Problem Solving

In the figure shown, the triangle is inscribed in the semicircle. If the length of line segment AB is 8 and the length of line segment BC is 6, what is the length of arc ABC?

If k and n are positive integers such that n > k, then k ! + (n − k) * (k − 1) ! is equivalent to which of the following?

Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?

In the figure shown, what is the value of x ?

The graph of which of the following equations is a straight line that is parallel to line l in the figure above?

Of the land owned by a farmer, 90 percent was cleared for planting. Of the cleared land, 40 percent was planted with soybeans and 50 percent of the cleared land was planted with wheat. If the remaining 720 acres of cleared land was planted with corn, how many acres did the farmer own?

According to a certain estimate, the depth N(t), in centimeters, of the water in a certain tank at t hours past 2:00 in the morning is given by N (t) = − 20 (t − 5) 2 + 500 for 0 ≤ t ≤ 10 . According to this estimate, at what time in the morning does the depth of the water in the tank reach its maximum?

If the average (arithmetic mean) of the four numbers 3, 15, 32, and (N + 1) is 18, then N =

If 1/3 of the total number of marbles in the three bags listed in the table above are blue, how many marbles are there in bag Q?

A certain experimental mathematics program was tried out in 2 classes in each of 32 elementary schools and involved 37 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are

If mn ≠ 0 and 25 percent of n equals 37 1 2 percent of m, what is the value of 12 n m ?

The table shows the amount budgeted and the amount spent for each of three accounts in a certain company.For which of these accounts did the amount spent differ from the amount budgeted by more than 6 percent of the amount budgeted ?

If n = 20! + 17, then n is divisible by which of the following?

A manufacturer of a certain product can expect that between 0.3 percent and 0.5 percent of the units manufactured will be defective. If the retail price is $2,500 per unit and the manufacturer offers a full refund for defective units, how much money can the manufacturer expect to need to cover the refunds on 20,000 units?

Seven pieces of rope have an average (arithmetic mean) length of 68 centimeters and a median length of 84 centimeters. If the length of the longest piece of rope is 14 centimeters more than 4 times the length of the shortest piece of rope, what is the maximum possible length, in centimeters, of the longest piece of rope?

If x^2 − 2 < 0, which of the following specifies all the possible values of x?

Four extra-large sandwiches of exactly the same size were ordered for m students, where m > 4. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?

Abdul, Barb, and Carlos all live on the same straight road, on which their school is also located. The school is halfway between Abdul’s house and Barb’s house. Barb’s house is halfway between the school and Carlos’s house. If the school is 4 miles from Carlos’s house, how many miles is Abdul’s house from Carlos’s house?

While a family was away on vacation, they paid a neighborhood boy $11perweektomowtheirlawnand$4 per day to feed and walk their dog. If the family was away for exactly 3 weeks, how much did they pay the boy for his services?

In the xy-coordinate plane, which of the following points must lie on the line kx + 3y = 6 for every possible value of k?