Problem Solving

If (a + b) = 4, and ab = 7/4, what is the value of a^2 – b^2?

In ΔPQS above, if PQ =3 and PS = 4, then PR =?

If x, y, and z are single-digit integers and 100(x) + 1,000(y) + 10(z) = N, what is the units' digit of the number N?

When an object is dropped, the number of feet N that it falls is given by the formula N = 1 2 g t 2 , where t is the time in seconds since it was dropped and g is 32.2. If it takes 5 seconds for the object to reach the ground, how many feet does it fall during the last 2 seconds?

A, B, and C each drove 100-mile legs of a 300-mile course at speeds of 40, 50, and 60 miles per hour, respectively. What fraction of the total time did A drive?

A certain elevator has a safe weight limit of 2,000 pounds. What is the greatest possible number of people who can safely ride on the elevator at one time with the average (arithmetic mean) weight of half the riders being 180 pounds and the average weight of the others being 215 pounds?

Ken left a job paying $75,000peryeartoacceptasalesjobpaying$45,000 per year plus 15 percent commission. If each of his sales is for $750, what is the least number of sales he must make per year if he is not to lose money because of the change?

If x is the product of three consecutive positive integers, which of the following must be true? I. x is an integer multiple of 3. II. x is an integer multiple of 4. III. x is an integer multiple of 6.

A certain type of concrete mixture is to be made of cement, sand and gravel in a ratio 1:3:5 by weight. What is the greatest number of kilograms of this mixture that can be made with 5 kilograms of cement ?

The figure above represents a rectangular parking lot that is 30 meters by 40 meters and an attached semicircular driveway that has an outer radius of 20 meters and an inner radius of 10 meters. If the shaded region is not included, what is the area, in square meters, of the lot and driveway?

A hospital pharmacy charges $0.40 per fluidram of a certain medicine but allows a discount of 15 percent to Medicare patients. How much should the pharmacy charge a Medicare patient for 3 fluidounces of the medicine? (128 fluidrams = 16 fluidounces)

An instructor scored a student’s test of 50 questions by subtracting 2 times the number of incorrect answers from the number of correct answers. If the student answered all of the questions and received a score of 38, how many questions did that student answer correctly?

A factory normally produces x units per working day. In a month with 22 working days, no units are produced in the first y working days because of a strike. How many units must be produced per day on each of the rest of the working days of the month in order to have an average of x units per working day for the entire month?

q = 3 √ q = 3 r = 1 + 2 3 √ r = 1 + 2 3 s = 3 + 3 √ s = 3 + 3 If q, r and s are the numbers shown above, which of the following shows their order from greatest to least?

Trucking transportation rates are x dollars per metric ton per kilometer. How much does it cost, in dollars, to transport one dozen cars, which weigh two metric tons each, n kilometers by truck?

A manager has $6,000 budgeted for raises for 4 full-time and 2 part-time employees. Each of the full-time employees receives the same raise, which is twice the raise that each of the part-time employees receives. What is the amount of the raise that each full-time employee receives?

A milliner bought a job lot of hats 1/4 of which were brown. The milliner sold 2/3 of the hats including 4/5 of the brown hats. What fraction of the unsold hats were brown?

If each side of ΔACD above has length 3 and if AB has length 1, what is the area of region BCDE?

A rectangular floor is covered by a rug except fo a strip p meters along each of the four edges. If the floor is m meters by n meteres, What is the area of the rug in square meters?

If a sequence of 8 consecutive odd integers with increasing values has 9 as its 7th term, what is the sum of the terms of the sequence?