User contributions
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- 03:52, 8 October 2014 (diff | hist) . . (+371) . . N 2007 iTest Problems/Problem 58 (Created page with "== Problem == Let <math>T=\text{TNFTPP}</math>. For natural numbers <math>k,n\geq 2</math>, we define <cmath>S(k,n)=\left\lfloor\frac{2^{n+1}+1}{2^{n-1}+1}\right\rfloor+\left\lfl...")
- 03:50, 8 October 2014 (diff | hist) . . (-1) . . m 2007 iTest Problems (→Problem 58)
- 03:49, 8 October 2014 (diff | hist) . . (+3,403) . . m 2007 iTest Problems
- 23:03, 7 October 2014 (diff | hist) . . (+510) . . N 2007 iTest Problems/Problem 50 (Created page with "== Problem == A block <math>Z</math> is formed by gluing one face of a solid cube with side length <math>6</math> onto one of the circular faces of a right circular cylinder wit...")
- 23:03, 7 October 2014 (diff | hist) . . (+13) . . 2007 iTest Problems
- 23:03, 7 October 2014 (diff | hist) . . (+181) . . N 2007 iTest Problems/Problem 49 (Created page with "== Problem == How many <math>7</math>-element subsets of <math>\{1, 2, 3,\ldots , 14\}</math> are there, the sum of whose elements is divisible by <math>14</math>? == Solution ==")
- 23:02, 7 October 2014 (diff | hist) . . (+369) . . N 2007 iTest Problems/Problem 48 (Created page with "== Problem == Let a and b be relatively prime positive integers such that <math>a/b</math> is the maximum possible value of <math>\sin^2x_1+\sin^2x_2+\sin^2x_3+\cdots+\sin^2x_{2...")
- 23:02, 7 October 2014 (diff | hist) . . (+619) . . N 2007 iTest Problems/Problem 47 (Created page with "== Problem == Let <math>\{X_n\}</math> and <math>\{Y_n\}</math> be sequences defined as follows: <math>X_0=Y_0=X_1=Y_1=1</math>, <cmath>\begin{align*}X_{n+1}&=X_n+2X_{n-1}\qqu...")
- 23:01, 7 October 2014 (diff | hist) . . (+382) . . N 2007 iTest Problems/Problem 46 (Created page with "== Problem == Let <math>(x,y,z)</math> be an ordered triplet of real numbers that satisfies the following system of equations: <cmath>\begin{align*}x+y^2+z^4&=0,\\y+z^2+x^4&=0,...")
- 23:01, 7 October 2014 (diff | hist) . . (+221) . . N 2007 iTest Problems/Problem 45 (Created page with "== Problem == Find the sum of all positive integers <math>B</math> such that <math>(111)_B=(aabbcc)_6</math>, where <math>a,b,c</math> represent distinct base <math>6</math> dig...")
- 23:01, 7 October 2014 (diff | hist) . . (+357) . . N 2007 iTest Problems/Problem 44 (Created page with "== Problem == A positive integer <math>n</math> between <math>1</math> and <math>N=2007^{2007}</math> inclusive is selected at random. If <math>a</math> and <math>b</math> are n...")
- 23:00, 7 October 2014 (diff | hist) . . (+638) . . N 2007 iTest Problems/Problem 43 (Created page with "== Problem == Bored of working on her computational linguistics thesis, Erin enters some three-digit integers into a spreadsheet, then manipulates the cells a bit until her spre...")
- 23:00, 7 October 2014 (diff | hist) . . (+752) . . N 2007 iTest Problems/Problem 42 (Created page with "== Problem == During a movie shoot, a stuntman jumps out of a plane and parachutes to safety within a <math>100</math> foot by <math>100</math> foot square field, which is entir...")
- 22:59, 7 October 2014 (diff | hist) . . (+538) . . N 2007 iTest Problems/Problem 41 (Created page with "== Problem == The sequence of digits <math>123456789101112131415161718192021\ldots</math> is obtained by writing the positive integers in order. If the <math>10^{nth}</math> dig...")
- 22:58, 7 October 2014 (diff | hist) . . (+194) . . N 2007 iTest Problems/Problem 40 (Created page with "== Problem == Let <math>S</math> be the sum of all <math>x</math> such that <math>1\leq x\leq 99</math> and <math>\{x^2\}=\{x\}^2</math>. Compute <math>\lfloor S\rfloor</math>. ...")
