Number Properties

A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10 4 − 10 2) (0.00 12 ¯ ¯) (10 4 − 10 2) (0.00 12 ¯) ?

In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?

If n = 4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?

The positive integer n is divisible by 25. If √ n n √ is greater than 25, which of the following could be the value of n/25 ?

If n is a positive integer, then n(n+1)(n+2) is

If the quotient a/b positive, which of the following must be true?

For which of the following values of n is (100+n)/n NOT an integer?

If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true? I. c - a = 2 II. abc is an even integer. III. (a + b + c)/3 is an integer.

What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?

The sum of prime numbers that are greater than 60 but less than 70 is

A student’s average (arithmetic mean) test score on 4 tests is 80. What must be the student’s score on a 5th test for the student’s average score on the 5 tests to be 82?

If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2 i * 3 k * 5 m * 7 p , then i + k + m + p =

What is the units digit of 13 4 ∗ 17 2 ∗ 29 3 ?

Fermat primes are prime numbers that can be written in the form 2 k + 1 , where k is an integer and a power of 2. Which of the following is NOT a Fermat prime

Which of the following CANNOT be a value of 1 x − 1 ?

If p is an even integer and q is an odd integer, which of the following must be an odd integer?

Which of the following is NOT equal to the square of an integer:

If x is equal to the sum of the even integers from 40 to 60 inclusive, and y is the number of even integers from 40 to 60 inclusive, what is the value of x+y?

R is the set of positive odd integers less than 50, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?

In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors?