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• 2000 AMC 12 Problems/Problem 13
  ...ut were never zero. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. How many people are in the family? <math>\text {(A)}\ 3 \qquad \text {(B)}\ 4 \qquad \text {(C)}\ 5 \qquad \text {(D)}\ 6 \qqu
  6 KB (996 words) - 18:14, 29 June 2023
• 2008 AMC 10B Problems/Problem 17
  ...he mayor's work. On three separate occasions a pollster selects a voter at random. What is the probability that on exactly one of these three occasions the v <math>\mathrm{(A)}\ {{{0.063}}} \qquad \mathrm{(B)}\ {{{0.189}}} \qquad \mathrm{(C)}\ {{{0.2
  1 KB (202 words) - 12:42, 30 January 2024
• 2008 iTest Problems
  ...s as a Renewable Energy Engineer for the Southern Company, and Hannah runs a lab at Jupiter Falls University where she researches biomass (renewable fue When the Kubiks went on vacation to San Diego last year, they spent a day at the San Diego Zoo.
  71 KB (11,749 words) - 01:31, 2 November 2023
• 1990 AJHSME Problems
  <math>\text{(A)}\ 947 \qquad \text{(B)}\ 1037 \qquad \text{(C)}\ 1047 \qquad \text{(D)}\ 1 <math>\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad
  15 KB (2,059 words) - 15:03, 6 October 2021
• 1998 AJHSME Problems
  <math>\text{(A)}\ \dfrac{6}{x} \qquad \text{(B)}\ \dfrac{6}{x+1} \qquad \text{(C)}\ \dfrac If <math>\begin{tabular}{r|l}a&b \\ \hline c&d\end{tabular} = \text{a}\cdot \text{d} - \text{b}\cdot \text{c}</math>, what is the value of <math>
  14 KB (1,920 words) - 19:31, 31 January 2024
• 2011 AMC 8 Problems
  ...math> apples at a cost of <math> 50 </math> cents per apple. She paid with a 5-dollar bill. How much change did Margie receive? <math>\textbf{(A) }\ \textdollar 1.50 \qquad \textbf{(B) }\ \textdollar 2.00 \qquad \textbf{
  16 KB (2,371 words) - 17:34, 9 January 2024
• 2011 AMC 8 Problems/Problem 12
  ...arlos, and Diego are seated at random around a square table, one person to a side. What is the probability that Angie and Carlos are seated opposite eac <math> \textbf{(A) } \frac14 \qquad\textbf{(B) } \frac13 \qquad\textbf{(C) } \frac12 \qquad\t
  1 KB (211 words) - 19:30, 30 May 2024
• Mathtime Version 1 Issue 2
  ...e the positive integer <math>n</math> such that <math>n^2+20n+40</math> is a perfect square. (Proposed by djmathman) ...umber of ordered integer pairs <math>(a,b)</math> such that <math>a^2+b^2|(a+b)^2</math>. (Proposed by djmathman)
  15 KB (2,444 words) - 21:46, 1 January 2012
• 2012 AMC 10A Problems/Problem 23
  <math> \text{(A)}\ 60\qquad\text{(B)}\ 170\qquad\text{(C)}\ 290\qquad\text{(D)}\ 320\qquad\ Note that if <math>n</math> is the number of friends each person has, then <math>n</math> can be any integer from <math>1</math> to <math>4<
  5 KB (815 words) - 17:53, 12 October 2023
• 2012 AMC 10B Problems
  <math> \textbf{(A)}\ 48\qquad\textbf{(B)}\ 56\qquad\textbf{(C)}\ 64\qquad\textbf{(D)}\ 72\qqu A circle of radius 5 is inscribed in a rectangle as shown. The ratio of the length of the rectangle to its width
  18 KB (2,350 words) - 18:48, 9 July 2023
• 2012 AMC 10B Problems/Problem 18
  ...bility that a person who is chosen at random from this population and gets a positive test result actually has the disease. Which of the following is cl <math>\textbf{(A)}\ \frac{1}{98}\qquad\textbf{(B)}\ \frac{1}{9}\qquad\textbf{(C)}\ \frac{1}{
  2 KB (379 words) - 14:00, 22 August 2022
• 2012 AIME I Problems/Problem 3
  ...eople so that exactly one person receives the type of meal ordered by that person. ...ath>9</math> to account for the <math>9</math> different ways in which the person to receive the correct meal could be picked. Note, this implies that the di
  3 KB (572 words) - 18:56, 13 June 2023
• 2012 AIME I Problems
  ...s with three not necessarily distinct digits, <math>abc</math>, with <math>a \neq 0</math> and <math>c \neq 0</math> such that both <math>abc</math> and ...eople so that exactly one person receives the type of meal ordered by that person.
