Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus
GET READY FOR THE AMC 12 WITH AoPS
Learn with outstanding instructors and top-scoring students from around the world in our AMC 12 Problem Series online course.
CHECK SCHEDULE

Difference between revisions of "2004 AMC 12A Problems"
Line 21: Line 21:
  
 
== Problem 4 ==
 
== Problem 4 ==
 +
Bertha has <math>6</math> daughters and no sons. Some of her daughters have <math>6</math> daughters, and the rest have none. Bertha has a total of <math>30</math> daughters and granddaughters, and no great-granddaughters. How many of Bertha's daughters and grand-daughters have no children?
 +
 +
<math>\mathrm {(A)} 22 \qquad \mathrm {(B)} 23 \qquad \mathrm {(C)} 24 \qquad \mathrm {(D)} 25 \qquad \mathrm {(E)} 26</math>
  
 
[[2004 AMC 12A/Problem 4|Solution]]
 
[[2004 AMC 12A/Problem 4|Solution]]
  
 
== Problem 5 ==
 
== Problem 5 ==
 +
The graph of the line <math>y=mx+b</math> is shown. Which of the following is true?
 +
 +
{{image}}
 +
 +
<math>\mathrm {(A)} mb<-1 \qquad \mathrm {(B)} -1<mb<0 \qquad \mathrm {(C)} mb=0 \qquad \mathrm {(D)} 0<mb<1 \qquad \mathrm {(E)} mb>1</math>
  
 
[[2004 AMC 12A/Problem 5|Solution]]
 
[[2004 AMC 12A/Problem 5|Solution]]

Revision as of 11:40, 29 September 2007

Problem 1

Alicia earns $20$ dollars per hour, of which $1.45\%$ is deducted to pay local taxes. How many cents per hour of Alicia's wages are used to pay local taxes?

$\mathrm {(A)} 0.0029 \qquad \mathrm {(B)} 0.029 \qquad \mathrm {(C)} 0.29 \qquad \mathrm {(D)} 2.9 \qquad \mathrm {(E)} 29$

Solution

Problem 2

On the AMC 12, each correct answer is worth $6$ points, each incorrect answer is worth $0$ points, and each problem left unanswered is worth $2.5$ points. If Charlyn leaves $8$ of the $25$ problems unanswered, how many of the remaining problems must she answer correctly in order to score at least $100$?

$\mathrm {(A)} 11 \qquad \mathrm {(B)} 13 \qquad \mathrm {(C)} 14 \qquad \mathrm {(D)} 16 \qquad \mathrm {(E)} 17$

Solution

Problem 3

For how many ordered pairs of positive integers $(x,y)$ is $x+2y=100$?

$\mathrm {(A)} 33 \qquad \mathrm {(B)} 49 \qquad \mathrm {(C)} 50 \qquad \mathrm {(D)} 99 \qquad \mathrm {(E)} 100$

Solution

Problem 4

Bertha has $6$ daughters and no sons. Some of her daughters have $6$ daughters, and the rest have none. Bertha has a total of $30$ daughters and granddaughters, and no great-granddaughters. How many of Bertha's daughters and grand-daughters have no children?

$\mathrm {(A)} 22 \qquad \mathrm {(B)} 23 \qquad \mathrm {(C)} 24 \qquad \mathrm {(D)} 25 \qquad \mathrm {(E)} 26$

Solution

Problem 5

The graph of the line $y=mx+b$ is shown. Which of the following is true?

An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.

$\mathrm {(A)} mb<-1 \qquad \mathrm {(B)} -1<mb<0 \qquad \mathrm {(C)} mb=0 \qquad \mathrm {(D)} 0<mb<1 \qquad \mathrm {(E)} mb>1$

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

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

See also

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2004_AMC_12A_Problems&oldid=17161"