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- 01:42, 23 September 2014 (diff | hist) . . (+719) . . N 1967 AHSME Problems/Problem 28 (Created page with "== Problem == Given the two hypotheses: <math>\text{I}</math> Some Mems are not Ens and <math>\text{II}</math> No Ens are Veens. If "some" means "at least one", we can conclude ...")
- 01:40, 23 September 2014 (diff | hist) . . (+587) . . N 1967 AHSME Problems/Problem 27 (Created page with "== Problem == Two candles of the same length are made of different materials so that one burns out completely at a uniform rate in <math>3</math> hours and the other in <math>4</...")
- 01:37, 23 September 2014 (diff | hist) . . (+789) . . N 1967 AHSME Problems/Problem 26 (Created page with "== Problem == If one uses only the tabular information <math>10^3=1000</math>, <math>10^4=10,000</math>, <math>2^{10}=1024</math>, <math>2^{11}=2048</math>, <math>2^{12}=4096</ma...")
- 01:35, 23 September 2014 (diff | hist) . . (+617) . . N 1967 AHSME Problems/Problem 25 (Created page with "== Problem == For every odd number <math>p>1</math> we have: <math>\textbf{(A)}\ (p-1)^{\frac{1}{2}(p-1)}-1 \; \text{is divisible by} \; p-2\qquad \textbf{(B)}\ (p-1)^{\frac{1}{...")
- 01:34, 23 September 2014 (diff | hist) . . (+409) . . N 1967 AHSME Problems/Problem 24 (Created page with "== Problem == The number of solution-pairs in the positive integers of the equation <math>3x+5y=501</math> is: <math>\textbf{(A)}\ 33\qquad \textbf{(B)}\ 34\qquad \textbf{(C)}\ ...")
- 01:32, 23 September 2014 (diff | hist) . . (+438) . . N 1967 AHSME Problems/Problem 23 (Created page with "== Problem == If <math>x</math> is real and positive and grows beyond all bounds, then <math>\log_3{(6x-5)}-\log_3{(2x+1)}</math> approaches: <math>\textbf{(A)}\ 0\qquad \textbf...")
- 01:30, 23 September 2014 (diff | hist) . . (+643) . . N 1967 AHSME Problems/Problem 22 (Created page with "== Problem == For natural numbers, when <math>P</math> is divided by <math>D</math>, the quotient is <math>Q</math> and the remainder is <math>R</math>. When <math>Q</math> is d...")
- 01:28, 23 September 2014 (diff | hist) . . (+854) . . N 1967 AHSME Problems/Problem 21 (Created page with "== Problem == In right triangle <math>ABC</math> the hypotenuse <math>\overline{AB}=5</math> and leg <math>\overline{AC}=3</math>. The bisector of angle <math>A</math> meets the...")
- 01:26, 23 September 2014 (diff | hist) . . (+705) . . N 1967 AHSME Problems/Problem 20 (Created page with "== Problem == A circle is inscribed in a square of side <math>m</math>, then a square is inscribed in that circle, then a circle is inscribed in the latter square, and so on. I...")
- 01:24, 23 September 2014 (diff | hist) . . (+592) . . N 1967 AHSME Problems/Problem 19 (Created page with "== Problem == The area of a rectangle remains unchanged when it is made <math>2 \frac{1}{2}</math> inches longer and <math>\frac{2}{3}</math> inch narrower, or when it is made <m...")
- 01:23, 23 September 2014 (diff | hist) . . (+397) . . N 1967 AHSME Problems/Problem 18 (Created page with "== Problem == If <math>x^2-5x+6<0</math> and <math>P=x^2+5x+6</math> then <math>\textbf{(A)}\ P \; \text{can take any real value} \qquad \textbf{(B)}\ 20<P<30\\ \textbf{(C)}\ 0<...")
- 01:22, 23 September 2014 (diff | hist) . . (+553) . . N 1967 AHSME Problems/Problem 16 (Created page with "== Problem == Let the product <math>(12)(15)(16)</math>, each factor written in base <math>b</math>, equals <math>3146</math> in base <math>b</math>. Let <math>s=12+15+16</math>...")
- 01:21, 23 September 2014 (diff | hist) . . (+533) . . N 1967 AHSME Problems/Problem 17 (Created page with "== Problem == If <math>r_1</math> and <math>r_2</math> are the distinct real roots of <math>x^2+px+8=0</math>, then it must follow that: <math>\textbf{(A)}\ |r_1+r_2|>4\sqrt{2}\...")
