2013 AMC 8 Problems: Difference between revisions

Revision as of 18:44, 20 November 2013

Problem 1

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 2

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 3

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 4

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 5

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 6

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 7

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 8

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$ Solution

Problem 9

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 10

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 11

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 12

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 13

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 14

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 15

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 16

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 17

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 18

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 19

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 20

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 21

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 22

p $\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 23

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 24

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 25

p

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing

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2013 AMC 8 Problems: Difference between revisions

Revision as of 18:44, 20 November 2013

Contents

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

@@ Line 1: / Line 1: @@
 ==Problem 1==
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 1|Solution]]
+[[2013 AMC 8 Problems/Problem 1|Solution]]
 ==Problem 2==
-In the country of East Westmore, statisticians estimate there is a baby born every <math> 8 </math> hours and a death every day. To the nearest hundred, how many people are added to the population of East Westmore each year?
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 2|Solution]]
+[[2013 AMC 8 Problems/Problem 2|Solution]]
 ==Problem 3==
-On February 13 <math>\emph{The Oshkosh Northwester}</math> listed the length of daylight as 10 hours and 24 minutes, the sunrise was <math> 6:57\textsc{am} </math>, and the sunset as <math> 8:15\textsc{pm} </math>. The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set?
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 3|Solution]]
+[[2013 AMC 8 Problems/Problem 3|Solution]]
 ==Problem 4==
-Peter's family ordered a 12-slice pizza for dinner. Peter ate one slice and shared another slice equally with his brother Paul. What fraction of the pizza did Peter eat?
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 4|Solution]]
+[[2013 AMC 8 Problems/Problem 4|Solution]]
 ==Problem 5==
-In the diagram, all angles are right angles and the lengths of the sides are given in centimeters. Note the diagram is not drawn to scale. What is , <math> X </math> in centimeters?
+p
-<asy>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-pair A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R;
-A=(4,0);
-B=(7,0);
-C=(7,4);
-D=(8,4);
-E=(8,5);
-F=(10,5);
-G=(10,7);
-H=(7,7);
-I=(7,8);
-J=(5,8);
-K=(5,7);
-L=(4,7);
-M=(4,6);
-N=(0,6);
-O=(0,5);
-P=(2,5);
-Q=(2,3);
-R=(4,3);
-draw(A--B--C--D--E--F--G--H--I--J--K--L--M--N--O--P--Q--R--cycle);
-label("$X$",(3.4,1.5));
-label("6",(7.6,1.5));
-label("1",(7.6,3.5));
-label("1",(8.4,4.6));
-label("2",(9.4,4.6));
-label("2",(10.4,6));
-label("3",(8.4,7.4));
-label("1",(7.5,7.8));
-label("2",(6,8.5));
-label("1",(4.7,7.8));
-label("1",(4.3,7.5));
-label("1",(3.5,6.5));
-label("4",(1.8,6.5));
-label("1",(-0.5,5.5));
-label("2",(0.8,4.5));
-label("2",(1.5,3.8));
-label("2",(2.8,2.6));</asy>
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+[[2013 AMC 8 Problems/Problem 5|Solution]]
-[[2012 AMC 8 Problems/Problem 5|Solution]]
 ==Problem 6==
-A rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph. The photograph measures 8 inches high and 10 inches wide. What is the area of the border, in square inches?
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 6|Solution]]
+[[2013 AMC 8 Problems/Problem 6|Solution]]
 ==Problem 7==
-Isabella must take four 100-point tests in her math class. Her goal is to achieve an average grade of 95 on the tests. Her first two test scores were 97 and 91. After seeing her score on the third test, she realized she can still reach her goal. What is the lowest possible score she could have made on the third test?
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 7|Solution]]
+[[2013 AMC 8 Problems/Problem 7|Solution]]
 ==Problem 8==
-A shop advertises everything is "half price in today's sale." In addition, a coupon gives a 20% discount on sale prices. Using the coupon, the price today represents what percentage off the original price?
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 8|Solution]]
+[[2013 AMC 8 Problems/Problem 8|Solution]]
 ==Problem 9==
-The Fort Worth Zoo has a number of two-legged birds and a number of four-legged mammals. On one visit to the zoo, Margie counted 200 heads and 522 legs. How many of the animals that Margie counted were two-legged birds?
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 9|Solution]]
+[[2013 AMC 8 Problems/Problem 9|Solution]]
 ==Problem 10==
-How many 4-digit numbers greater than 1000 are there that use the four digits of 2012?
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 10|Solution]]
