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If one number is chosen at random from the first 1,000 positive integers, what is the probability that the number chosen has at least one digit with the number 6?
Give your answer as a fraction.
List L consists of k consecutive integers, where k is an odd integer. The median of the integers in L is m. Which of the following statements must be true?

Indicate all that is/are true.
Let a be the greatest integer such that $$5^{a}$$ is a factor of 1,500, and let b be the greatest integer such that $$3^{b}$$ is a factor of 33,333,333. Which of the following statements are true?

Indicate all such statements.
How many positive factors does 1,575 have?
Of the positive integers that are less than 25, how many are equal to the sum of a positive multiple of 4 and a positive multiple of 5?
How many integers from 1 to 603, inclusive, are multiples of 2 or 3?
k and n are both positive even integers

Quantity A

The remainder when $$k^{2}$$ +n is divided by 2

Quantity B

The remainder when $$k^{n}$$ is divided by 2


If the ones digit of $$7^{n}$$ is 9, then the value of n could be?

Indicate all such numbers.
n, k and r are all positive integers

If $$n^{k}$$=10r+3, then k could be?

Indicate all that are possible.
n, k and r are all positive integers

If $$n^{k}$$=10r+3, then n could be?

Indicate all that are possible.
What is the units digit of $$2^{2222}$$?
What is the units digit of ($$4^{32}$$ - $$3^{32}$$)?
What is the units digit of $$2^{2012}$$+$$3^{2012}$$+$$5^{2012}$$+$$7^{2012}$$?

Quantity A

The remainder when $$3^{64}$$ is divided by 8

Quantity B

1


What is the remainder when $$(345,606)^{2}$$ is divided by 20?
When a positive integer (less than 100) is divided by 5 and 6, the remainder is 3 and 2, respectively.

Quantity A

The greatest possible number of such integers

Quantity B

4


When the product of four prime numbers a, b, c and d is divided by 77, the result is a multiple of 5. When the product of these four prime numbers is divided by 7, the result could be?

Indicate all such numbers.
What is the greatest prime divisor of $$3^{100}$$- $$3^{97}$$?

Quantity A

The number of tenths equal to 1.4

Quantity B

The number of hundredths equal to 1.3


In a survey of drivers, 36% of male drivers hate driving at night, while 48% of female drivers hate driving at night. As a whole, 45% of all drivers hate driving at night. What is the ratio of male drivers to all the drivers in the survey?

Give your answer as a fraction.

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