The mean of three numbers is 6 more than the least of the numbers, and it is 7 less than the greatest number. The median of the three numbers is 8. What is the sum of the three numbers? 

The function f(x) = 3x² – 6x –11 is graphed on a coordinate plane. What is the smallest y-coordinate of any points of the function?  

A rhombus of side length 5 units has a short diagonal of length 6 units. What is the area of the rhombus? 

The measures of the four interior angles of a convex quadrilateral are 4x, 3x + 20, 2x + 40 and x + 80 degrees. What is the measure of the smallest interior angle of the quadrilateral? 

 A study of 100 boys and 100 girls found that 60% of girls and 20% of boys enjoy the game Quirk. What percent of the children in the study who enjoy Quirk are girls? 

A square and a circle overlap such that a vertex of the square is at the center of the circle. The 4-inch radius of the circle is one-half the length of a side of the square. What is the area of the portion of the square region that is outside the circular region? Express your answer in terms of π.

A bird collection has exactly four types of birds (eagles, doves, crows and sparrows). The eagles and doves make up 60% of the collection, and the doves and crows make up 20% of the collection. If the 18 crows in the collection represent 5% of the total number of birds, how many of the birds are sparrows? 

A 20-foot-high rectangular room has a floor that measures 18’ by 15’. Its doorway measures 3’ by 12’, and its only window measures 7’ by 10’. How many square feet of wall space does the room have?  

An integer is pseudoperfect if it is the sum of two or more of its positive divisors. (A divisor may be used only once in the sum.) For instance, 20 is pseudoperfect because its divisors 1, 4, 5 and 10 have a sum of 20. What is the sum of all the pseudoperfect integers between 50 and 60?  

An acute angle of a right triangle is 30°, and the hypotenuse is 40 units. What is the area of the triangle? Express your answer as a decimal to the nearest tenth. 

A Super-Duper bouncy ball is dropped straight down from a height of 80 feet. Each time the ball hits the ground it bounces straight back up ¾ of the height from which it just fell. How many total feet had the ball traveled when it hit the ground the third time?

  A tank contains 10,000 gallons of water at the beginning of the day on June 1. Each day, 1% of the water in the tank at the beginning of the day is lost to evaporation. How much water is left at the end of the last day of June? Express your answer to the nearest whole number.

To create a unique house paint color, Melton mixes together a sample that is 12 gallons of red, 2.5 gallons of yellow and 0.5 gallons of blue paint. He then mixes a main batch of paint using 30 gallons of yellow paint and enough red and blue paint so as to maintain the original ratio. How many total gallons of paint did he use when making the sample and the main batch? 

A positive 16-digit integer is such that any two consecutive digits form a multiple of either 19 or 31. If the digit 2 appears only once, what is the sum of the 16 digits? 

A jar contains 100 red marbles, 100 blue marbles and 100 white marbles. All 300 marbles are the same size. How many distinct color combinations are possible when three marbles are selected from the jar? The order in which the marbles are selected does not matter. 

To pass a 30-question test, Johnny needs to answer at least 60% of the questions correctly. When Johnny received his graded test back, he saw that he needed to have answered exactly two more questions correctly to have passed the test. How many questions did he answer correctly? 

Terrell wondered how many blades of grass were in his 60-foot by 90-foot rectangular backyard. He picked a square region three inches on a side, which contained 520 blades of grass. If the grass was uniformly distributed throughout the backyard, how many blades were in the entire backyard?

Let B(n) denote the sum of the digits of the binary (base 2) representation of n. Let T(n) denote the sum of the digits of the ternary (base 3) representation of n. For example, B(9) = B(1001₂) = 2 and T(9) = T(100₃) = 1. What is the smallest positive integer n greater than 1 such that B(n) = T(n)? 

Gary can select any positive two-digit integer between 23 and 98 and write it as “AB” with tens digit A and ones digit B. When he subtracts the sum A + B from his integer, the difference will be a new two-digit integer, “JK.” What is the value of J + K?  

The faces of a cubical die are each labeled with a different prime number, and each of the six smallest prime numbers (2, 3, 5, 7, 11, 13) is on exactly one face of the die. The die will be rolled twice. What is the probability that the product of the two numbers rolled will be even? Express your answer as a common fraction