If a rectangle with an area of 400 ft\(^2\) is divided into two smaller rectangles with areas in the ratio of 3:1, what is the least possible value of the perimeter of the smaller rectangle? 

There are 240 pairs of numbers such as {7,5318} or {17,358} that can be formed using each of the digits 1, 3, 5, 7 and 8 exactly once. What is the largest possible product of two such numbers? 

In trapezoid ABCD, angles A and D are right angles, and AB = 4 units, DC = 16 units and BC = 15 units. The trapezoid is revolved 360° around side AD to form the frustum of a cone. What is the volume of this frustum? Express your answer in terms of π.

A box contains only quarters and dimes. If there were 10% more quarters, the total value of the money in the box would increase by 7.5% . What is the ratio of the number of quarters to the number of dimes in the box? Express your answer as a common fraction. 

Three numbers have a sum of 5 and the sum of their squares is 29. If the product of the three numbers is –10, what is the least of the three numbers? Express your answer in simplest radical form.

In how many ways can four different positive integers be placed in four boxes, one per box, so the sum of the integers is 13?

The ratio of Barbara’s cell phone bill to Tina’s cell phone bill was 7:5. Barbara’s bill was $14 more than Tina’s bill. How much was Barbara’s bill?

Xavier gave Yvonne and Zeena the same number of marbles as each already had. Then Yvonne gave Xavier and Zeena the same number of marbles as each already had. Then Zeena gave Xavier and Yvonne the same number of marbles as each already had. At that point, each person had 48 marbles. How many fewer marbles did Xavier have at the end than he had at the start?

The prime factorization of 75 is written, without exponents, as 3 × 5 × 5. The sum of the prime factors is 3 + 5 + 5 = 13. For how many whole numbers is the sum of each number's prime factors, without exponents, equal to 13?

Five integers form an arithmetic sequence with a mean of 18. If the mean of the squares of the five integers is 374, what is the largest of the five original integers?

Each of the letters A, B, C, D, E, F and G in the figure shown will be replaced with a different value from the set {1, 2, 3, 4, 5, 6, 7}. If the sums of the four numbers in each of the three quadrilaterals are each 15, what is the sum of all numbers that can replace A?

A 6-ft ladder is leaning against a wall so that the base of the ladder makes a 45° angle with the floor. The base of the ladder is then pushed in toward the wall so that its distance from the wall is one-third of what it was originally. In feet, how much farther up the wall does the top of the ladder reach? Express your answer as a decimal to the nearest hundredth

A rectangular prism has dimensions in the ratio of 1:2:3. If the shortest edge is 2 ft, what is the longest distance between any two vertices? Express your answer as a decimal to the nearest hundredth.

If \(5\sqrt{x}-30=2\sqrt{x}+54\), then what is the value of \(x^2\)

The deck used in the card game Krypto contains three each of cards numbered 1 to 10, two each of cards numbered 11 to 17, and one each of cards numbered 18 to 25. When five cards are dealt from the deck, what is the probability that all five cards will be 10 or less? Express your answer as a decimal to the nearest thousandth.

Tito’s bill was 19.50 dollars before the 6% sales tax was added. Tito wants to leave a tip of at least 20% of the bill amount before tax is added. What is the least amount he should pay for the bill, tax and tip?

What is the 2012th digit after the decimal point in the decimal expansion of \(\dfrac{8}{81}\) ? 

The number of units in the length of the line segment with endpoints (–4, –5) and (4,2) is a value between two consecutive positive integers. What is the sum of those two integers?

Beginning January 1st, Marte will put $100 in her savings account at the start of every month. The bank pays 4.8% annual interest compounded monthly (0.4% each month) at the end of each month. Assume the bank rounds the interest amount to the nearest cent. How much money will Marte have in her account at the end of the year? Express your answer to the nearest cent. 

A cruise ship must average 22 mi/h for 10 hours to make its next port on schedule. During the first 4 hours, bad weather caused it to reduce its speed to 16 mi/h. What should its speed be for the remainder of the trip to make it to the next port on schedule?