- 01:19, 23 September 2014 (diff | hist) . . (+638) . . N 1967 AHSME Problems/Problem 15 (Created page with "== Problem == The difference in the areas of two similar triangles is <math>18</math> square feet, and the ratio of the larger area to the smaller is the square of an integer. T...")
- 01:18, 23 September 2014 (diff | hist) . . (+385) . . N 1967 AHSME Problems/Problem 14 (Created page with "== Problem == The number of distinct points common to the curves <math>x^2+4y^2=1</math> and <math>4x^2+y^2=4</math> is: <math>\text{(A) } 0 \quad \text{(B) } 1 \quad \text{(C) ...")
- 01:16, 23 September 2014 (diff | hist) . . (+654) . . N 1967 AHSME Problems/Problem 13 (Created page with "== Problem == A triangle <math>ABC</math> is to be constructed given a side <math>a</math> (opposite angle <math>A</math>). angle <math>B</math>, and <math>h_c</math>, the altitu...")
- 01:15, 23 September 2014 (diff | hist) . . (+508) . . N 1967 AHSME Problems/Problem 12 (Created page with "== Problem == If the (convex) area bounded by the x-axis and the lines <math>y=mx+4</math>, <math>x=1</math>, and <math>x=4</math> is <math>7</math>, then <math>m</math> equals: ...")
- 01:13, 23 September 2014 (diff | hist) . . (+472) . . N 1967 AHSME Problems/Problem 11 (Created page with "== Problem == If the perimeter of rectangle <math>ABCD</math> is <math>20</math> inches, the least value of diagonal <math>\overline{AC}</math>, in inches, is: <math>\textbf{(A)...")
- 01:12, 23 September 2014 (diff | hist) . . (+514) . . N 1967 AHSME Problems/Problem 10 (Created page with "== Problem == If <math>\frac{a}{10^x-1}+\frac{b}{10^x+2}=\frac{2 \cdot 10^x+3}{(10^x-1)(10^x+2)}</math> is an identity for positive rational values of <math>x</math>, then the va...")
- 01:10, 23 September 2014 (diff | hist) . . (+789) . . N 1967 AHSME Problems/Problem 9 (Created page with "== Problem == Let <math>K</math>, in square units, be the area of a trapezoid such that the shorter base, the altitude, and the longer base, in that order, are in arithmetic prog...")
- 01:08, 23 September 2014 (diff | hist) . . (+584) . . N 1967 AHSME Problems/Problem 8 (Created page with "== Problem == To <math>m</math> ounces of a <math>m\%</math> solution of acid, <math>x</math> ounces of water are added to yield a <math>(m-10)\%</math> solution. If <math>m>25<...")
- 01:06, 23 September 2014 (diff | hist) . . (+352) . . N 1967 AHSME Problems/Problem 6 (Created page with "== Problem == If <math>f(x)=4^x</math> then <math>f(x+1)-f(x)</math> equals: <math> \text{(A)}\ 4\qquad\text{(B)}\ f(x)\qquad\text{(C)}\ 2f(x)\qquad\text{(D)}\ 3f(x)\qquad\text{...")
- 01:04, 23 September 2014 (diff | hist) . . (+635) . . N 1967 AHSME Problems/Problem 7 (Created page with "== Problem == If <math>\frac{a}{b}<-\frac{c}{d}</math> where <math>a</math>, <math>b</math>, <math>c</math>, and <math>d</math> are real numbers and <math>bd \not= 0</math>, then...")
- 01:03, 23 September 2014 (diff | hist) . . (0) . . m 1967 AHSME Problems/Problem 4 (→See also)
- 01:03, 23 September 2014 (diff | hist) . . (+581) . . N 1967 AHSME Problems/Problem 5 (Created page with "== Problem == A triangle is circumscribed about a circle of radius <math>r</math> inches. If the perimeter of the triangle is <math>P</math> inches and the area is <math>K</math...")
- 01:00, 23 September 2014 (diff | hist) . . (+518) . . N 1967 AHSME Problems/Problem 4 (Created page with "== Problem == Given <math>\frac{\log{a}}{p}=\frac{\log{b}}{q}=\frac{\log{c}}{r}=\log{x}</math>, all logarithms to the same base and <math>x \not= 1</math>. If <math>\frac{b^2}{a...")
- 00:58, 23 September 2014 (diff | hist) . . (+515) . . N 1967 AHSME Problems/Problem 3 (Created page with "== Problem == The side of an equilateral triangle is <math>s</math>. A circle is inscribed in the triangle and a square is inscribed in the circle. The area of the square is: ...")
