2010代数部分1-1.doc

2010 AMC8竞赛培训-代数部分数的运算(1996AJHSME-4) (A) (B) (C) (D) (E) Key: B （2008-18）The number n is doubled and then has y added to it. The result is then divided by 2 and has the original number n subtracted from it. The final result is(A) n (B) y (C) n + y (D) (E) Key: E （200AMC8-10）For any positive integer n, define n to be the sum of the positive factors of n. For example, □6 = 1 + 2 + 3 + 6 = 12.Find □(□11) . (A) 13 (B) 20 (C) 24 (D) 28 (E) 30 Key: D （200AMC8-15）Let a, b and c be numbers with 0 a b c. Which of thfollowing is impossible? (A) a+c b (B) ab c (C) a + b c (D) ac b (E) = a Key: A （200AMC8-7）Blake and Jenny each took four 100-point tests. Blake averaged 78 on the four tests. Jenny scored 10 points higher than Blake on the rst test, 10 points lower than him on the second test, and 20 points higher on both the third and fourth tests. What is the difference between Jennys average and Blakes average on these four tests? (A) 10 (B) 15 (C) 20 (D) 25 (E) 40 Key: A 整数的性质 (2003AMC8-19) How many integers between 1000 and 2000 have all three of the numbers 15, 20 and 25 as factors? (A) 4 (B) 5 (C) 6 (D) 8 (E) 15 Key: C (2007GAUSS8-15)Sally picks four consecutive positive integers. She divides each integer by four, and then adds the remainders together. The sum of the remainders is ? (A) 6 (B) 1 (C) 2 (D) 3 (E) 4 Key: A （200AMC8-19）A whole number larger than 2 leaves a remainder of 2 when divided by each of the numbers 3, 4, 5 and 6. The smallest such number lies between which two numbers?(A)40 and 49 (B)60 and 79 (C)100and129 (D)210and249 (E)320and 369 Key: B (2007AMC8-18) The product of the two 99-digit numbers 303,030,303,…,030,303 and 505,050,505, . . . ,050,505 has thousands digit A and units digit B. What is the sum ofA and B? (A) 3 (B) 5 (C) 6 (D) 8 (E) 10 Key: D （2002GAUSS-20）The units digit (that is, the last digit) of is?(A) 7 (B) 1 (C) 3 (D) 9 (E) 5 Key: D （2008-24）The sum of all of the digits of the integers from 98 to 101 is 9 + 8 + 9