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Let n be an integer greater than 30. When n is divided by 12, the remainder is 11. What is the remainder when (6n+1) is divided by 9?
What`s the remainder when $$3^{73}$$ is divided by 5?
x and y are prime numbers

x+y is odd

x < y

Quantity A

x

Quantity B

3


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.
k and n are consecutive positive odd integers.

Quantity A

The least common multiple of k and n

Quantity B

kn


y=105n (n is a positive integer)

y is both the square of an integer, and a multiple of 30

What is the least possible value of n?
If a, b and c are integers such that 0 < a < b < c < 2a, what is the greatest common factor of $$84^{a}$$, $$126^{b}$$, and $$98^{c}$$?
Each of the 1,800 households that participated in a survey owned either one car, two cars, or no cars. If 740 of the households owned only one car and at least $$\frac{1}{3}$$ of the households owned two cars, what is the greatest possible value of the ratio of the number of households that owned no cars to the number of households that owned two cars?

Give your answer as a fraction.
Today a certain machine is worth 20 percent less than it was worth a year ago, and it is worth x percent less than it was worth two years ago. A year ago the machine was worth 20 percent less than it was worth two years ago.

Quantity A

x

Quantity B

40


A pianist agreed to perform one concert at a fee $$12\frac{1}{2}$$ percent less than her usual fee and a second concert at a fee 20 percent greater than the first fee. The fee for the second concert was what percent greater than her usual fee?
Last year the value of one share of a certain stock increased by 10 percent from January to June, and the value of one share of the stock increased by 50 percent from January to December. What was the percent increase in the value of one share of the stock from June to December of last year?

Give your answer to the nearest whole percent.

_____%
The speed of light is 3*$$10^{8}$$ meters per second, rounded to the nearest $$10^{8}$$ meters per second. A "light-hour" is the distance that light travels in an hour.

Quantity A

The number of kilometers in a light-hour

Quantity B

$$10^{10}$$


It costs d dollars to buy t thumbtacks. At this rate, what is the cost of t+2,500 thumbtacks, in dollars?
One day in 1997 at a gas station in the United States near the border of Canada, gasoline was selling for $1.20 per gallon (United States dollars). On that day, 1 United States dollar could be exchanged for 1.25 Canadian dollars. If gasoline was being sold at an equivalent rate at a gas station across the border in Canada, which of the following calculations gives an approximate price, in Canadian dollars, for a liter of gasoline at the Canadian gas station that day? (1 gallon is approximately 3.785 liters.)
Which of the following is the best estimate of $$\frac{(16.8)(10^{3})}{(0.51)(10^{-11})}$$?
If x is an integer, then what is the least possible value of $$3^{x}$$ + $$3^{-x}$$ ?
r is a positive integer, k=2r+1, and h=5k-3

Quantity A

The units digit of h

Quantity B

2


The operation a¤b is defined for all numbers a and b by a¤b=a+3b+6. If c¤c=c, what is the value of c?
The operation  is defined by r s=12 $$r^{-1}$$(s+3) for all positive numbers r and s. If x 3=18, what is the value of x?
The operation is defined by x✸y=$$\frac{x^{2}}{y}$$+$$\frac{x}{y}$$ for all numbers x and y, where y≠0. What is the value of (9✸ (-9))+((-9) ✸9)?

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