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• 2009 AIME I Problems/Problem 1
  ...s <math>3</math> distinct digits which, when read from left to right, form a geometric sequence. Find the difference between the largest and smallest g ...onal of the form <math>k/3</math> for some integer <math>k</math>, because a whole number should be attained for the 3rd term as well. When <math>k = 1<
  2 KB (360 words) - 03:32, 16 January 2023
• 2009 AIME I Problems/Problem 7
  ...tions, so we try <math>125</math>: <cmath>3n + 2 = 125</cmath> <cmath>3n = 123</cmath> <cmath>n = \boxed{041}</cmath> <math>25</math> - that gives a non-integer <math>n</math>.
  2 KB (340 words) - 00:26, 9 January 2023
• 1989 AJHSME Problems
  <math>\text{(A)}\ 150 \qquad \text{(B)}\ 199 \qquad \text{(C)}\ 200 \qquad \text{(D)}\ 249 <math>\text{(A)}\ .012 \qquad \text{(B)}\ .0246 \qquad \text{(C)}\ .12 \qquad \text{(D)}\
  13 KB (1,765 words) - 11:55, 22 November 2023
• 1988 AJHSME Problems/Problem 3
  <math>\text{(A)}\ .1 \qquad \text{(B)}\ .123 \qquad \text{(C)}\ .2 \qquad \text{(D)}\ .3 \qquad \text{(E)}\ .6</math> {{AJHSME box|year=1988|num-b=2|num-a=4}}
  544 bytes (64 words) - 23:54, 4 July 2013
• 1989 AJHSME Problems/Problem 14
  <math>\text{(A)}\ 58 \qquad \text{(B)}\ 123 \qquad \text{(C)}\ 149 \qquad \text{(D)}\ 171 \qquad \text{(E)}\ 176</math> ...math>a</math> is three digit and <math>b</math> is two digit, we set <math>a=245</math> and <math>b=96</math>. Their difference is <math>149\rightarrow
  887 bytes (126 words) - 11:49, 30 July 2023
• 2010 AIME I Problems/Problem 4
  Jackie and Phil have two fair coins and a third coin that comes up heads with [[probability]] <math>\frac47</math>. J ...is <math>3+10x+11x^2+4x^3</math>. (<math>ax^n</math> means there are <math>a</math> ways to get <math>n</math> heads, eg there are <math>10</math> ways
  3 KB (470 words) - 22:15, 27 August 2023
• 2011 AIME I Problems/Problem 3
  .../math> the <math>y</math>-axis. In the new coordinate system, point <math>A</math> is on the positive <math>x</math>-axis, and point <math>B</math> is ...>L</math> has slope <math>\frac{5}{12}</math> and contains the point <math>A=(24,-1)</math>, we may write the point-slope equation for <math>L</math> as
  4 KB (699 words) - 16:01, 13 April 2024
• 2003 AMC 10B Problems
  <math>\textbf{(A)} -1 \qquad\textbf{(B)} -\frac{2}{3} \qquad\textbf{(C)} \frac{2}{3} \qquad\ ...<math> \ </math><math>1</math> more than a pink pill, and Al's pills cost a total of <math> \ </math><math>546</math> for the two weeks. How much does
  15 KB (2,166 words) - 21:17, 16 February 2021
• 2003 AMC 10B Problems/Problem 25
  <math>\textbf{(A) } 27 \qquad\textbf{(B) } 30 \qquad\textbf{(C) } 33 \qquad\textbf{(D) } 81 ...three). However certain numbers can be added to make the sum of the digits a multiple of three.
  6 KB (882 words) - 11:45, 12 November 2023
• 1996 AJHSME Problems/Problem 14
  <math>\text{(A)}\ 27 \qquad \text{(B)}\ 29 \qquad \text{(C)}\ 31 \qquad \text{(D)}\ 33 \qq ...e the three numbers on the right to <math>123</math>, the first number has a maximum value of <math>6</math>. This is the maximum for the intersection
  2 KB (254 words) - 00:24, 5 July 2013
• 1997 AHSME Problems
  If <math>\texttt{a}</math> and <math>\texttt{b}</math> are digits for which <math> \begin{array}{ccc}& 2 & a\\ \times & b & 3\\ \hline & 6 & 9\\ 9 & 2\\ \hline 9 & 8 & 9\end{array} </m
  17 KB (2,590 words) - 13:38, 19 February 2020
• 1997 AHSME Problems/Problem 14
  ...h>, and <math>1997</math> were <math>39</math>, <math>60</math>, and <math>123</math>, respectively, then the population in <math>1996</math> was <math> \textbf{(A)}\ 81\qquad\textbf{(B)}\ 84\qquad\textbf{(C)}\ 87\qquad\textbf{(D)}\ 90\qqu
  1 KB (217 words) - 14:13, 5 July 2013
• 2003 AMC 10B Problems/Problem 24
  ...d\textbf{(C)}\ 0\qquad\textbf{(D)}\ \frac{27}{20}\qquad\textbf{(E)}\ \frac{123}{40} </math> ...{x}{y}-2y=\frac{9\cdot 5}{8\cdot 3}+\frac{6}{5}=\boxed{\textbf{(E)}\ \frac{123}{40}}</cmath>
  4 KB (779 words) - 16:16, 12 March 2024
• Primitive Pythagorean Triple
  27 120 123 [9 - 40 - 41] 123 164 205 [3 - 4 - 5]
  55 KB (3,565 words) - 11:05, 21 May 2020
• 1964 AHSME Problems/Problem 3
  When a positive integer <math>x</math> is divided by a positive integer <math>y</math>, the quotient is <math>u</math> and the rem <math>\textbf{(A)}\ 0 \qquad
  2 KB (296 words) - 06:04, 31 December 2023
• 1991 AHSME Problems/Problem 26
  .../math>, for <math>k = 1,2,...,n</math>. For example, <math>321</math> is a cute <math>3</math>-digit integer because <math>1</math> divides <math>3</m <math>\text{(A) } 0\quad
  4 KB (604 words) - 03:40, 24 February 2018
• 1974 AHSME Problems
  <math> \mathrm{(A)\ } 4x+3y=xy \qquad \mathrm{(B) \ }y=\frac{4x}{6-y} \qquad \mathrm{(C) \ } <math> \mathrm{(A)\ } -\frac{h}{3} \qquad \mathrm{(B) \ }\frac{h}{3} \qquad \mathrm{(C) \ }
  15 KB (2,151 words) - 14:04, 19 February 2020
• 1974 AHSME Problems/Problem 26
  <math> \mathrm{(A)\ } 100 \qquad \mathrm{(B) \ }125 \qquad \mathrm{(C) \ } 123 \qquad \mathrm{(D) \ } 30 \qquad \mathrm{(E) \ }\text{none of these} </m ...th> 1 </math> and <math> 30^4 </math>, so our final answer is <math> 125-2=123, \boxed{\text{C}} </math>}$
  895 bytes (116 words) - 02:27, 4 May 2024
• 1974 AHSME Answer Key
  #A #A
  2 KB (233 words) - 06:08, 20 January 2023
• 1980 USAMO Problems/Problem 2
  Find the maximum possible number of three term arithmetic progressions in a monotone sequence of <math>n</math> distinct reals. If <math>n = 3</math>, there will be one ascending triplet (123). Let's only consider the ascending order for now.
  2 KB (405 words) - 19:04, 9 August 2023

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