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• 2000 AMC 12 Problems
  ...ntegers such that the product <math>I \cdot M \cdot O = 2001 </math>. What is the largest possible value of the sum <math>I + M + O</math>? == Problem 3 ==
  13 KB (1,948 words) - 10:35, 16 June 2024
• 2001 AMC 12 Problems
  The sum of two numbers is <math>S</math>. Suppose <math>3</math> is added to each number and then each of the resulting numbers is doubled. What is the sum of the final two
  13 KB (1,957 words) - 12:53, 24 January 2024
• 2002 AMC 12B Problems
  ...ne numbers in the set <math>\{9, 99, 999, 9999, \ldots, 999999999\}</math> is a <math>9</math>-digit number <math>M</math>, all of whose digits are disti What is the value of
  10 KB (1,547 words) - 04:20, 9 October 2022
• 2003 AMC 12B Problems
  Which of the following is the same as <cmath>\frac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21}?</cmath>
  13 KB (1,987 words) - 18:53, 10 December 2022
• 2004 AMC 12B Problems
  <math>(\mathrm {A}) 3\qquad (\mathrm {B}) 6 \qquad (\mathrm {C}) 9 \qquad (\mathrm {D}) 12 \qquad ...>d</math> are 0, 1, 2, and 3, although not necessarily in that order. What is the maximum possible value of the result?
  13 KB (2,049 words) - 13:03, 19 February 2020
• 2005 AMC 12B Problems
  ...property that <math>x\%</math> of <math>x</math> is <math>4</math>. What is <math>x</math>? == Problem 3 ==
  12 KB (1,781 words) - 12:38, 14 July 2022
• 2006 AMC 12B Problems/Problem 2
  .../math>, define <math>x\spadesuit y = (x + y)(x - y)</math>. What is <math>3\spadesuit(4\spadesuit 5)</math>? <math>3\spadesuit -9=-72 \Rightarrow \text{(A)}</math>
  473 bytes (71 words) - 10:44, 4 July 2013
• 2006 AMC 12B Problems/Problem 4
  ...</math>. Mary will pay with a twenty-dollar bill. Which of the following is closest to the percentage of the <math>20.00</math> that she will receive i The total price of the items is <math>(8-.01)+(5-.01)+(3-.01)+(2-.01)+(1-.01)=19-.05=18.95</math>
  1 KB (152 words) - 16:11, 8 December 2013
• 2006 AMC 12B Problems/Problem 5
  ...hile Bob is also walking east, but at a speed of 5 miles per hour. If Bob is now 1 mile west of John, how many minutes will it take for Bob to catch up ...Bob is catching up to John is <math>5-3=2</math> miles per hour. Since Bob is one mile behind John, it will take <math>\frac{1}{2} \Rightarrow \text{(A)}
  654 bytes (115 words) - 21:47, 1 August 2020
• 2006 AMC 12B Problems/Problem 7
  The first child can be seated in <math>3</math> spaces. <math>3 \times 2 \times 2 = 12 \Rightarrow \text{(B)}</math>
  1 KB (213 words) - 15:33, 9 April 2024
• 2006 AMC 12B Problems/Problem 8
  ...>y = \frac 14x + b</math> intersect at the point <math>(1,2)</math>. What is <math>a + b</math>?<!-- don't remove the following tag, for PoTW on the Wik <math>\frac{3}{4}(x+y)=a+b</math>
  1 KB (235 words) - 00:46, 6 January 2022
• 2006 AMC 12B Problems/Problem 9
  ...ces for <math>a</math> and <math>b</math>. Thus there are altogether <math>3+10+21=\boxed{34}</math> such integers. If it was 2, there is 1 possibility for the hundreds digit, 3 for the ones digit.
  3 KB (409 words) - 17:10, 30 April 2024
• 2006 AMC 12B Problems/Problem 13
  ...s <math> ABCD</math> is 24, and <math> \angle BAD = 60^\circ</math>. What is the area of rhombus <math> BFDE</math>? ...n, B=(2,0), C=(3, sqrt(3)), D=(1, sqrt(3)), E=(1, 1/sqrt(3)), F=(2, 2/sqrt(3));
  3 KB (447 words) - 03:49, 16 January 2021
• 2006 AMC 12B Problems/Problem 14
  ...> and <math>N</math> are all positive integers with <math>N>1</math>. What is the cost of the jam Elmo uses to make the sandwiches? ...ply that if <math>B=2</math> and <math>J=3</math>, then <math>4B+5J=4(2)+5(3)=23</math>. The problem asks for the total cost of jam, or <math>N(5J)=11(1
  1 KB (227 words) - 17:21, 8 December 2013
• 2006 AMC 12B Problems/Problem 15
  ...h> \overline{BC}</math> are common external tangents to the circles. What is the area of hexagon <math> AOBCPD</math>? ...bf{(B) } 24\sqrt {2} \qquad \textbf{(C) } 36 \qquad \textbf{(D) } 24\sqrt {3} \qquad \textbf{(E) } 32\sqrt {2}</math>
  3 KB (458 words) - 16:40, 6 October 2019
• 2006 AMC 12B Problems/Problem 16
  ...>C</math> at <math>(0,0)</math> and <math>(7,1)</math>, respectively. What is its area? \mathrm{(A)}\ 20\sqrt {3}
  1 KB (210 words) - 12:36, 2 July 2024
• 2006 AMC 12B Problems/Problem 17
  ...<math>6</math> on each die are in the ratio <math>1:2:3:4:5:6</math>. What is the probability of rolling a total of <math>7</math> on the two dice? The probability of getting an <math>x</math> on one of these dice is <math>\frac{x}{21}</math>.
  1 KB (188 words) - 22:10, 9 June 2016
• 2006 AMC 12B Problems/Problem 18
  ...can easily be shown that each location that satisfies these two conditions is indeed reachable. If the object only makes <math>1</math> move, it is obvious that there are only 4 possible points that the object can move to.
  2 KB (354 words) - 16:57, 28 December 2020
• 2006 AMC 12B Problems/Problem 19
  ..."and the last two digits just happen to be my age." Which of the following is not the age of one of Mr. Jones's children? First, The number of the plate is divisible by <math>9</math> and in the form of
  4 KB (696 words) - 09:47, 10 August 2015
• 2006 AMC 12B Problems/Problem 20
  ...th>x</math> be chosen at random from the interval <math>(0,1)</math>. What is the probability that Here <math>\lfloor x\rfloor</math> denotes the greatest integer that is less than or equal to <math>x</math>.
  3 KB (485 words) - 14:09, 21 May 2021

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