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• 08:32, 2 January 2022 (diff | hist) . . (+1,755)‎ . . 2020 CIME II Problems/Problem 9 ‎ (→‎Solution)
• 08:37, 30 December 2021 (diff | hist) . . (+1,909)‎ . . N 2020 CIME II Problems/Problem 10 ‎ (Created page with "First suppose that <math>c=1</math>. Then <math>a+b+1=ab\Rightarrow (a-1)(b-1)=2</math> from whence we have <math>(a,b,c)\in\{(2,3,1),(3,2,1)\}</math>. Now suppose that <math...") (current)
• 23:07, 29 December 2021 (diff | hist) . . (+1,292)‎ . . 2020 CIME I Problems/Problem 6 ‎ (→‎Solution)
• 15:49, 6 June 2018 (diff | hist) . . (+1,157)‎ . . 1985 AIME Problems/Problem 11 ‎ (→‎Solution)
• 06:40, 23 March 2015 (diff | hist) . . (+2,221)‎ . . 2015 AIME I Problems/Problem 10 ‎ (→‎Solution 3: and solution 4)
• 00:58, 17 March 2013 (diff | hist) . . (+367)‎ . . N 1991 AHSME Problems/Problem 11 ‎ (Created page with "Jack and Jill run 10 km. They start at the same point, run 5 km up a hill, and reurn to the starting point by the same route. Jack has a 10 minute head start and runs at the rate...")
• 00:53, 17 March 2013 (diff | hist) . . (+592)‎ . . N 1991 AHSME Problems/Problem 8 ‎ (Created page with "Liquid <math>X</math> does not mix with water. Unless obstructed, it spreads out on the surface of water to form a circular film <math>0.1</math>cm thick. A rectangular box measu...")
• 00:48, 17 March 2013 (diff | hist) . . (+140)‎ . . N 1991 AHSME Problems ‎ (Created page with "Link to full test below. http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1991&sid=23c56fcb006bee49b72650509fbedb9b")
• 00:39, 17 March 2013 (diff | hist) . . (+292)‎ . . N 1991 AHSME Problems/Problem 12 ‎ (Created page with "The measures (in degrees) of the interior angles of a convex hexagon form an arithmetic sequence of integers. Let <math>m</math> be the measure of the largest interior angle of t...")
• 00:35, 17 March 2013 (diff | hist) . . (+259)‎ . . N 1991 AHSME Problems/Problem 7 ‎ (Created page with "\If <math>x=\frac{a}{b}</math>, <math>a\neq b</math> and <math>b\neq 0</math>, then <math>\frac{a+b}{a-b}=</math> (A) <math>\frac{x}{x+1}</math> (B) <math>\frac{x+1}{x-1}</math>...")
• 00:33, 17 March 2013 (diff | hist) . . (+393)‎ . . N 1991 AHSME Problems/Problem 24 ‎ (Created page with "The graph, <math>G</math> of <math>y=\log_{10}x</math> is rotated <math>90^{\circ}</math> counter-clockwise about the origin to obtain a new graph <math>G'</math>. Which of the f...")
• 00:29, 17 March 2013 (diff | hist) . . (+449)‎ . . N 1991 AHSME Problems/Problem 16 ‎ (Created page with "One hundred students at Century High School participated in the AHSME last year, and their mean score was 100. The number of non-seniors taking the AHSME was <math>50\%</math> mo...")
• 00:26, 17 March 2013 (diff | hist) . . (+199)‎ . . N 1991 AHSME Problems/Problem 4 ‎ (Created page with "Which of the following triangles cannot exist? (A) An acute isosceles triangle (B) An isosceles right triangle (C) An obtuse right triangle (D) A scalene right triangle (E) A sc...")
• 00:24, 17 March 2013 (diff | hist) . . (+218)‎ . . N 1991 AHSME Problems/Problem 6 ‎ (Created page with "If <math>x\geq 0</math>, then <math>\sqrt{x\sqrt{x\sqrt{x}}}=</math> (A) <math>x\sqrt{x}</math> (B) <math>x \sqrt[4]{x}</math> (C) <math>\sqrt[8]{x}</math> (D) <math>\sqrt[8]{x^...")
