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题目内容
In how many different ways can we use 0, 1, 2, 3, 4, to form a 4-digit number which must be a multiple of 3 (None of the five numbers can be used more than once)?
What is the remainder when $$3^{35}$$ is divided by 5?
What is the remainder when $$3^{283}$$ is divided by 5？

Quantity A

The remainder when $$7^{13}$$ is divided by 10

Quantity B

7
The remainder is 4 when positive integer n is divided by 5, and remainder is 5 when n is divided by 6. What is the remainder when n is divided by 15?
Positive integer n is between 44 and 53, inclusive. The remainder is 2 when n is divided by 3,and the remainder is 1 when n is divided by 4. What is the value of n?
p=$$n^{2}$$+1 where p is a prime number and n is an integer.

Quantity A: p

Quantity B: 17
How many primes can be formed when someone selects two different numbers from 2,3,4,5 as the tens digit and units digit, respectively?
The cubic root of n is a prime，what could be the possible value of n？

Indicate all such items.
How many positive integers less than 20 are the product of two different prime integers?
What is the greatest prime factor of 510?
Quantity A: The number of the prime factors of 27

Quantity B: The number of the prime factors of 12
For all integers $$x$$ greater than $$1$$, the function $$p(x)$$ is defined as the number of different prime factors of $$x$$. What is the value of $$\frac{p(12)}{p(9)}$$?
The number of attendees at a certain convention is less than 1,000 and is divisible by 50.

Which of the following statement individually provide(s) sufficient additional information to determine the number of attendees at the convention?

Indicate all such statement.
Jim exercises every third day. For example, if he exercises on a Monday, the next day he will exercise is the following Thursday. If Jim exercised last Monday, how many weeks from last Monday will be the next Monday that he exercises?
Both train A and train B provide 24-hour service throughout the day. Train A passes by a certain station every 12 minutes, while Train B passes by the same station every 20 minutes. For how many times can these two trains pass by the station at the same time from 06:00AM to 10:30AM in the same day?

Indicate all such values.

What is the value of x+y?

Quantity A

The average of all the interior angles inside a quadrilateral

Quantity B

The average of all the interior angles inside a pentagon
As$$\frac{5}{3} \times \frac{6}{4} \times \frac{7}{5} \times ... \times \frac{x}{y}$$ =20, the numerator of the latter fraction is 1 more than the numerator of the former fraction, and the denominator of the latter fraction is 1 more than the denominator of the former fraction, what is the value of x+y?
x,y and z are three integers between -10 and 10,inclusive. What is the least possible value of $$\frac{x-y}{z}$$?

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