- 02:47, 15 September 2014 (diff | hist) . . (+7,655) . . 1966 AHSME Problems
- 02:41, 15 September 2014 (diff | hist) . . (+155) . . 1966 AHSME Problems/Problem 2
- 02:38, 15 September 2014 (diff | hist) . . (+611) . . 1966 AHSME Problems/Problem 6
- 02:36, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 40 (→Solution)
- 02:36, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 39 (→Solution)
- 02:35, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 38 (→Solution)
- 02:35, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 37 (→Solution)
- 02:35, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 36 (→Solution)
- 02:35, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 35 (→Solution)
- 02:34, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 34 (→Solution)
- 02:34, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 33 (→Solution)
- 02:34, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 32 (→Solution) (current)
- 02:33, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 31 (→Solution)
- 02:33, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 30 (→Solution)
- 02:33, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 29 (→Solution)
- 02:33, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 28 (→Solution) (current)
- 02:32, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 27 (→Solution)
- 02:32, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 26 (→Solution)
- 02:32, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 25 (→Solution)
- 02:32, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 24 (→Solution)
- 02:31, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 23 (→Solution)
- 02:31, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 22 (→Solution)
- 02:31, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 21 (→Solution)
- 02:30, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 20 (→Solution) (current)
- 02:30, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 19 (→Solution) (current)
- 02:30, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 18 (→Solution)
- 02:30, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 17 (→Solution)
- 02:29, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 16 (→Solution)
- 02:29, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 15 (→Solution)
- 02:29, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 14 (→Solution)
- 02:29, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 13 (→Solution) (current)
- 02:28, 15 September 2014 (diff | hist) . . (+21) . . 1966 AHSME Problems/Problem 12 (→Solution)
- 02:28, 15 September 2014 (diff | hist) . . (+22) . . 1966 AHSME Problems/Problem 11 (→Solution)
- 02:25, 15 September 2014 (diff | hist) . . (+583) . . 1966 AHSME Problems/Problem 4
- 01:40, 15 September 2014 (diff | hist) . . (+862) . . N 1966 AHSME Problems/Problem 40 (Created page with "== Problem == In this figure <math>AB</math> is a diameter of a circle, centered at <math>O</math>, with radius <math>a</math>. A chord <math>AD</math> is drawn and extended to m...")
- 01:32, 15 September 2014 (diff | hist) . . (+700) . . N 1966 AHSME Problems/Problem 39 (Created page with "== Problem == In base <math>R_1</math> the expanded fraction <math>F_1</math> becomes <math>.373737\cdots</math>, and the expanded fraction <math>F_2</math> becomes <math>.737373...")
- 01:26, 15 September 2014 (diff | hist) . . (+669) . . N 1966 AHSME Problems/Problem 38 (Created page with "== Problem == In triangle <math>ABC</math> the medians <math>AM</math> and <math>CN</math> to sides <math>BC</math> and <math>AB</math>, respectively, intersect in point <math>O<...")
- 01:22, 15 September 2014 (diff | hist) . . (+635) . . N 1966 AHSME Problems/Problem 37 (Created page with "== Problem == Three men, Alpha, Beta, and Gamma, working together, do a job in 6 hours less time than Alpha alone, in 1 hour less time than Beta alone, and in one-half the time n...")
- 01:18, 15 September 2014 (diff | hist) . . (+482) . . N 1966 AHSME Problems/Problem 36 (Created page with "== Problem == Let <math>(1+x+x^2)^n=a_1x+a_2x^2+ \cdots + a_{2n}x^{2n}</math> be an identity in <math>x</math>. If we let <math>s=a_0+a_2+a_4+\cdots +a_{2n}</math>, then <math>s<...")
- 01:13, 15 September 2014 (diff | hist) . . (+612) . . N 1966 AHSME Problems/Problem 35 (Created page with "== Problem == Let <math>O</math> be an interior point of triangle <math>ABC</math>, and let <math>s_1=OA+OB+OC</math>. If <math>s_2=AB+BC+CA</math>, then <math>\text{(A) for eve...")
- 01:00, 15 September 2014 (diff | hist) . . (+587) . . N 1966 AHSME Problems/Problem 34 (Created page with "== Problem == Let <math>r</math> be the speed in miles per hour at which a wheel, <math>11</math> feet in circumference, travels. If the time for a complete rotation of the wheel...")
