23 September 2014

• 01:0001:00, 23 September 2014 diff hist +739 N 1967 AHSME Problems/Problem 39 Created page with "== Problem == Given the sets of consecutive integers <math>\{1\}</math>,<math> \{2, 3\}</math>,<math> \{4,5,6\}</math>,<math> \{7,8,9,10\}</math>,<math>\; \cdots \; </math>, wher..."
• 00:5900:59, 23 September 2014 diff hist +1,055 N 1967 AHSME Problems/Problem 38 Created page with "== Problem == Given a set <math>S</math> consisting of two undefined elements "pib" and "maa", and the four postulates: <math>P_1</math>: Every pib is a collection of maas, <math..."
• 00:5700:57, 23 September 2014 diff hist +882 N 1967 AHSME Problems/Problem 37 Created page with "== Problem == Segments <math>AD=10</math>, <math>BE=6</math>, <math>CF=24</math> are drawn from the vertices of triangle <math>ABC</math>, each perpendicular to a straight line <..."
• 00:5500:55, 23 September 2014 diff hist +560 N 1967 AHSME Problems/Problem 36 Created page with "== Problem == Given a geometric progression of five terms, each a positive integer less than <math>100</math>. The sum of the five terms is <math>211</math>. If <math>S</math> ..."
• 00:5400:54, 23 September 2014 diff hist +457 N 1967 AHSME Problems/Problem 35 Created page with "== Problem == The roots of <math>64x^3-144x^2+92x-15=0</math> are in arithmetic progression. The difference between the largest and smallest roots is: <math>\textbf{(A)}\ 2\qqu..."
• 00:5300:53, 23 September 2014 diff hist +688 N 1967 AHSME Problems/Problem 34 Created page with "== Problem == Points <math>D</math>, <math>E</math>, <math>F</math> are taken respectively on sides <math>AB</math>, <math>BC</math>, and <math>CA</math> of triangle <math>ABC</m..."
• 00:5200:52, 23 September 2014 diff hist +969 N 1967 AHSME Problems/Problem 33 Created page with "== Problem == <asy> fill(circle((4,0),4),grey); fill((0,0)--(8,0)--(8,-4)--(0,-4)--cycle,white); fill(circle((7,0),1),white); fill(circle((3,0),3),white); draw((0,0)--(8,0),blac..."
• 00:4900:49, 23 September 2014 diff hist +625 N 1967 AHSME Problems/Problem 32 Created page with "== Problem == In quadrilateral <math>ABCD</math> with diagonals <math>\overline{AC}</math> and <math>\overline{BD}</math> intersecting at <math>O</math>, <math>\overline{BO}=4</m..."
• 00:4800:48, 23 September 2014 diff hist +592 N 1967 AHSME Problems/Problem 31 Created page with "== Problem == Let <math>D=a^2+b^2+c^2</math>, where <math>a</math>, <math>b</math>, are consecutive integers and <math>c=ab</math>. Then <math>\sqrt{D}</math> is: <math>\textbf..."
• 00:4700:47, 23 September 2014 diff hist +639 N 1967 AHSME Problems/Problem 30 Created page with "== Problem == A dealer bought <math>n</math> radios for <math>d</math> dollars, <math>d</math> a positive integer. He contributed two radios to a community bazaar at half their ..."
• 00:4300:43, 23 September 2014 diff hist +710 N 1967 AHSME Problems/Problem 29 Created page with "== Problem == <math>\overline{AB}</math> is a diameter of a circle. Tangents <math>\overline{AD}</math> and <math>\overline{BC}</math> are drawn so that <math>\overline{AC}</mat..."
• 00:4200:42, 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 ..."
• 00:4000:40, 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</..."
• 00:3700:37, 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..."
• 00:3500:35, 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}{..."
• 00:3400:34, 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)}\ ..."
• 00:3200:32, 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..."
• 00:3000:30, 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..."
• 00:2800:28, 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..."
• 00:2600:26, 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..."
• 00:2400:24, 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..."
• 00:2300:23, 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<..."
• 00:2200:22, 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>..."
• 00:2100:21, 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}\..."
• 00:1900:19, 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..."
• 00:1800:18, 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) ..."
• 00:1600:16, 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..."
• 00:1500:15, 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: ..."
• 00:1300:13, 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)..."
• 00:1200:12, 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..."
• 00:1000:10, 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..."
• 00:0800:08, 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<..."
• 00:0600:06, 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{..."
• 00:0400:04, 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..."
• 00:0300:03, 23 September 2014 diff hist 0 m 1967 AHSME Problems/Problem 4 →See also
• 00:0300:03, 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..."
• 00:0000:00, 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..."

22 September 2014

• 23:5823:58, 22 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: ..."

15 September 2014

• 01:4701:47, 15 September 2014 diff hist +7,655 1966 AHSME Problems No edit summary
• 01:4101:41, 15 September 2014 diff hist +155 1966 AHSME Problems/Problem 2 No edit summary
• 01:3801:38, 15 September 2014 diff hist +611 1966 AHSME Problems/Problem 6 No edit summary
• 01:3601:36, 15 September 2014 diff hist +21 1966 AHSME Problems/Problem 40 →Solution
• 01:3601:36, 15 September 2014 diff hist +21 1966 AHSME Problems/Problem 39 →Solution
• 01:3501:35, 15 September 2014 diff hist +21 1966 AHSME Problems/Problem 38 →Solution
• 01:3501:35, 15 September 2014 diff hist +21 1966 AHSME Problems/Problem 37 →Solution
• 01:3501:35, 15 September 2014 diff hist +21 1966 AHSME Problems/Problem 36 →Solution
• 01:3501:35, 15 September 2014 diff hist +21 1966 AHSME Problems/Problem 35 →Solution
• 01:3401:34, 15 September 2014 diff hist +21 1966 AHSME Problems/Problem 34 →Solution
• 01:3401:34, 15 September 2014 diff hist +21 1966 AHSME Problems/Problem 33 →Solution
• 01:3401:34, 15 September 2014 diff hist +21 1966 AHSME Problems/Problem 32 →Solution current