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Which of the following is an equation of a line that does NOT contain any points in the xy-plane for which both coordinates are integers?
n is an integer.

Quantity A

$$(-1)^{n}(-1)^{n+2}$$

Quantity B

1


n is a positive integer.

Quantity A

The remainder when $$3^{4n}$$ is divided by 10

Quantity B

1


Which of the following must be a factor of the product of 5 consecutive positive integers?

Indicate all such numbers.
A restaurant has a total of 16 tables, each of which can seat a maximum of 4 people. If 50 people were sitting at the tables in the restaurant, with no tables empty, what is the greatest possible number of tables that could be occupied by just 1 person?
A set consists of all three-digit positive integers with the following properties. Each integer is of the form JKL, where J, K, and L 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?
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.
If the ones digit of $$7^{n}$$ is 9, then the value of n could be?

Indicate all such numbers.
What is the units digit of ($$4^{32}$$ - $$3^{32}$$)?


(4, 6) is the center of the circle above.

Quantity A

The radius of the circle

Quantity B

6


P, Q, and T are three distinct points in a plane.

Quantity A

The number of lines in the plane that pass through points P, Q and T

Quantity B

1


In 1998, how many of the imported towels were not imported from China?
If the average (arithmetic mean) number of towels imported from China per month was the same for the last 3 months of 2000 as it was for the first 9 months of 2000, approximately how many million dozen towels were imported from China during the 12 months of 2000?
In 1999, the ratio of the number of towels imported from China to the total number of towels imported from countries other than China was closets to which of the following?
Dr. Bradley treated a different number of patients on each of the 5 working days last week, and the least number of patients treated on any of the days was 20. No patient was treated on more than one day.

Quantity A

The least possible total number of patients that Dr. Bradley treated on the 5 working days last week

Quantity B

110


k, m, and p are integers.

If k and m are negative integers, which of the following must be negative integers?

Indicate all such integers.
The positive integer x is 7 greater than a multiple of 13, and 2512 < $$x^{2}$$ < 3596

Quantity A

x

Quantity B

55


n is an integer such that 111 ≤ n ≤ 114.

Quantity A

The remainder when n is divided by 31

Quantity B

16


If $$\frac{1}{3}$$+$$\frac{1}{5}$$+$$\frac{1}{7}$$+$$\frac{1}{9}$$+$$\frac{1}{11}$$=$$\frac{m}{(3*5*7*9*11)}$$, then what is the remainder when m is divided by 5?
N and P are both positive integers.

The remainder when N is divided by 53 is 21.

The remainder when P is divided by 53 is 25.

What is the remainder when N*P is divided by 53?

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