Problem Solving

If the length of a diagonal of a square is 2 √ x 2 x √ , what is the area of the square in terms of x ?

10, 4, 26, 16 What is the median of the numbers shown?

The figure above represents a semicircular archway over a flat street. The semicircle has a center at O and a radius of 6 feet. What is the height h, in feet, of the archway 2 feet from its center?

In the figure above, what are the coordinates of point R ?

Ron is 4 inches taller than Amy, and Barbara is 1 inch taller than Ron. If Barbara's height is 65 inches, what is the median height, in inches, of these three people?

The figure shown above represents a modern painting that consists of four differently colored rectangles, each of which has length l and width w. If the area of the painting is 4,800 square inches, what is the width, in inches, of each of the four rectangles?

The parallelogram shown has four sides of equal length. What is the ratio of the length of the shorter diagonal to the length of the longer diagonal?

In the figure above, what is the ratio of the measure of angle B to the measure of angle A?

The window in the figure above consists of a rectangle and a semicircle with dimensions as shown. What is the area, in square feet, of the window?

A flat patio was built alongside a house as shown in the figure above. If all angles shown are right angles, what is the area of the patio in square feet?

2018.OG.05.026.q.png [ 32.11 KiB | Viewed 51824 times ] In the figure shown, AC = 2 and BD = DC = 1. What is the measure of angle ABD?

If the circumference of a circle inscribed in a square is 25π, what is the perimeter of the square?

In the xy-coordinate plane, if the point (0,2) lies on the graph of the line 2x + ky = 4, what is the value of the constant k ?

If rectangle ABCD is inscribed in the circle above, what is the area of the circular region?

The sum of the first hundred positive integers is divisible by?

In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play Football. 7 play both Hockey and Cricket, 4 play Cricket and Football and 5 play Hockey and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?

A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer?

If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t ?

Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?

Among a group of 2,500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from the 2,500 people, what is the probability that the person selected will be one who invests in municipal bonds but NOT in oil stocks?