- 00:57, 15 September 2014 (diff | hist) . . (+476) . . N 1966 AHSME Problems/Problem 33 (Created page with "== Problem == If <math>ab \ne 0</math> and <math>|a| \ne |b|</math>, the number of distinct values of <math>x</math> satisfying the equation <cmath>\frac{x-a}{b}+\frac{x-b}{a}=\...")
- 00:51, 15 September 2014 (diff | hist) . . (0) . . 1966 AHSME Problems/Problem 32
- 00:51, 15 September 2014 (diff | hist) . . (+961) . . N 1966 AHSME Problems/Problem 32 (Created page with "== Problem == Let <math>M</math> be the midpoint of side <math>AB</math> of triangle <math>ABC</math>. Let <math>P</math> be a point on <math>AB</math> between <math>A</math> and...")
- 00:42, 15 September 2014 (diff | hist) . . (+560) . . N 1966 AHSME Problems/Problem 31 (Created page with "== Problem == Triangle <math>ABC</math> is inscribed in a circle with center <math>O'</math>. A circle with center <math>O</math> is inscribed in triangle <math>ABC</math>. <math...")
- 00:37, 15 September 2014 (diff | hist) . . (+413) . . N 1966 AHSME Problems/Problem 30 (Created page with "== Problem == If three of the roots of <math>x^4+ax^2+bx+c=0</math> are <math>1</math>, <math>2</math>, and <math>3</math> then the value of <math>a+c</math> is: <math>\text{(A)...")
- 00:34, 15 September 2014 (diff | hist) . . (+392) . . N 1966 AHSME Problems/Problem 29 (Created page with "== Problem == The number of positive integers less than <math>1000</math> divisible by neither <math>5</math> nor <math>7</math> is: <math>\text{(A) } 688 \quad \text{(B) } 686 ...")
- 00:31, 15 September 2014 (diff | hist) . . (+531) . . N 1966 AHSME Problems/Problem 27 (Created page with "== Problem == At his usual rate a man rows 15 miles downstream in five hours less time than it takes him to return. If he doubles his usual rate, the time downstream is only one ...")
- 00:28, 15 September 2014 (diff | hist) . . (+502) . . N 1966 AHSME Problems/Problem 26 (Created page with "== Problem == Let <math>m</math> be a positive integer and let the lines <math>13x+11y=700</math> and <math>y=mx-1</math> intersect in a point whose coordinates are integers. The...")
- 00:24, 15 September 2014 (diff | hist) . . (+391) . . N 1966 AHSME Problems/Problem 25 (Created page with "== Problem == If <math>F(n+1)=\frac{2F(n)+1}{2}</math> for <math>n=1,2,\cdots</math> and <math>F(1)=2</math>, then <math>F(101)</math> equals: <math>\text{(A) } 49 \quad \text{(...")
- 00:22, 15 September 2014 (diff | hist) . . (+397) . . N 1966 AHSME Problems/Problem 24 (Created page with "== Problem == If <math>Log_M{N}=Log_N{M},M \ne N,MN>0,M \ne 1, N \ne 1</math>, then <math>MN</math> equals: <math>\text{(A) } \frac{1}{2} \quad \text{(B) } 1 \quad \text{(C) } 2...")
- 00:18, 15 September 2014 (diff | hist) . . (+497) . . N 1966 AHSME Problems/Problem 23 (Created page with "== Problem == If <math>x</math> is real and <math>4y^2+4xy+x+6=0</math>, then the complete set of values of <math>x</math> for which <math>y</math> is real, is: <math>\text{(A) ...")
- 00:12, 15 September 2014 (diff | hist) . . (+699) . . N 1966 AHSME Problems/Problem 22 (Created page with "== Problem == Consider the statements: (I)<math>\sqrt{a^2+b^2}=0</math>, (II) <math>\sqrt{a^2+b^2}=ab</math>, (III) <math>\sqrt{a^2+b^2}=a+b</math>, (IV) <math>\sqrt{a^2+b^...")
- 23:46, 14 September 2014 (diff | hist) . . (+4,619) . . 1966 AHSME Problems
- 23:35, 14 September 2014 (diff | hist) . . (+743) . . N 1966 AHSME Problems/Problem 28 (Created page with "== Problem == Five points <math>O,A,B,C,D</math> are taken in order on a straight line with distances <math>OA = a</math>, <math>OB = b</math>, <math>OC = c</math>, and <math>OD ...")
