Silas has a clock that gains 15 minutes each hour; for instance, if it shows the correct time at 2:00 p.m., one hour later it will show a time of 3:15 p.m. when it should show 3:00 p.m. Last night, Silas set the clock to the correct time at 10:00 p.m. While he was sleeping, the clock stopped working, and it showed a time of 4:00 a.m. That was 4 hours before he woke up. At what time did Silas wake up? 

A cylinder’s radius is equal to its height. If its surface area is 100π units\(^2\) , what is its volume? Express your answer in terms of π.

Two standard six-sided dice are to be rolled. If the sum is an even number greater than 7, then what is the probability that both dice are even? Express your answer as a common fraction.

Sam went to the bank to withdraw $440.00. He received 30 bills altogether. There were some five-, some ten- and some twenty-dollar bills. Sam received four times as many twenty-dollar bills as five-dollar bills. How many ten-dollar bills did Sam receive?

There is a moving sidewalk in the local shopping mall. When Marlow stands still on the moving sidewalk, it takes her 180 seconds to get from one end of the sidewalk to the other end. Walking beside the moving sidewalk at a constant rate, it takes Marlow 90 seconds to travel the same distance. If Marlow were to get on the sidewalk and walk at her same rate, in the same direction as the moving sidewalk, how many seconds would it take her to get from one end of the sidewalk to the other end?

The integer sides of a triangle are in the ratio 3:4:6. If the perimeter of the triangle is 26 inches, what is the length of the longest side?

What is the greatest possible distance between some point on a square of side length 2 units and some point on its inscribed circle? Express your answer in simplest radical form.  

Kevin and Evan have a set of 10 freshly inked stamps, one for each digit 0 through 9. When freshly inked, each stamp makes exactly 20 impressions. Kevin and Evan will stamp consecutive integers beginning with 1 and continuing until not enough ink remains to stamp the next consecutive number. What is the last number Kevin and Evan will be able to stamp? 

A regular octagon has side length \(2\sqrt{2}\) inches. What is the median length of all its diagonals? Express your answer in simplest radical form. 

At one school, the ratio of students who have one or more younger siblings to those who have no younger siblings is 6 to 5. If 180 students do not have a younger sibling, how many students at this school have one or more younger siblings? 

If x > 0, then 2% of 5% of 3x equals what percent of x? Express your answer to the nearest tenth.

If four people each randomly pick an integer from 1 to 10, inclusive, what is the probability that at least two of the people pick the same integer? Express your answer to the nearest tenth

Each rectangle in a collection has a length 1 cm more than three times its width. What is the maximum possible width of one of these rectangles if its perimeter is less than or equal to 150 cm? Express your answer as a decimal to the nearest tenth.

John has an 8-inch by 10-inch photo that he wants to shrink so that its perimeter is exactly 27 inches. After the photo has been reduced in size, what will be the area of the new photo?

In the land of Binaria, the currency consists of coins worth 1¢, 2¢, 4¢, 8¢, 16¢, 32¢ and 64¢. Bina has two of each coin. How many combinations of her coins have a combined value of 50¢?

A runner completes the first mile of a 26-mile race in 5 minutes. After that, each mile takes 1% longer than the previous mile. How many minutes does it take the runner to complete 26 miles? Express your answer to the nearest whole number.

In a beauty contest, 51 contestants must be narrowed down to a first-, second- and third-place finalist. In how many ways can the three finalists be chosen?

Given that 12, v, w, x, y, z is an arithmetic sequence whose median is 20.75, what is the sum of these six numbers? Express your answer as a decimal to the nearest tenth.

As a used-car salesperson, Noah has a monthly sales quota, which is the minimum number
of cars he must sell each month. Noah had not sold any cars in June, as of the 24th of the
month. However, on June 25th, Noah sold half of the number of cars in his monthly quota,
plus one more car. On June 26th, he sold half of the remaining number of cars he needed to
sell, plus one more car. The same pattern continued until June 30th, when Noah sold half of
the remaining cars he needed to sell, plus one more car and reached his monthly sales quota.
Noah has a monthly sales quota to sell how many cars?

A 5-gallon and a 20-gallon jug can be used to measure exactly 5 gallons or 20 gallons of water, respectively. They can also be used to measure 15 gallons by filling the 20-gallon jug with water, dumping 5 gallons into the 5-gallon jug and having 15 gallons of water left in the 20-gallon jug. Using similar processes, what is the sum of all positive integer numbers of gallons that can be obtained using only the 5-gallon and the 20-gallon jugs?