2001 AMC 10A ws-25.pdf - The median of the list n n 3 n 4 n 5 n 6 n 8 n 10 n 12 n 15 is 10 What is the mean(A 4(B 6(C 7(D 10(E 11 2001 AMC 10

2001 AMC 10A ws-25.pdf - The median of the list n n 3 n 4 n...

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The median of the listn, n+3, n+4, n+5, n+6, n+8, n+10, n+12, n+15is 10. What is the mean? (A)4(B)6(C)7(D)10(E)112001 AMC 10, Problem #1“The middle number in the 9-number list isn+ 6.”Solution(E)The middle number in the 9-number list isn+6, which is given as 10.Thusn= 4. Add the terms together to get9n+ 63 = 9·4 + 63 = 99.Thus the mean is99/9 = 11. Difficulty: Medium NCTM Standard: Number and Operations Standard for Grades 9–12: Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Mathworld.com Classification: Probability and Statistics > Rank Statistics > Median Calculus and Analysis > Special Functions > Means
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A numberxis 2 more than the product of its reciprocaland its additive inverse.In which interval does thenumber lie? 6 2001 AMC 10, Problem #2 “The reciprocal of x is 1 x , and the additive inverse of x is - x .” Solution Difficulty: Medium-hard NCTM Standard: Number and Operations Standard for Grades 9–12: Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Mathworld.com Classification: Number Theory > Arithmetic > Multiplication and Division > Reciprocal Algebra > Group Theory > Group Properties > Additive Inverse
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The sum of two numbers isS. Suppose 3 is added toeach number and then each of the resulting numbersis doubled. What is the sum of the final two numbers? 2001 AMC 10, Problem #32001 AMC 12, Problem #1“The order ofarithmetic operationsisadd 3thendouble the sum.”Solution(E)Suppose the two numbers areaandb. Then the desired sum is2(a+ 3) + 2(b+ 3) = 2(a+b) + 12 = 2S+ 12.Difficulty:MediumNCTM Standard:Number and Operations Standard for Grades 9–12: Understand meanings ofoperations and how they relate to one another. Mathworld.com Classification: Number Theory > Arithmetic > General Arithmetic
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What is the maximum number for the possible pointsof intersection of a circle and a triangle? Difficulty: Medium-easy NCTM Standard: Geometry Standard for Grades 9–12: Explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them. Mathworld.com Classification: Geometry > Plane Geometry > Circles Geometry > Plane Geometry > Triangles > Special Triangles > Other Triangles > Triangle
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How many of the twelve pentominoes pictured below have at least one line of symmetry?
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