Number Properties

If the units digit of 5 , 610.37 10 k is 6, what is the value of k?

For the positive integers a, b, and k, a^k||b means that a^k is a divisor of b, but a^(k + 1) is not a divisor of b. If k is a positive integer and 2^k||72, then k is equal to

If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

If p/q < 1, and p and q are positive integers, which of the following must be greater than 1 ?

If 3 < x < 100, for how many values of x is x/3 the square of a prime number?

If n = 33 43 + 43 33 what is the units digit of n?

If M is the least common multiple of 90, 196, and 300, which of the following is NOT a factor of M?

Set X consists of eight consecutive integers. Set Y consists of all the integers that result from adding 4 to each of the integers in set X and all the integers that result from subtracting 4 from each of the integers in set X. How many more integers are there in set Y than in set X ?

Five batches of 100 nails each are taken from a production line. The numbers of defective nails in the first four batches are 2, 4, 3, and 5, respectively. If the fifth batch has either 1, 2, or 6 defective nails, for which of these values does the average (arithmetic mean) number of defective nails per batch for the five batches equal the median number of defective nails for the five batches?

If p, q, r, and s are as shown on the number line above, which of the following products is greatest?

Bouquets are to be made using white tulips and red tulips, and the ratio of the number of white tulips to the number of red tulips is to be the same in each bouquet. If there are 15 white tulips and 85 red tulips available for the bouquets, what is the greatest number of bouquets that can be made using all the tulips available?

If x and y are positive numbers such that x + y = 1, which of the following could be the value of 100x + 200y?

For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 301?

If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is

If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?

How many prime numbers between 1 and 100 are factors of 7,150?

The sum of the first hundred positive integers is divisible by?

If n is the product of the integers from 1 to 8, inclusive, how many different prime factors greater than 1 does n have?

If n is an integer, which of the following must be even?

On a scale that measures the intensity of a certain phenomenon, a reading of n+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n. On that scale, the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3?