- 23:27, 14 September 2014 (diff | hist) . . (+961) . . N 1966 AHSME Problems/Problem 21 (Created page with "== Problem == An "<math>n</math>-pointed star" is formed as follows: the sides of a convex polygon are numbered consecutively <math>1,2,\cdots ,k,\cdots,n,\text{ }n\ge 5</math>; ...")
- 23:16, 14 September 2014 (diff | hist) . . (+568) . . N 1966 AHSME Problems/Problem 20 (Created page with "== Problem == The negation of the proposition "For all pairs of real numbers <math>a,b</math>, if <math>a=0</math>, then <math>ab=0</math>" is: There are real numbers <math>a,b</...")
- 23:05, 14 September 2014 (diff | hist) . . (+638) . . N 1966 AHSME Problems/Problem 19 (Created page with "== Problem == Let <math>s_1</math> be the sum of the first <math>n</math> terms of the arithmetic sequence <math>8,12,\cdots</math> and let <math>s_2</math> be the sum of the fir...")
- 22:57, 14 September 2014 (diff | hist) . . (+471) . . N 1966 AHSME Problems/Problem 18 (Created page with "== Problem == In a given arithmetic sequence the first term is <math>2</math>, the last term is <math>29</math>, and the sum of all the terms is <math>155</math>. The common diff...")
- 22:53, 14 September 2014 (diff | hist) . . (+364) . . N 1966 AHSME Problems/Problem 17 (Created page with "== Problem == The number of distinct points common to the curves <math>x^2+4y^2=1</math> and <math>4x^2+y^2=4</math> is: <math>\text{(A) } 0 \quad \text{(B) } 1 \quad \text{(C) ...")
- 22:45, 14 September 2014 (diff | hist) . . (+429) . . N 1966 AHSME Problems/Problem 16 (Created page with "== Problem == If <math>\frac{4^x}{2^{x+y}}=8</math> and <math>\frac{9^{x+y}}{3^{5y}}=243</math>, <math>x</math> and <math>y</math> real numbers, then <math>xy</math> equals: <ma...")
- 22:39, 14 September 2014 (diff | hist) . . (+29) . . 1966 AHSME Problems/Problem 15
- 22:39, 14 September 2014 (diff | hist) . . (+30) . . 1966 AHSME Problems/Problem 14
- 22:39, 14 September 2014 (diff | hist) . . (+30) . . 1966 AHSME Problems/Problem 13
- 22:38, 14 September 2014 (diff | hist) . . (+30) . . 1966 AHSME Problems/Problem 11
- 22:37, 14 September 2014 (diff | hist) . . (+29) . . 1966 AHSME Problems/Problem 12
- 22:35, 14 September 2014 (diff | hist) . . (-1) . . 1966 AHSME Problems/Problem 12 (→Problem)
- 22:29, 14 September 2014 (diff | hist) . . (+299) . . N 1966 AHSME Problems/Problem 15 (Created page with "== Problem == If <math>x-y>x</math> and <math>x+y<y</math>, then <math>\text{(A) } y<x \quad \text{(B) } x<y \quad \text{(C) } x<y<0 \quad \text{(D) } x<0,y<0 \quad \text{(E) } ...")
- 22:23, 14 September 2014 (diff | hist) . . (+555) . . N 1966 AHSME Problems/Problem 14 (Created page with "== Problem == The length of rectangle <math>ABCD</math> is 5 inches and its width is 3 inches. Diagonal <math>AC</math> is divided into three equal segments by points <math>E</ma...")
- 22:14, 14 September 2014 (diff | hist) . . (+400) . . N 1966 AHSME Problems/Problem 13 (Created page with "== Problem == The number of points with positive rational coordinates selected from the set of points in the <math>xy</math>-plane such that <math>x+y \le 5</math>, is: <math>\t...")
- 22:08, 14 September 2014 (diff | hist) . . (+376) . . N 1966 AHSME Problems/Problem 12 (Created page with "== Problem == The number of real values of <math>x</math> which satisfy the equation <cmath>(2^{6x+3})(4^{3x+6})=8^{4x+5}</cmath> is: <math>\text{(A) zero} \qquad \text{(B) on...")
- 21:58, 14 September 2014 (diff | hist) . . (+90) . . 1966 AHSME Problems/Problem 11
- 21:56, 14 September 2014 (diff | hist) . . (+514) . . N 1966 AHSME Problems/Problem 11 (Created page with "== Problem == The sides of triangle <math>BAC</math> are in the ratio <math>2:3:4</math>. <math>BD</math> is the angle-bisector drawn to the shortest side <math>AC</math>, dividi...")
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