- 22:58, 7 October 2014 (diff | hist) . . (+240) . . N 2007 iTest Problems/Problem 39 (Created page with "== Problem == Let a and b be relatively prime positive integers such that a/b is the sum of the real solutions to the equation <math>\sqrt[3]{3x-4}+\sqrt[3]{5x-6}=\sqrt[3]{x-2}+...")
- 22:58, 7 October 2014 (diff | hist) . . (+117) . . N 2007 iTest Problems/Problem 38 (Created page with "== Problem == Find the largest positive integer that is equal to the cube of the sum of its digits. == Solution ==")
- 22:57, 7 October 2014 (diff | hist) . . (+872) . . N 2007 iTest Problems/Problem 37 (Created page with "== Problem == Rob is helping to build the set for a school play. For one scene, he needs to build a multi-colored tetrahedron out of cloth and bamboo. He begins by fitting three...")
- 22:57, 7 October 2014 (diff | hist) . . (+358) . . N 2007 iTest Problems/Problem 36 (Created page with "== Problem == Let b be a real number randomly selected from the interval <math>[-17,17]</math>. Then, m and n are two relatively prime positive integers such that m/n is the pro...")
- 22:56, 7 October 2014 (diff | hist) . . (+206) . . N 2007 iTest Problems/Problem 35 (Created page with "== Problem == Find the greatest natural number possessing the property that each of its digits except the first and last one is less than the arithmetic mean of the two neighbor...")
- 22:56, 7 October 2014 (diff | hist) . . (+258) . . N 2007 iTest Problems/Problem 34 (Created page with "== Problem == Let <math>a/b</math> be the probability that a randomly selected divisor of <math>2007</math> is a multiple of <math>3</math>. If <math>a</math> and <math>b</math>...")
- 22:55, 7 October 2014 (diff | hist) . . (+177) . . N 2007 iTest Problems/Problem 33 (Created page with "== Problem == How many <math>\textit{odd}</math> four-digit integers have the property that their digits, read left to right, are in strictly decreasing order? == Solution ==")
- 22:54, 7 October 2014 (diff | hist) . . (+832) . . N 2007 iTest Problems/Problem 32 (Created page with "== Problem == When a rectangle frames a parabola such that a side of the rectangle is parallel to the parabola's axis of symmetry, the parabola divides the rectangle into region...")
- 22:53, 7 October 2014 (diff | hist) . . (+245) . . N 2007 iTest Problems/Problem 31 (Created page with "== Problem == Let <math>x</math> be the length of one side of a triangle and let y be the height to that side. If <math>x+y=418</math>, find the maximum possible <math>\textit{i...")
- 22:53, 7 October 2014 (diff | hist) . . (+819) . . N 2007 iTest Problems/Problem 30 (Created page with " == Problem == While working with some data for the Iowa City Hospital, James got up to get a drink of water. When he returned, his computer displayed the “blue screen of deat...")
- 22:53, 7 October 2014 (diff | hist) . . (+174) . . N 2007 iTest Problems/Problem 29 (Created page with "== Problem == Let <math>S</math> be equal to the sum <math>1+2+3+\cdots+2007</math>. Find the remainder when <math>S</math> is divided by <math>1000</math>. == Solution ==")
- 22:52, 7 October 2014 (diff | hist) . . (+151) . . N 2007 iTest Problems/Problem 28 (Created page with "== Problem == The space diagonal (interior diagonal) of a cube has length 6. Find the <math>\textit{surface area}</math> of the cube. == Solution ==")
- 22:51, 7 October 2014 (diff | hist) . . (+186) . . N 2007 iTest Problems/Problem 27 (Created page with "== Problem == The face diagonal of a cube has length <math>4</math>. Find the value of n given that <math>n\sqrt2</math> is the <math>\textit{volume}</math> of the cube. == Sol...")
- 22:51, 7 October 2014 (diff | hist) . . (+563) . . N 2007 iTest Problems/Problem 26 (Created page with "== Problem == Julie runs a website where she sells university themed clothing. On Monday, she sells thirteen Stanford sweatshirts and nine Harvard sweatshirts for a total of �...")
- 22:50, 7 October 2014 (diff | hist) . . (+100) . . m 2007 iTest Problems
- 22:46, 7 October 2014 (diff | hist) . . (+6,367) . . m 2007 iTest Problems
- 22:36, 7 October 2014 (diff | hist) . . (+2,753) . . 2007 iTest Problems
- 22:30, 7 October 2014 (diff | hist) . . (+270) . . N 2007 iTest Problems/Problem 52 (Created page with "== Problem == Let <math>T=TNFTPP</math>. Let <math>R</math> be the region consisting of points <math>(x,y)</math> of the Cartesian plane satisfying both <math>|x|-|y|\le T-500</...")
