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倍数、约数与质数   题数:14
If n is a positive integer and r is the remainder when (n – 1)(n + 1) is divided by 24, what is the value of r?(1) 2 is not a factor of n.(2) 3 is not a factor of n.
A school administrator will assign each student in a group of n students to one of m classrooms. If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?(1)It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it.(2)It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it.
If a, b, k, and m are positive integers, is ak a factor of bm?(1) a is a factor of b.(2) k ≤ m
What is the greatest common factor of the positive integers j and k?(1) k = j + 1(2) jk is divisible by 5.
If n and k are positive integers, is n divisible by 6?(1) n = k(k + 1)(k - 1)(2) k – 1 is a multiple of 3.
How many different factors does the integer n have? (1) n = a4b3 ​, where a and b are different positive prime numbers.(2) The only positive prime numbers that are factors of n are 5 and 7.
What is the greatest common factor of the positive integers j and k?(1) k = j + 1(2) jk is divisible by 5.
If positive integer x is a multiple of 6 and positive integer y is a multiple of 14, is xy a multiple of 105?(1) x is a multiple of 9.(2) y is a multiple of 25.
If x and y are nonzero integers, is 18 a factor of xy2?(1) x is a multiple of 54.(2) y is a multiple of 6.
A certain carton holds fewer than 50 books. What is the number of books in the carton?(1) The books in the carton can be divided into 3 stacks of X books each, with 2 books left over.(2) The books in the carton can be divided into Y stacks of 7 books each, with 2 books left over.
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