GMAT
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 k, m, and t are positive integers and $$\frac k 6+\frac m 4=\frac t {12}$$, do t and 12 have a common factor greater than 1 ?(1)k is a multiple of 3.(2)m is a multiple of 3.
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.
Is x an integer?(1)$$\frac x 2$$ is an integer.(2)2x is an integer.
Is n an integer?(1)$${n}^{2}$$ is an integer.(2)$$\sqrt{n}$$ is an integer.
If n and t are positive integers, is n a factor of t?(1)$$n=3^{n-2}$$(2)$$t=3^{n}$$
For any positive integer x, the 2-height of x is defined to be the greatest nonnegative integer n such that $${2}^{n}$$ is a factor of x. If k and m are positive integers, is the 2-height of k greater than the 2-height of m ? (1) $$k>{m}$$ (2)$$\frac{K}{M}$$ is an even integer.
If x is a positive integer, then is x prime?(1) 3x + 1 is prime.(2) 5x + 1 is prime.
Is the product of two positive integers x and y divisible by the sum of x and y?(1) x=y(2) x=2