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题目内容
What is the remainder when $$3^{27}$$ is divided by 5?
What's the remainder when $$9^{78}$$ is divided by 5?
x and y are positive integers less than 30 where x is a prime, y is odd but not a prime.

Which of the following CANNOT be x+y?
mn=p, where p is a prime. What is the value of m+n in terms of p?
The sum of two prime numbers is 43.

Quantity A

The product of the two prime numbers

Quantity B

83
Both m and n are primes, m < n, and m+n is an odd number

Quantity A

m

Quantity B

3
The number of children in a family is a prime number and is less than 10. If there are one more boys than girls and both the number of boys and girls are primes, then how many children does the family have?
f(100)=the product of all the even integers from 2 to 100, inclusive

Quantity A

40

Quantity B

The largest prime factor of f(100)
P is a prime number

Quantity A

The sum of all prime factors of 5*P

Quantity B

The sum of all prime factors of 6*P
What is the greatest prime factor of $$79^{2}$$-$$50^{2}$$?
$$d$$ is the greatest common divisor of 36 and 60, $$m$$ is the least common multiple of 36 and 60.

Quantity A

$$\frac{36}{d}$$

Quantity B

$$\frac{m}{60}$$
Two librarians, Robert and Patricia,cataloged a combined total of 180 new books,each of which was cataloged by only one of the two librarians. Although they spent the same amount of time cataloging their books, Robert spent an average of 15 minutes per book whereas Patricia spent an average of 12 minutes per book.

Quantity A

The number of books cataloged by Robert

Quantity B

60

Quantity A

x+y

Quantity B

z

Line l is parallel to line m, ∠ECA=38°，and ∠ACB=48°. What is the degree of ∠CBF?

Line l is parallel with line m

Quantity A

AD

Quantity B

BC
Angle A measures $$r$$ degrees. The complement of angle A measures $$90-r$$ degrees, and the supplement of angle A measures $$180-r$$ degrees. If the measure of angle A is greater than the measure of its complement and less than one-half the measure of its supplement, which of the following gives all possible values of $$r$$?


What is the measure of the unknown angle?
The degree measure of each angle of a regular polygon with $$n$$ sides is between $$100$$ and $$130$$. Which of the following could be the value of $$n$$?

Indicate all such integers.

Quantity A

The sum of interior angles of a pentagon plus 90°

Quantity B

The sum of interior angles of a hexagon

Quantity A

The average degree of all interior angles in a trapezoid

Quantity B

The average degree of all interior angles in a pentagon

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