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3. The Answer Forms must be submitted through the Google Form provided no later than January 8 4. The publication, reproduction or communication of the prob- lems or solutions of this test during the period when students are eligible to participate seriously jeopardizes the integrity of the results. Dissemination at any time via copier, telephone, email, internet or media of any type is a violation of the com- petition rules. The CMC American Mathematics Competitions are supported by atmchallenge AOPS12142015 CantonMathGuy eisirrational FedeX333X illogical 21 Th3Numb3rThr33 tree3
Mock 2018 AMC 12B Problems 6 22. Let 3θbe a real number in the open interval (0, π) such thatcot(3θ) = 2/11. Then sin(θ) + cos(θ) =abcfor integersa, b,andc,with gcd(a, c) = 1 andbnot divisible by the square of any prime.Computea+b+c. (A)8(B)10(C)13(D)17(E)22 23.Let{an}be an infinite increasing sequence of positive inte-gers such thata1= 1 and for eachi2,aiis the smallest positiveinteger greater thanai-1with the property thatai6= 2ajfor every1j < i. What is the sum of the digits ofa2018? 24.LetN={1,2, ...,11}andw, x, y, zbe 4 not necessarily dis-tinct elements ofN. For how many ordered quadruplets (w, x, y, z)is the numberwx2+y3z4+ 5 a multiple of 11? 25. On a board there is written a positive integer 1n2018.Alice and Bernard decide to play a game. Alice starts: she choosesa positive divisor ofnsmaller thann(ifn= 1, she is forced tochoose 1), subtracts 1 from the chosen divisor and gives the numberto Bernard, who repeats the same process. The game continues likethat until one of the two players is forced to say 0; in which thatplayer loses the game. For how many values ofndoes Alice has awinning strategy? Mock 2018 AMC 12B Problems 3 7.How many positive integers, where all digits are non-zero, aredivisible by 11 and have the property that the sum of its digits is11? (A)0(B)6(C)24(D)infinitely many(E)more than 24 but finitely many

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• Fall '19
• International Mathematical Olympiad, United States of America Mathematical Olympiad, American Mathematics Competitions, American Invitational Mathematics Examination

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