MC 2023 N16T

A set of 6 positive integers has a unique mode 4, median 5 and mean 6. What is the maximum possible value for the range of the 6 integers?

If a, b and c are positive integers such that a<b<c and abc=90, what is the least possible value of a +b+c?

A treasure chest hold 100 grams of gold, silver and bronze coins. The gold, silver and bronze coins each weigh 6 grams, 2 grams, and 5 grams, respectively and are worth 30 droubles, 8 droubles and 15 droubles, respectively. The chest has at least one of each kind of coin. What is the greatest possible total value, in droubles, in the chest?

In the figure 2 semicircles have the same center and two congruent circles are inscribed in the larger semicircle so that they are tangent to each other, to both semicircles and to the diameter of the larger semicircle. What percent of the area inside the larger semicircle is not shaded? Express your answer to the nearest tenth.

In a parallelogram with vertices at A(-1,-2), B(4,1), C(3,4) and D(-2,1), the distance between the two longest sides can be expressed as a common fraction in simplest form as a times square root of b divide by c. What is a + b + c?

Earth is a sphere with a radius of 6400 km. If the total volume of Earth were used to evenly cover a hollow sphere so that the covering were exactly 4 km thick, what would be the radius of the hollow sphere? Express your answer as a whole number to the nearest thousand.