• 00:20, 17 March 2013 (diff | hist) . . (+232)‎ . . N 1991 AHSME Problems/Problem 27 ‎ (Created page with "If <math>x+\sqrt{x^2-1}+\frac{1}{x-\sqrt{x^2-1}}=20</math> then <math>x^2+\sqrt{x^4-1}+\frac{1}{x^2+\sqrt{x^4-1}}=</math> (A) <math>5.05</math> (B) <math>20</math> (C) <math>51....")
• 00:17, 17 March 2013 (diff | hist) . . (+500)‎ . . N 1991 AHSME Problems/Problem 29 ‎ (Created page with "Equilateral triangle <math>ABC</math> has <math>P</math> on <math>AB</math> and <math>Q</math> on <math>AC</math>. The triangle is folded along <math>PQ</math> so that vertex <ma...")
• 00:11, 17 March 2013 (diff | hist) . . (+484)‎ . . N 1991 AHSME Problems/Problem 30 ‎ (Created page with "For any set <math>S</math>, let <math>|S|</math> denote the number of elements in <math>S</math>, and let <math>n(S)</math> be the number of subsets of <math>S</math>, including ...")
• 00:05, 17 March 2013 (diff | hist) . . (+135)‎ . . N 1991 AHSME Problems/Problem 20 ‎ (Created page with "The sum of all real <math>x</math> such that <math>(2^x-4)^3+(4^x-2)^3=(4^x+2^x-6)^3</math> is (A) 3/2 (B) 2 (C) 5/2 (D) 3 (E) 7/2")
• 00:03, 17 March 2013 (diff | hist) . . (+217)‎ . . N 1991 AHSME Problems/Problem 18 ‎ (Created page with "If <math>S</math> is the set of points <math>z</math> in the complex plane such that <math>(3+4i)z</math> is a real number, then <math>S</math> is a (A) right triangle (B) cir...")
• 00:00, 17 March 2013 (diff | hist) . . (+281)‎ . . N 1991 AHSME Problems/Problem 14 ‎ (Created page with "If <math>x</math> is the cube of a positive integer and <math>d</math> is the number of positive integers that are divisors of <math>x</math>, then <math>d</math> could be (A) <...")
• 23:57, 16 March 2013 (diff | hist) . . (+228)‎ . . N 1991 AHSME Problems/Problem 10 ‎ (Created page with "Point <math>P</math> is <math>9</math> units from the center of a circle of radius <math>15</math>. How many different chords of the circle contain <math>P</math> and have intege...")
• 23:55, 16 March 2013 (diff | hist) . . (0)‎ . . 1991 AHSME ‎
• 23:54, 16 March 2013 (diff | hist) . . (+149)‎ . . N 1991 AHSME Problems/Problem 3 ‎ (Created page with "<math>(4^{-1}-3^{-1})^{-1}=</math> (A) <math>-12</math> (B) <math>-1</math> (C) <math>\frac{1}{12}</math> (D) <math>1</math> (E) <math>12</math>")
• 23:52, 16 March 2013 (diff | hist) . . (+146)‎ . . N 1991 AHSME Problems/Problem 2 ‎ (Created page with "<math>|3-\pi|=</math> (A) <math>\frac{1}{7}</math> (B) <math>0.14</math> (C) <math>3-\pi</math> (D) <math>3+\pi</math> (E) <math>\pi-3</math>")
• 23:49, 16 March 2013 (diff | hist) . . (+298)‎ . . N 1991 AHSME Problems/Problem 1 ‎ (Created page with "If for any three distinct numbers <math>a</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 (A) <math>-...")
• 05:14, 1 April 2012 (diff | hist) . . (-1,306)‎ . . 2012 AIME I Problems/Problem 13 ‎ (→‎Solution)
• 05:12, 1 April 2012 (diff | hist) . . (+4,437)‎ . . 2012 AIME I Problems/Problem 13 ‎ (→‎Solution)
• 14:42, 2 March 2012 (diff | hist) . . (+3,841)‎ . . N 2012 AMC 12B Problems/Problem 23 ‎ (Created page with "==Solution 1== Since <math>z_0</math> is a root of <math>P</math>, and <math>P</math> has integer coefficients, <math>z_0</math> must be algebraic. Since <math>z_0</math> is alg...")
