User contributions
- 09:32, 2 January 2022 (diff | hist) . . (+1,755) . . 2020 CIME II Problems/Problem 9 (→Solution) (current)
- 09:37, 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)
- 00:07, 30 December 2021 (diff | hist) . . (+1,292) . . 2020 CIME I Problems/Problem 6 (→Solution)
- 16:49, 6 June 2018 (diff | hist) . . (+1,157) . . 1985 AIME Problems/Problem 11 (→Solution)
- 07:40, 23 March 2015 (diff | hist) . . (+2,221) . . 2015 AIME I Problems/Problem 10 (→Solution 3: and solution 4)
- 01:58, 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...")
- 01:53, 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...")
- 01:48, 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")
- 01:39, 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...")
- 01:35, 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>...")
- 01:33, 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...")
- 01:29, 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...")
- 01:26, 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...")
- 01:24, 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^...")
- 01:20, 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....")
- 01:17, 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...")
- 01:11, 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 ...")
- 01:05, 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")
- 01:03, 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...")
- 01:00, 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) <...")
- 00:57, 17 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...")
- 00:55, 17 March 2013 (diff | hist) . . (0) . . 1991 AHSME
- 00:54, 17 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>")
- 00:52, 17 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>")
- 00:49, 17 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>-...")
- 06:14, 1 April 2012 (diff | hist) . . (-1,306) . . 2012 AIME I Problems/Problem 13 (→Solution)
- 06:12, 1 April 2012 (diff | hist) . . (+4,437) . . 2012 AIME I Problems/Problem 13 (→Solution)
- 15:42, 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...")
- 01:37, 1 March 2012 (diff | hist) . . (+1,689) . . 2012 AMC 12B Problems/Problem 17 (→Solution)
- 00:48, 1 March 2012 (diff | hist) . . (+1,091) . . 2012 AMC 12B Problems/Problem 12
- 00:20, 1 March 2012 (diff | hist) . . (+589) . . 2012 AMC 12B Problems/Problem 13 (→Solution)
- 22:28, 29 February 2012 (diff | hist) . . (+196) . . 1989 AHSME Problems/Problem 14
- 22:17, 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...")
- 22:04, 29 February 2012 (diff | hist) . . (+300) . . 1989 AHSME Problems/Problem 6
- 10:56, 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...")
- 10:24, 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 ...")
- 10:20, 19 February 2012 (diff | hist) . . (-126) . . 1989 AHSME Problems/Problem 2
- 09:54, 19 February 2012 (diff | hist) . . (+8) . . 1989 AHSME Problems/Problem 1
- 06:53, 19 February 2012 (diff | hist) . . (+397) . . 1989 AHSME Problems (→Problem 30)
- 06:49, 19 February 2012 (diff | hist) . . (0) . . 1989 AHSME Problems (→Problem 27)
- 06:48, 19 February 2012 (diff | hist) . . (+274) . . 1989 AHSME Problems (→Problem 27)
- 06:45, 19 February 2012 (diff | hist) . . (+332) . . 1989 AHSME Problems (→Problem 25)
- 06:43, 19 February 2012 (diff | hist) . . (+386) . . 1989 AHSME Problems (→Problem 22)
- 06:39, 19 February 2012 (diff | hist) . . (+215) . . 1989 AHSME Problems (→Problem 29)
- 06:35, 19 February 2012 (diff | hist) . . (+289) . . 1989 AHSME Problems (→Problem 28)
- 06:34, 19 February 2012 (diff | hist) . . (+355) . . 1989 AHSME Problems (→Problem 26)
- 06:33, 19 February 2012 (diff | hist) . . (+406) . . 1989 AHSME Problems (→Problem 24)
- 06:28, 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...")
- 06:24, 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 ...")
- 06:08, 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...")
- 06:03, 19 February 2012 (diff | hist) . . (+304) . . N 1989 AHSME Problems/Problem 6 (Created page with "If <math>a,b>0</math> and the triangle in the first quadrant bounded by the co-ordinate axes and the graph of <math>ax+by=6</math> has area 6, then <math>ab=</math> <math> \math...")
- 05:59, 19 February 2012 (diff | hist) . . (+352) . . N 1989 AHSME Problems/Problem 26 (Created page with "A regular octahedron is formed by joining the centers of adjoining faces of a cube. The ratio of the volume of the octahedron to the volume of the cube is <math> \mathrm{(A) \fr...")
- 05:52, 19 February 2012 (diff | hist) . . (+370) . . N 1989 AHSME Problems/Problem 13 (Created page with "Let <math>a</math>, <math>b</math>, <math>c</math>, and <math>d</math> be integers with <math>a<2b</math>, <math>b<3c</math>, and <math>c<4d</math>. If <math>d<100</math>, the la...")
- 05:47, 19 February 2012 (diff | hist) . . (+377) . . N 1989 AHSME Problems/Problem 19 (Created page with "A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of lengths 3, 4, and 5. What is the area of the triangle? <math> \mathrm{(A) ...")
- 05:44, 19 February 2012 (diff | hist) . . (+353) . . N 1989 AHSME Problems/Problem 18 (Created page with "The set of all real numbers for which <cmath>x+\sqrt{x^2+1}-\frac{1}{x+\sqrt{x^2+1}}</cmath> is a rational number is the set of all (A) integers <math>x</math> (B) rational <m...")
