4799.pdf - AoPS Community 2001 AMC 10 www.artofproblemsolving.com\/community\/c4799 by#H34N1 Silverfalcon mysmartmouth worthawholebean rrusczyk 1 The

4799.pdf - AoPS Community 2001 AMC 10...

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AoPS Community 2001 AMC 10 AMC 10 2001 by #H34N1, Silverfalcon, mysmartmouth, worthawholebean, rrusczyk 1 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 2 A number x is 2 more than the product of its reciprocal and its additive inverse. In which interval does the number lie? (A) - 4 x ≤ - 2 (B) - 2 < x 0 (C) 0 < x 2 (D) 2 < x 4 (E) 4 < x 6 3 The sum of two numbers is S . Suppose 3 is added to each number and then each of the re- sulting numbers is doubled. What is the sum of the final two numbers? (A) 2 S + 3 (B) 3 S + 2 (C) 3 S + 6 (D) 2 S + 6 (E) 2 S + 12 4 What is the maximum number of possible points of intersection of a circle and a triangle? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 5 How many of the twelve pentominoes pictured below have at least one line of symmetry? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7 6 Let P ( n ) and S ( n ) denote the product and the sum, respectively, of the digits of the integer n . For example, P (23) = 6 and S (23) = 5 . Suppose N is a two-digit number such that N = © 2019 AoPS Incorporated 1
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AoPS Community 2001 AMC 10 P ( N ) + S ( N ) . What is the units digit of N ? (A) 2 (B) 3 (C) 6 (D) 8 (E) 9 7 When the decimal point of a certain positive decimal number is moved four places to the right, the new number is four times the reciprocal of the original number. What is the original num- ber?
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