# George is eating from a bag of potato chips the

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10. George is eating from a bag of potato chips. The caloric total ofa potato chip is entirely composed of integral (in grams) amounts offats, proteins, and carbohydrates, which have 9,4,and 4 calories pergram, respectively. After doing some research, George finds that asingle potato chip has 30 calories. In total, the bag has 120 gramsof fat. How many total calories does the bag have? (A)450(B)900(C)1200(D)1500(E)1800 11. How many positive integers, where all digits are non-zero, aredivisible by 11 and have the property that the sum of its digits is 11?
Mock 2018 AMC 10B Problems 4 12.Let4ABCbe an acute triangle and letObe its circumcen-ter.DefineDas the intersection, different fromA, between theA-altitude and the circumcircle of4ABC.LetPandQbe themidpoints ofABandACrespectively. What is the area ofABDCif the area ofAPOQis 48? 13.Determine the sum of all two-digit positive integers with themost odd positive integer factors. 14. There exist distinct elementsa, b, c, d, e, fof the set{1,2,3,4,5,6,7}so that the positive difference between (x-a)(x-b)(x-c) and(x-d)(x-e)(x-f) is alwaysnfor any choice ofx. What isn? (A)2(B)12(C)26(D)34(E)57 15.Call a time of the dayab:cd:efconsecutiveifabcdefcanbe written as the concatenation of at least consecutive 2 positiveintegers, in strictly increasing order. For example, 13 : 14 : 15 and12 : 01 : 21 are consecutive times because 13,14,15 and 120,121 areconsecutive integers, while 11 : 12 : 15 is not. How many consecu-tive times are there in a 24 hour period? 16. The exact value of s 2 2 1 + r 2 2 2 + q 2 2 3 + p 2 2 4 + . . . is a + b for positive integers a and b . Compute the sum of the digits of a · b . (A) 5 (B) 6 (C) 7 (D) 8 (E) 9 17. The least common multiple of 5 positive distinct integers, (a1, a2, a3, a4, a5),is 1000. What is the sum of all possible values of gcd (a1, a2, a3, a4, a5)? Mock 2018 AMC 10B Problems 5 18. For every positive integern, we define the operationn=n·n!.What is the remainder when 1+ 2+· · ·+ 17is divided by 23?

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• Fall '19
• International Mathematical Olympiad, American Mathematics Competitions, American Invitational Mathematics Examination

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