  10 KB (1,617 words) - 14:49, 2 June 2023
• Mock AIME I 2012 Problems
  A circle of maximal area is inscribed in the region bounded by the graph of < A permutation of the numbers <math>\{2</math>, <math>3</math>, <math>4</math>
  7 KB (1,309 words) - 11:13, 8 April 2012
• 2006 SMT/General Problems
  After a cyclist has gone <math> \frac{2}{3} </math> of his route, he gets a flat tire. Finishing on foot, he spends twice as long walking as he did rid A customer enters a supermarket. The probability that the customer buys bread is <math> 0.60 </
  10 KB (1,477 words) - 16:02, 27 May 2012
• 2013 AMC 10B Problems
  <math> \textbf{(A)}\ -1 \qquad\textbf{(B)}\ \frac{5}{36} \qquad\textbf{(C)}\ \frac{7}{12} \q ...f Mr. Green's steps is <math>2</math> feet long. Mr. Green expects a half a pound of potatoes per square foot from his garden. How many pounds of pota
  12 KB (1,926 words) - 21:54, 6 October 2022
• 1991 AHSME Problems
  ...math>, <math>b</math>, and <math>c</math> we define <math>f(a,b,c)=\frac{c+a}{c-b}</math>, then <math>f(1,-2,-3)</math> is <math> \textbf{(A) } -2 \qquad \textbf{(B) } -\frac{2}{5} \qquad \textbf{(C) } -\frac{1}{4} \
  16 KB (2,451 words) - 04:27, 6 September 2021
• 1990 AHSME Problems
  <math>\textbf{(A)}\ \pm\frac{1}{2}\qquad\textbf{(B)}\ \pm 1\qquad\textbf{(C)}\ \pm 2\qquad\t <math>\textbf{(A) } -16\qquad
  14 KB (2,099 words) - 01:15, 10 September 2021
• 1986 AHSME Problems
  <math>\textbf{(A)}\ 2y \qquad <math>\textbf{(A)}\ y = \frac{1}{3} x + 8 \qquad
  17 KB (2,512 words) - 18:30, 12 October 2023
• 1963 AHSME Problems
  <math>\textbf{(A)}\ (0,0)\qquad <math>\textbf{(A)}\ -14 \qquad
  20 KB (3,122 words) - 14:17, 20 February 2020
• 2014 AMC 8 Problems/Problem 12
  ...e correct baby pictures. What is the probability that a reader guessing at random will match all three correctly? <math> \textbf{(A) }\frac{1}{9}\qquad\textbf{(B) }\frac{1}{6}\qquad\textbf{(C) }\frac{1}{4}\q
  2 KB (310 words) - 11:12, 2 July 2023
• 2015 UNCO Math Contest II Problems
  The positive integers are <math>1, 2, 3, 4, \ldots </math> A polynomial is quadratic if its highest power term has power two. If P is a polynomial that satisfies <math>P(x^2 +1) = 5x^4 +7x^2 +19</math>, then wha
  7 KB (1,151 words) - 15:11, 20 August 2020
• 2015 AMC 10B Problems
  <math> \textbf{(A) } -2 \qquad\textbf{(B) } \dfrac{1}{16} \qquad\textbf{(C) } \dfrac{7}{4} \q Marie does three equally time-consuming tasks in a row without taking breaks. She begins the first task at 1:00 PM and finishe
  14 KB (2,247 words) - 11:38, 26 March 2024
• Gmaas
  ...Plenipotentiary GMAAS cannot get rid of a language that's been around for a <math>999999999999999999999999999999999999999999^{9999999999999999999999999 ...ke and reciprocated the fee," you must pay <math>1,000,000</math> to solve a problem using the Games theorem. You wouldn't waste that much money to solv