- 05:22, 19 February 2012 (diff | hist) . . (+182) . . N 1989 AHSME Problems/Problem 14 (Created page with "<math>\cot 10+\tan 5=</math> <math> \mathrm{(A) \csc 5 } \qquad \mathrm{(B) \csc 10 } \qquad \mathrm{(C) \sec 5 } \qquad \mathrm{(D) \sec 10 } \qquad \mathrm{(E) \sin 15 } </m...")
- 05:17, 19 February 2012 (diff | hist) . . (+287) . . N 1989 AHSME Problems/Problem 28 (Created page with "Find the sum of the roots of <math>\tan^2x-9\tan x+1=0</math> that are between <math>x=0</math> and <math>x=2\pi</math> radians. <math> \mathrm{(A) \frac{\pi}{2} } \qquad \math...")
- 05:04, 19 February 2012 (diff | hist) . . (+238) . . N 1989 AHSME Problems/Problem 2 (Created page with "<math>\sqrt{\frac{1}{9}+\frac{1}{16}}=</math> (A) <math>\frac{1}{5}</math>\hskip.5in (B)<math>\frac{1}{4}</math>\hskip.5in (C)<math>\frac{2}{7}</math>\hskip.5in (D)<math>\...")
- 23:48, 18 February 2012 (diff | hist) . . (+155) . . N 1988 AHSME Problems/Problem 15 (Created page with "Suppose that <math>a</math> and <math>b</math> are integers such that <math>x^2-x-1</math> is a factor of <math>ax^3+bx^2+1</math>. What is <math>b</math>?")
- 23:34, 18 February 2012 (diff | hist) . . (+74) . . N 1993 AHSME Problems/Problem 28 (Created page with "How many triangles can be formed with vertices on a 4 by 4 grid of points?")
- 23:28, 18 February 2012 (diff | hist) . . (+217) . . N 1992 AHSME Problems/Problem 23 (Created page with "Let <math>S</math> be a subset of <math>\{1,2,3,...,50\}</math> such that no pair of distinct elements in <math>S</math> has a sum divisible by <math>7</math>. What is the maximu...")
- 23:25, 18 February 2012 (diff | hist) . . (+229) . . N 1992 AHSME Problems/Problem 17 (Created page with "The 2-digit integers from 19 to 92 are written consecutively to form the integer <math>N=192021\cdots9192</math>. Suppose that <math>3^k</math> is the highest power of 3 that is ...")
- 23:22, 18 February 2012 (diff | hist) . . (+218) . . N 1991 AHSME Problems/Problem 15 (Created page with "A circular table has 60 chairs around it. There are <math>N</math> people seated at this table in such a way that the next person seated must sit next to someone. What is the sma...")
- 23:14, 18 February 2012 (diff | hist) . . (+240) . . N 1991 AHSME Problems/Problem 21 (Created page with "For all real numbers <math>x</math> except <math>x=0</math> and <math>x=1</math> the function <math>f(x)</math> is defined by <math>f(x/(1-x))=1/x</math>. Suppose <math>0\leq t\l...")
- 22:58, 18 February 2012 (diff | hist) . . (+227) . . N 1990 AHSME Problems/Problem 30 (Created page with "Let <math>R_n=\frac{1}{2}(a^n+b^n)</math> for each non-negative integer <math>n</math> where <math>a=3+2\sqrt{2}</math> and <math>b=3-2\sqrt{2}</math>. The value of <math>R_{1234...")
- 22:53, 18 February 2012 (diff | hist) . . (+515) . . N 1991 AHSME Problems/Problem 26 (Created page with "An <math>n</math>-digit positive integer is cute if its <math>n</math> digits are an arrangement of the set <math>\{1,2,...,n\}</math> and its first <math>k</math> digits form a...")
- 22:46, 18 February 2012 (diff | hist) . . (+388) . . N 1992 AHSME Problems/Problem 21 (Created page with "For a finite sequence <math>A=(a_1,a_2,...,a_n)</math> of numbers, the ''Cesáro sum'' of A is defined to be <math>\frac{S_1+\cdots+S_n}{n}</math> , where <math>S_k=a_1+\cdots+...")
- 22:35, 18 February 2012 (diff | hist) . . (+88) . . N 1990 AHSME Problems/Problem 11 (Created page with "How many positive integers less than 50 have an odd number of positive integer divisors?")
- 22:32, 18 February 2012 (diff | hist) . . (+446) . . N 1991 AHSME Problems/Problem 17 (Created page with "A positive integer <math>N</math> is a ''palindrome'' if the integer obtained by reversing the sequence of digits of <math>N</math> is equal to <math>N</math>. The year 1991 is t...")
- 06:03, 13 February 2012 (diff | hist) . . (+1,168) . . 2012 AMC 12A Problems/Problem 18 (→Solution)
- 05:17, 13 February 2012 (diff | hist) . . (+726) . . 2012 AMC 12A Problems/Problem 16 (→Solution)
- 05:32, 20 February 2011 (diff | hist) . . (+1,470) . . 2011 AMC 12A Problems/Problem 24 (→Solution 1)
- 05:00, 20 February 2011 (diff | hist) . . (+1,397) . . 2011 AMC 12A Problems/Problem 23 (→Solution)