The integers a, b, and c are positive, and a>b>c. When a, b, and c are divided by 3, the remainders are 0, 1, and 1, respectively.

For all positive even integers n. n* represents the product of all even integers from 2 to n, inclusive. For example, 12*=12×10×8×6×4×2. What is the greatest prime factor of 20*+22*?

In a game, the cards in a certain deck are distributed to players one at a time until each player has the same number of cards and there are not enough cards left in the deck to distribute one more card to each player. The number of cards in the deck is between 60 and 100. If the cards in the deck are distributed o 5 players, 2 cards will be left in the deck. If the cards in the deck are distributed to 6 players, 4 cards will be left in the deck. If the cards in the deck are distributed to 7 players, how many cards will be left in the deck?

Let a be the greatest integer such that is a factor of 1,500, and let b be the greatest integer such that is a factor of 33,333,333. Which of the following statements are true? Indicate all such statements.

A set consists of all three-digit positive integers with the following properties.Each integer is of the form JKL,where J,K,and I are digits;all the digits are nonzero;and the two-digit integers JK and KL are each divisible by 9.How many integers are in the set?

The number of children in a certain family is a prime number less than 10. The number of boys in the family is greater than the number of girls, and the number of boys is a prime number. If at least 1 of the children in the family is a girl, which of the following could be the number of boys in the family?Indicate all such numbers.

x and y are integers.

x and y are integers.

a and b are distinct odd prime numbers.

When the integer n is divided by 33, the remainder is 24. Which of the following must be a divisor of n?

4.What is the length of an edge of the smallest solid cube that can be made by placing together solid rectangular blocks of size 7 by 6 by 3?

Light travels at approximately 186,000 miles per second.Which of the following is closest to the number of miles that light travels in 3 hours.

The number n is the least positive integer for which 108n is the square of an intege

The number n is the least positive integer for which 108n is the square of an intege

If x=2y+1, and y=2w, where w, x, and y are integers, which of the following must be an odd integer?

If x=2y+1, and y=2w, where w, x, and y are integers, which of the following must be an odd integer?