  69 KB (11,805 words) - 20:49, 18 December 2019
• 2017 AMC 12B Problems
  <math>\textbf{(A)}\ 1\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 20\qquad\ <math>\textbf{(A)}\ y+x^2\qquad\textbf{(B)}\ y+xz\qquad\textbf{(C)}\ y+y^2\qquad\textbf{(D)}
  15 KB (2,343 words) - 18:26, 25 December 2020
• 2017 AMC 12B Problems/Problem 25
  ...may have exactly the same <math>5</math> members. The site statistics show a curious fact: The average, over all subsets of size <math>9</math> of the s <math>\textbf{(A) } 477 \qquad \textbf{(B) } 482 \qquad \textbf{(C) } 487 \qquad \textbf{(D)
  3 KB (574 words) - 11:18, 21 May 2023
• 2017 AMC 12B Problems/Problem 22
  ...n urn---one green, one red, and two white. The players each draw a ball at random without replacement. Whoever gets the green ball gives one coin to whoever <math>\textbf{(A)}\quad \dfrac{7}{576} \qquad \qquad \textbf{(B)}\quad \dfrac{5}{192} \qquad
  12 KB (1,935 words) - 11:37, 16 December 2023
• 2020 AMC 12B Problems
  <math>\textbf{(A) }5 \qquad \textbf{(B) }4 + \sqrt{7} + \sqrt{10} \qquad \textbf{(C) } 10 \q ...^2-11^2} \cdot \frac{(70-11)(70+11)}{(100-7)(100+7)}</cmath><math>\textbf{(A) } 1 \qquad \textbf{(B) } \frac{9951}{9950} \qquad \textbf{(C) } \frac{4780
  16 KB (2,417 words) - 01:03, 28 April 2022
• 1963 AHSME Problems/Problem 36
  A person starting with <math>\$64</math> and making <math>6</math> bets, wins three ...occurring in random order. The chance for a win is equal to the chance for a loss.
  1 KB (209 words) - 18:22, 15 July 2018
• Basic Programming With Python
  (Note: This is a really long article. To learn the most from this article, you need to read ...ll two-digit positive integers <math>x</math> such that <math>5x</math> is a two-digit positive integer.'''
  33 KB (5,277 words) - 22:14, 3 June 2023
• 2019 AMC 10C Problems
  Here are the problems from the 2019 AMC 10C, a mock contest created by the AoPS user fidgetboss_4000. ...<math>m+c=2018</math>, and <math>a+c=2019</math>, find the value of <math>a+m+c+10</math>.
  12 KB (1,917 words) - 12:14, 29 November 2021
• 2020 AMC 10B Problems
  <math>\textbf{(A)}\ -20 \qquad\textbf{(B)}\ -3 \qquad\textbf{(C)}\ 3 \qquad\textbf{(D)}\ 5 \ <math>\textbf{(A)}\ 24 \qquad\textbf{(B)}\ 25 \qquad\textbf{(C)}\ 28 \qquad\textbf{(D)}\ 40
  16 KB (2,496 words) - 20:09, 19 May 2024
• 2019 AMC 10B Problems/Problem 22
  ...y simultaneously chooses one of the other two players independently and at random and gives <math>\$1</math> to that player. What is the probability that aft <math>\textbf{(A) } \frac{1}{7} \qquad\textbf{(B) } \frac{1}{4} \qquad\textbf{(C) } \frac{1}
  9 KB (1,568 words) - 11:15, 18 October 2023
• What is the definition of Pure Mathematics?
  ...is welcomed to edit, BUT ONLY IN GOOD WAYS! The AoPS Secret Governemtn has a backup of this page. ...ng it. For example, can a butterfly that flaps its wings in Brazil trigger a tornado in Texas?