- 22:29, 7 October 2014 (diff | hist) . . (+147) . . N 2007 iTest Problems/Problem 51 (Created page with "== Problem == Find the highest point (largest possible <math>y</math>-coordinate) on the parabola <cmath>y=-2x^2+ 28x+ 418</cmath> == Solution ==")
- 22:28, 7 October 2014 (diff | hist) . . (+812) . . N 2007 iTest Problems/Problem 25 (Created page with "== Problem == Ted's favorite number is equal to <cmath>1\cdot{2007\choose 1}+2\cdot {2007\choose 2}+3\cdot {2007\choose 3} + \cdots + 2007\cdot {2007 \choose 2007}</cmath> Find...")
- 22:28, 7 October 2014 (diff | hist) . . (+687) . . N 2007 iTest Problems/Problem 22 (Created page with "== Problem == Find the value of <math>c</math> such that the system of equations <cmath> |x+y|=2007 \\ |x-y|=c</cmath> has exactly two solutions <math>(x,y)</math> in real numbe...")
- 22:27, 7 October 2014 (diff | hist) . . (+603) . . N 2007 iTest Problems/Problem 21 (Created page with "== Problem == Find the largest integer <math>n</math> such that <math>2007^{1024}-1</math> is divisible by <math>2^n</math> <math>\text{(A) } 1\qquad \text{(B) } 2\qquad \text{...")
- 22:26, 7 October 2014 (diff | hist) . . (+602) . . N 2007 iTest Problems/Problem 20 (Created page with "== Problem == Find the largest integer <math>n</math> such that <math>2007^{1024}-1</math> is divisible by <math>2^n</math> <math>\text{(A) } 1\qquad \text{(B) } 2\qquad \text...")
- 22:26, 7 October 2014 (diff | hist) . . (+511) . . N 2007 iTest Problems/Problem 16 (Created page with "== Problem == How many lattice points lie within or on the border of the circle in the <math>xy</math>-plane defined by the equation <cmath>x^2+y^2=100</cmath> <math>\text{(A) }...")
- 22:25, 7 October 2014 (diff | hist) . . (+19) . . 2007 iTest Problems/Problem 17 (→Problem)
- 22:24, 7 October 2014 (diff | hist) . . (+770) . . N 2007 iTest Problems/Problem 17 (Created page with "== Problem == If <math>x</math> and <math>y</math> are acute angles such that <math>x+y=\frac{\pi}{4}</math> and <math>\tan{y}=\frac{1}{6}</math>, find the value of <math>\tan{x...")
- 22:23, 7 October 2014 (diff | hist) . . (+974) . . N 2007 iTest Problems/Problem 18 (Created page with "== Problem == Suppose that <math>x^3+px^2+qx+r</math> is a cubic with a double root at <math>a</math> and another root at b, where <math>a</math> and <math>b</math> are real num...")
- 22:22, 7 October 2014 (diff | hist) . . (+1,635) . . N 2007 iTest Problems/Problem 19 (Created page with "== Problem == ===Problem 19=== One day Jason finishes his math homework early, and decides to take a jog through his neighborhood. While jogging, Jason trips over a leprechaun. ...")
- 22:21, 7 October 2014 (diff | hist) . . (+1,588) . . m 2007 iTest Problems (→Problem 19)
- 22:18, 7 October 2014 (diff | hist) . . (-6) . . m 2007 iTest Problems/Problem 15 (→Problem)
- 22:15, 7 October 2014 (diff | hist) . . (+986) . . N 2007 iTest Problems/Problem 15 (Created page with "== Problem == Form a pentagon by taking a square of side length 1 and an equilateral triangle of side length 1 and placing the triangle so that one of its sides coincides with a...")
- 22:06, 7 October 2014 (diff | hist) . . (+156) . . m 1972 AHSME Problems
- 22:05, 7 October 2014 (diff | hist) . . (+32) . . m 1972 AHSME Problems
- 22:02, 7 October 2014 (diff | hist) . . (+22) . . m 1972 AHSME Problems
- 21:57, 7 October 2014 (diff | hist) . . (+17,609) . . N 1972 AHSME Problems (Created page with "== Problem 1 == The lengths in inches of the three sides of each of four triangles <math>I, II, III</math>, and <math>IV</math> are as follows: <math>\begin{array}{rlrl} \hbox...")
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