If negative integer a is multiplied by b and the result is greater than 0 but less than a, then which of the following must be true of b?

A number divisible by a positive even prime number must be

What are the greatest and smallest positive differences between any of the positive factors of 210?

On Monday, Janice started training for a marathon and ran one mile that day. On Tuesday, Janice ran one mile more than she did on Monday. She continues this training process for 12 days. The sum of the total number of miles Janice ran has how many distinct prime factors?_____

Last year, Melania had a total of $20,000 invested in two mutual funds, Capital Growth Fund and Venture Index Fund. At the end of the year, she analyzed her investments and found that her earnings on her shares of Capital Growth Fund were three times half of her earnings on her investment in Venture Index Fund. If she earned a total of $1,250 on her investments in the two funds, and had three times as much money invested in Capital Growth Fund as in Venture Index Fund, what percent interest did Melania earn on her investment in Venture Index Fund? percent interest =(eamings/investment)*100

a is the product of 3 and the square root of 2, b is the product of 2 and the square root of 3, and c is the product of 2 and the square root of 6. If x is the square of the sum of a and b, y is the product of 6 and the difference of 5 and c, and z is the product of 2 squared and 3 squared, what is $$x\frac{y}{z}$$?

The integer m is a multiple of 154, 250, and 264. Which of the following do NOT have to be factors of m?Indicate all possible values.

If when x is divided by z, the result is y remainder q, then which of the following must be true?

If $$x^ay^bz^c$$ equals the product of 154 and 56, z > y > x, and a > b > c, then what is the value of $$a^xb^yc^z$$?

If –3x + 1 < 7, then which of the following represents all possible values of x?

What is the smallest common multiple of 160 and 240?_____

When x is divided by 3, the remainder is 1. When x is divided by 7, the remainder is 2. How many positive integers less than 100 could be values for x?_____

If j is a multiple of 12, and k is a multiple of 21, then jk must be a multiple of which of the following?

$$x\frac{z}{y}=420$$In the equation above, x is an integer with 3 distinct prime factors, and y is a positive integer with no prime factors. If z is a positive, nonprime number, what is one possible value of z?_____

If w is a nonpositive integer, which of the following must be positive?Indicate all possible values.

Integers a and b are consecutive multiples of 6. Integers x and y are consecutive multiples of 8. In terms of a, b, x, and y, what is the ratio of the average of a and b and the average of x and y?

If If$$x^{2}y=(w)z $$, then which of the following could be true?Indicate all possible values.

If p and x are nonnegative numbers and y is a nonpositive number, then which of the following must be true?Indicate all possible values.

If $$\frac{2}{{3}^{x}}<0.02$$, what is the least integer value of x?

If x is divisible by 78, which of the following must be divisible by x?Indicate all possible values.