  35 KB (5,882 words) - 18:08, 28 June 2021
• GMAAS
  ...entiary Almighty Gmaas cannot get rid of a language that's been around for a <math>999999999999999999999999999999999999999999^{9999999999999999999999999
  85 KB (13,971 words) - 18:02, 16 May 2024
• 2019 AMC 8 Problems
  Ike and Mike go into a sandwich shop with a total of <math>\$30.00</math> to spend. Sandwiches cost <math>\$4.50</math> <math>\textbf{(A) }6\qquad\textbf{(B) }7\qquad\textbf{(C) }8\qquad\textbf{(D) }9\qquad\textb
  17 KB (2,585 words) - 15:27, 4 May 2024
• 2019 AMC 8 Problems/Problem 15
  ...lected at random, what is the probability that this person is also wearing a cap? <math>\textbf{(A) }\frac{14}{85}\qquad\textbf{(B) }\frac{7}{25}\qquad\textbf{(C) }\frac{2}{5
  3 KB (496 words) - 00:28, 6 May 2024
• 2020 AMC 10B Problems/Problem 16
  ...numbers previously chosen by either player. A player unable to choose such a number loses. Using optimal strategy, which player will win the game? <math>\textbf{(A)} \text{ Bela will always win.} \qquad \textbf{(B)} \text{ Jenn will always
  3 KB (530 words) - 16:31, 11 September 2023
• Combinatorics Challenge Problems
  Ms.Carr asks her students to read any 5 of the 10 books on a reading list. Harold randomly selects 5 books from this list, and Betty doe <math>3</math> points are chosen on the circumference of a circle to form a triangle. What is the probability that the triangle does not contain the ce
  8 KB (858 words) - 08:37, 1 May 2024
• 2020 FMC 10A Problems
  ...ain stops halfway between the bank and the store to pick up some food from a local restaurant. Then, he decides he instead wants to go to the park and h <math>\textbf{(A)}\ \dfrac{9}{16}\qquad\textbf{(B)}\ \dfrac{3}{16}\qquad\textbf{(C)}\ \dfrac
  14 KB (2,267 words) - 12:49, 9 June 2020
• 2020 FMC 12A Problems
  ...identical bottles. Given that Amy spent <math>3</math> more dollars to buy a standard pack of soda in <math>2020</math> than in <math>2019, </math> what <math>\textbf{(A)}\ 1.6 \qquad\textbf{(B)}\ 1.65 \qquad\textbf{(C)}\ 1.7 \qquad\textbf{(D)}\
  15 KB (2,388 words) - 13:24, 9 June 2020
• 2021 AMC 10B Problems
  <math>\textbf{(A)} ~9 \qquad\textbf{(B)} ~10 \qquad\textbf{(C)} ~18 \qquad\textbf{(D)} ~19 \ <math>\textbf{(A)} ~0 \qquad\textbf{(B)} ~4\sqrt{3}-6 \qquad\textbf{(C)} ~6 \qquad\textbf{(D
  17 KB (2,418 words) - 12:52, 5 November 2023
• 2021 ZeMC10 Problems/Problem 3
  ...uring those with CUBIC-27. If three patients with CUBIC-27 are selected at random, what is the probability that exactly one of the three patients will be suc <math>\textbf{(A) } 0.9 \% \qquad \textbf{(B) } 2.7 \% \qquad\textbf{(C) } 8.1 \% \qquad\te
  928 bytes (133 words) - 19:50, 1 September 2022
• 2023 AIME I Problems/Problem 1
  ...random order. The probability that every man stands diametrically opposite a woman is <math>\frac{m}{n},</math> where <math>m</math> and <math>n</math> ...<math>10\cdot8\cdot6\cdot4\cdot2</math> ways to place the five men each in a man-woman diameter. Finally, there are <math>9!</math> ways to place the ni
  11 KB (1,803 words) - 17:17, 12 January 2024
• Know the Facts: Gmaas
  ...e contributors section. WARNING: Security details will be checking once in a while, so please edit this page appropriately! ..., though his godly power can turn him into anything, he just prefers to be a cat. As you read on, you will discover more things about him then you will
  88 KB (14,928 words) - 13:54, 29 April 2024