+[[2013 AMC 8 Problems/Problem 10|Solution]]
 ==Problem 11==
-The mean, median, and unique mode of the positive integers 3, 4, 5, 6, 6, 7, and <math>x</math> are all equal. What is the value of <math>x</math>?
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 11|Solution]]
+[[2013 AMC 8 Problems/Problem 11|Solution]]
 ==Problem 12==
-What is the units digit of  <math>13^{2012}</math>?
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 12|Solution]]
+[[2013 AMC 8 Problems/Problem 12|Solution]]
 ==Problem 13==
-Jamar bought some pencils costing more than a penny each at the school bookstore and paid <math>
+p
-\textdollar 1.43 </math>. Sharona bought some of the same pencils and paid <math> \textdollar 1.87 </math>. How many more pencils did Sharona buy than Jamar?
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 13|Solution]]
+[[2013 AMC 8 Problems/Problem 13|Solution]]
 ==Problem 14==
-In the BIG N, a middle school football conference, each team plays every other team exactly once. If a total of 21 conference games were played during the 2012 season, how many teams were members of the BIG N conference?
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 14|Solution]]
+[[2013 AMC 8 Problems/Problem 14|Solution]]
 ==Problem 15==
-The smallest number greater than 2 that leaves a remainder of 2 when divided by 3, 4, 5, or 6 lies between what numbers?
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 15|Solution]]
+[[2013 AMC 8 Problems/Problem 15|Solution]]
 ==Problem 16==
-Each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is used only once to make two five-digit numbers so that they have the largest possible sum. Which of the following could be one of the numbers?
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 16|Solution]]
+[[2013 AMC 8 Problems/Problem 16|Solution]]
 ==Problem 17==
-A square with integer side length is cut into 10 squares, all of which have integer side length and at least 8 of which have area 1. What is the smallest possible value of the length of the side of the original square?
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 17|Solution]]
+[[2013 AMC 8 Problems/Problem 17|Solution]]
 ==Problem 18==
-What is the smallest positive integer that is neither prime nor square and that has no prime factor less than 50?
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 18|Solution]]
+[[2013 AMC 8 Problems/Problem 18|Solution]]
 ==Problem 19==
-In a jar of red, green, and blue marbles, all but 6 are red marbles, all but 8 are green, and all but 4 are blue. How many marbles are in the jar?
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 19|Solution]]
+[[2013 AMC 8 Problems/Problem 19|Solution]]
 ==Problem 20==
-What is the correct ordering of the three numbers <math> \frac{5}{19} </math>, <math> \frac{7}{21} </math>, and <math> \frac{9}{23} </math>, in increasing order?
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-<math> \textbf{(D)}\hspace{.05in}\frac{5}{19}<\frac{9}{23}<\frac{7}{21}\quad\textbf{(E)}\hspace{.05in}\frac{7}{21}<\frac{5}{19}<\frac{9}{23} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 20|Solution]]
+[[2013 AMC 8 Problems/Problem 20|Solution]]
 ==Problem 21==
-Marla has a large white cube that has an edge of 10 feet. She also has enough green paint to cover 300 square feet. Marla uses all the paint to create a white square centered on each face, surrounded by a green border. What is the area of one of the white squares, in square feet?
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 21|Solution]]
+[[2013 AMC 8 Problems/Problem 21|Solution]]
 ==Problem 22==
-Let <math> R </math>  be a set of nine distinct integers. Six of the elements are 2, 3, 4, 6, 9, and 14. What is the number of possible values of the median of <math> R </math> ?
+p
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 22|Solution]]
+[[2013 AMC 8 Problems/Problem 22|Solution]]
 ==Problem 23==
-An equilateral triangle and a regular hexagon have equal perimeters. If the area of the triangle is 4, what is the area of the hexagon?
+p
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 23|Solution]]
+[[2013 AMC 8 Problems/Problem 23|Solution]]
 ==Problem 24==
-A circle of radius 2 is cut into four congruent arcs. The four arcs are joined to form the star figure shown. What is the ratio of the area of the star figure to the area of the original circle?
+p
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-<asy>
+[[2013 AMC 8 Problems/Problem 24|Solution]]
-size(0,50);
-draw((-1,1)..(-2,2)..(-3,1)..(-2,0)..cycle);
-dot((-1,1));
-dot((-2,2));
-dot((-3,1));
-dot((-2,0));
-draw((1,0){up}..{left}(0,1));
-dot((1,0));
-dot((0,1));
-draw((0,1){right}..{up}(1,2));
-dot((1,2));
-draw((1,2){down}..{right}(2,1));
-dot((2,1));
-draw((2,1){left}..{down}(1,0));</asy>
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 24|Solution]]
 ==Problem 25==
-A square with area 4 is inscribed in a square with area 5, with one vertex of the smaller square on each side of the larger square. A vertex of the smaller square divides a side of the larger square into two segments, one of length <math> a </math>, and the other of length <math> b </math>. What is the value of <math> ab </math>?
+p
-<asy>
-draw((0,2)--(2,2)--(2,0)--(0,0)--cycle);
-draw((0,0.3)--(0.3,2)--(2,1.7)--(1.7,0)--cycle);
-label("$a$",(-0.1,0.15));
-label("$b$",(-0.1,1.15));</asy>
-<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\frac{1}2\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
+<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
-[[2012 AMC 8 Problems/Problem 25|Solution]]
+[[2013 AMC 8 Problems/Problem 25|Solution]]
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