SW-MOARML Practice Questions 12-13-09 Determine the distance from the point (1, 1) to the line + 2y = 5. x Given the sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, the integer is repeated times), n n … (where compute the sum of the first 150 terms. The two-digit integers from 19 to 92 are written consecutively to form the large integer = N is the highest power of 3 that is a factor of then = ? N, k 19202122…909192. If 3k What is the largest subset of = {1, 2, 3, 50} such that no pair of distinct elements of S F S … has a sum divisible by 7? Let sequence with + + = 17 and + + + + a1, a2, a4 a7 a10 a4 a5 a6 a7 ….. be an arithmetic + + + + + + = 77. If = 123, then = ? a8 a9 a10 a11 a12 a13 a14 ak k Find the largest positive value attained by the function, where is a real number where both x square roots are defined. First is chosen at random from the set {1, 2, 3, and then is chosen at a b …, 99, 100}, random from the same set. What is probability that the integer 3a + 7b has units digit 8? For any positive integer let , Find . n, Compute the smallest positive integer > 100 such that is divisible by , but not equal to it. n If (x2 + + 1)(x6 + + 1) = , compute the real value of x x3 x.
SW-MOARML Practice Questions 12-13-09 Determine the distance from the point (1, 1) to the line x + 2y = 5. Given the sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, … (where the integer n is repeated n times), compute the sum of the first 150 terms. The two-digit integers from 19 to 92 are written consecutively to form the large integer N = 19202122…909192. If 3k is the highest power of 3 that is a factor of N, then k = ? What is the largest subset S of F = {1, 2, 3, … 50} such that no pair of distinct elements of S has a sum divisible by 7? Let a1, a2, ….. be an arithmetic sequence with a4 + a7 + a10 = 17 and a4 + a5 + a6 + a7 + a8 + a9 + a10 + a11 + a12 + a13 + a14 = 77. If ak = 123, then k = ? Find the largest positive value attained by the function, where x is a real number where both square roots are defined. First a is chosen at random from the set {1, 2, 3, …, 99, 100}, and then b is chosen at random from the same set. What is probability that the integer 3a + 7b has units digit 8? For any positive integer n, let , Find . Compute the smallest positive integer n > 100 such that is divisible by , but not equal to it. If (x2 + x + 1)(x6 + x3 + 1) = , compute the real value of x.
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