|Solution]]

==Problem 3==

Jack and Jill are going swimming at a pool that is one mile from their house. They leave home simultaneously. Jill rides her bicycle to the pool at a constant speed of <math>10</math> miles per hour. Jack walks to the pool at a constant speed of <math>4</math> miles per hour. How many minutes before Jack does Jill arrive?

<math>\textbf{(A) }5\qquad\textbf{(B) }6\qquad\textbf{(C) }8\qquad\textbf{(D) }9\qquad \textbf{(E) }10</math>

[[2015 AMC 8 Problems/Problem 3|Solution]]

==Problem 4==

The Centerville Middle School chess team consists of two boys and three girls. A photographer wants to take a picture of the team to appear in the local newspaper. She decides to have them sit in a row with a boy at each end and the three girls in the middle. How many such arrangements are possible?

<math>\textbf{(A) }2\qquad\textbf{(B) }4\qquad\textbf{(C) }5\qquad\textbf{(D) }6\qquad \textbf{(E) }12</math>

[[2015 AMC 8 Problems/Problem 4|Solution]]

==Problem 5==

Billy's basketball team scored the following points over the course of the first 11 games of the season: <cmath>42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73</cmath> If his team scores 40 in the 12th game, which of the following statistics will show an increase?

<math>\textbf{(A) } \text{range} \qquad \textbf{(B) } \text{median} \qquad \textbf{(C) } \text{mean} \qquad \textbf{(D) } \text{mode} \qquad \textbf{(E) } \text{mid-range}</math>

[[2015 AMC 8 Problems/Problem 5|Solution]]

==Problem 6==

In <math>\bigtriangleup ABC</math>, <math>AB=BC=29</math>, and <math>AC=42</math>. What is the area of <math>\bigtriangleup ABC</math>?

<math>\textbf{(A) }100\qquad\textbf{(B) }420\qquad\textbf{(C) }500\qquad\textbf{(D) }609\qquad \textbf{(E) }701</math>

[[2015 AMC 8 Problems/Problem 6|Solution]]

==Problem 7==

Each of two boxes contains three chips numbered <math>1</math>, <math>2</math>, <math>3</math>. A chip is drawn randomly from each box and the numbers on the two chips are multiplied. What is the probability that their product is even?

<math>\textbf{(A) }\frac{1}{9}\qquad\textbf{(B) }\frac{2}{9}\qquad\textbf{(C) }\frac{4}{9}\qquad\textbf{(D) }\frac{1}{2}\qquad \textbf{(E) }\frac{5}{9}</math>

[[2015 AMC 8 Problems/Problem 7|Solution]]

==Problem 8== 

What is the smallest whole number larger than the perimeter of any triangle with a side of length <math>5</math> and a side of length <math>19</math>?

<math>\textbf{(A) }24\qquad\textbf{(B) }29\qquad\textbf{(C) }43\qquad\textbf{(D) }48\qquad \textbf{(E) }57</math>

[[2015 AMC 8 Problems/Problem 8|Solution]]

==Problem 9==

On her first day of work, Janabel sold one widget. On day two, she sold three widgets. On day three, she sold five widgets, and on each succeeding day, she sold two more widgets than she had sold on the previous day. How many widgets in total had Janabel sold after working <math>20</math> days?

<math>\textbf{(A) }39\qquad\textbf{(B) }40\qquad\textbf{(C) }210\qquad\textbf{(D) }400\qquad \textbf{(E) }401</math>

[[2015 AMC 8 Problems/Problem 9|Solution]]

==Problem 10==

How many integers between <math>1000</math> and <math>9999</math> have four distinct digits?

<math>\textbf{(A) }3024\qquad\textbf{(B) }4536\qquad\textbf{(C) }5040\qquad\textbf{(D) }6480\qquad \textbf{(E) }6561</math>

[[2015 AMC 8 Problems/Problem 10|Solution]]

==Problem 11==

In the small country of Mathland, all automobile license plates have four symbols. The first must be a vowel (A, E, I, O, or U), the second and third must be two different letters among the 21 non-vowels, and the fourth must be a digit (0 through 9). If the symbols are chosen at random subject to these conditions, what is the probability that the plate will read "AMC8"?

<math>\textbf{(A) } \frac{1}{22,050} \qquad \textbf{(B) } \frac{1}{21,000}\qquad \textbf{(C) } \frac{1}{10,500}\qquad \textbf{(D) } \frac{1}{2,100} \qquad \textbf{(E) } \frac{1}{1,050}</math>

[[2015 AMC 8 Problems/Problem 11|Solution]]

==Problem 12==

How many pairs of parallel edges, such as <math>\overline{AB}</math> and <math>\overline{GH}</math> or <math>\overline{EH}</math> and <math>\overline{FG}</math>, does a cube have?


<math>\textbf{(A) }6 \quad\textbf{(B) }12 \quad\textbf{(C) } 18 \quad\textbf{(D) } 24 \quad \textbf{(E) } 36</math> <asy> import three; currentprojection=orthographic(1/2,-1,1/2); /* three - currentprojection, orthographic */ draw((0,0,0)--(1,0,0)--(1,1,0)--(0,1,0)--cycle); draw((0,0,0)--(0,0,1)); draw((0,1,0)--(0,1,1)); draw((1,1,0)--(1,1,1)); draw((1,0,0)--(1,0,1));  draw((0,0,1)--(1,0,1)--(1,1,1)--(0,1,1)--cycle); label("$D$",(0,0,0),S); label("$A$",(0,0,1),N); label("$H$",(0,1,0),S); label("$E$",(0,1,1),N); label("$C$",(1,0,0),S); label("$B$",(1,0,1),N); label("$G$",(1,1,0),S); label("$F$",(1,1,1),N); </asy>

[[2015 AMC 8 Problems/Problem 12|Solution]]

==Problem 13==


==Problem 14==

Which of the following integers cannot be written as the sum of four consecutive odd integers?

<math>\textbf{(A)}\text{ 16}\qquad\textbf{(B)}\text{ 40}\qquad\textbf{(C)}\text{ 72}\qquad\textbf{(D)}\text{ 100}\qquad\textbf{(E)}\text{ 200}</math>

==Problem 15==

==Problem 16==

In a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No ninth grader is assigned more than one sixth-grade buddy. If <math>\tfrac{1}{3}</math> of all the ninth graders are paired with <math>\tfrac{2}{5}</math> of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy?

<math>
\textbf{(A) } \frac{2}{15} \qquad
\textbf{(B) } \frac{4}{11} \qquad
\textbf{(C) } \frac{11}{30} \qquad
\textbf{(D) } \frac{3}{8} \qquad
\textbf{(E) } \frac{11}{15}
</math>

==Problem 17==

Jeremy's father drives him to school in rush hour traffic in <math>20</math> minutes. One day there is no traffic, so his father can drive him <math>18</math> miles per hour faster and gets him to school in <math>12</math> minutes. How far in miles is it to school?

<math>
\textbf{(A) } 4 \qquad
\textbf{(B) } 6 \qquad
\textbf{(C) } 8 \qquad
\textbf{(D) } 9 \qquad
\textbf{(E) } 12
</math>

==Problem 18==

==Problem 19==

==Problem 20==

==Problem 21==

==Problem 22==

==Problem 23==

==Problem 24==

==Problem 25==