• 00:37, 1 March 2012 (diff | hist) . . (+1,689)‎ . . 2012 AMC 12B Problems/Problem 17 ‎ (→‎Solution)
• 23:48, 29 February 2012 (diff | hist) . . (+1,091)‎ . . 2012 AMC 12B Problems/Problem 12 ‎
• 23:20, 29 February 2012 (diff | hist) . . (+589)‎ . . 2012 AMC 12B Problems/Problem 13 ‎ (→‎Solution)
• 21:28, 29 February 2012 (diff | hist) . . (+196)‎ . . 1989 AHSME Problems/Problem 14 ‎
• 21:17, 29 February 2012 (diff | hist) . . (+723)‎ . . N 1989 AHSME Problems/Problem 16 ‎ (Created page with "Since the endpoints are (3,17) and (48,281), the line that passes through these 2 points has slope <math>m=\frac{281-17}{48-3}=\frac{264}{45}=\frac{88}{15}</math>. The equation o...")
• 21:04, 29 February 2012 (diff | hist) . . (+300)‎ . . 1989 AHSME Problems/Problem 6 ‎
• 09:56, 19 February 2012 (diff | hist) . . (+566)‎ . . N 1991 AHSME Problems/Problem 28 ‎ (Created page with "Initially an urn contains 100 white and 100 black marbles. Repeatedly 3 marbles are removed (at random) from the urn and replaced with some marbles from a pile outside the urn as...")
• 09:24, 19 February 2012 (diff | hist) . . (+216)‎ . . N 1989 AHSME Problems/Problem 3 ‎ (Created page with "Let <math>x</math> be the width of a rectangle so that the side of the square is <math>3x</math>. Since <math>2(3x)+2(x)=24</math> we have <math>x=3</math>. Thus the area of the ...")
• 09:20, 19 February 2012 (diff | hist) . . (-126)‎ . . 1989 AHSME Problems/Problem 2 ‎
• 08:54, 19 February 2012 (diff | hist) . . (+8)‎ . . 1989 AHSME Problems/Problem 1 ‎
• 05:53, 19 February 2012 (diff | hist) . . (+397)‎ . . 1989 AHSME Problems ‎ (→‎Problem 30)
• 05:49, 19 February 2012 (diff | hist) . . (0)‎ . . 1989 AHSME Problems ‎ (→‎Problem 27)
• 05:48, 19 February 2012 (diff | hist) . . (+274)‎ . . 1989 AHSME Problems ‎ (→‎Problem 27)
• 05:45, 19 February 2012 (diff | hist) . . (+332)‎ . . 1989 AHSME Problems ‎ (→‎Problem 25)
• 05:43, 19 February 2012 (diff | hist) . . (+386)‎ . . 1989 AHSME Problems ‎ (→‎Problem 22)
• 05:39, 19 February 2012 (diff | hist) . . (+215)‎ . . 1989 AHSME Problems ‎ (→‎Problem 29)
• 05:35, 19 February 2012 (diff | hist) . . (+289)‎ . . 1989 AHSME Problems ‎ (→‎Problem 28)
• 05:34, 19 February 2012 (diff | hist) . . (+355)‎ . . 1989 AHSME Problems ‎ (→‎Problem 26)
• 05:33, 19 February 2012 (diff | hist) . . (+406)‎ . . 1989 AHSME Problems ‎ (→‎Problem 24)
• 05:28, 19 February 2012 (diff | hist) . . (+403)‎ . . N 1989 AHSME Problems/Problem 24 ‎ (Created page with "Five people are sitting at a round table. Let <math>f\geq 0</math> be the number of people sitting next to at least 1 female and <math>m\geq0</math> be the number of people sitti...")
• 05:24, 19 February 2012 (diff | hist) . . (+289)‎ . . N 1989 AHSME Problems/Problem 8 ‎ (Created page with "For how many integers <math>n</math> between 1 and 100 does <math>x^2+x-n</math> factor into the product of two linear factors with integer coefficients? <math> \mathrm{(A) \ 0 ...")
• 05:08, 19 February 2012 (diff | hist) . . (+365)‎ . . N 1989 AHSME Problems/Problem 10 ‎ (Created page with "Consider the sequence defined recursively by <math>u_1=a</math> (any positive number), and <math>u_{n+1}=-1/(u_n+1)</math>, <math>n=1,2,3,...</math> For which of the following va...")

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