If n is an integer that is not equal to 0, which of the following must be greater than or equal to n?

I. 7n

II. n + 5

III. n2

If x is an even integer and y is an odd integer. Which of these expressions represents an odd integer?

I. xy

II. x-y

III. 3x+2y

If and is an odd integer, which of the following could be divisible by?

If x and y are integers and at least one of them is even, which of the following MUST be true?

Let equal the product of two numbers. If , then the two numbers COULD be which of the following?

Let a and b be positive integers such that _ab_2 is an even number. Which of the following must be true?

I. _a_2 is even

II. a_2_b is even

III. ab is even

If x is an even number, y is an odd number, and z is an even number, which of the following will always give an even number?

I. xyz

II. 2x+3y

III. z2 – y

In a group of philosophers, are followers of Durandus. Twice that number are followers of Ockham. Four times the number of followers of Ockham are followers of Aquinas. One sixth of the number of followers of Aquinas are followers of Scotus. How many total philosophers are in the group?

Which of the following integers has an even integer value for all positive integers and ?

is even

is even

Therefore, which of the following must be true about ?