15 Questions

Time--25 minutes

Numbers: All numbers used are real numbers.

Figures: The diagrams and figures that accompany these questions are for the purpose of providing information useful in answering the questions.  Unless it is stated that a figure is not drawn to scale, the diagrams and figures are drawn as accurately as possible.  All figures lie in a plane unless otherwise indicated.

1. If x = 4, then (x -7)(x + 2) is equal to

2. A taxicab charges $1.00 for the first one-fifth mile of a trip and $0.20 for each following one-fifth mile or part thereof. If a trip is 2.5 miles long, what is the fare?

3. Three valves, when opened individually, can drain the water from a certain tank in 3, 4, and 5 minutes respectively. What is the greatest part of the tank that can be drained in one minute by opening just two of the valves?

4. A candy assortment contains only chocolates and caramels.  If there are four times as many chocolates as caramels in the assortment, then caramels are what fraction of the assortment?

5. A jar contains between 50 and 60 marbles. If the marbles are counted out 3 at a time, 1 is left over; if they are counted out 4 at a time, 3 are left over. How many marbles are in the jar?

6. In a certain population, x out of every y persons are found to have characteristic * . If 200 persons are found to have characteristic *, then which  of the following expressions provides the total number of persons in the population?

 7. The total cost for one adult and two children's tickets for a movie is $16.50. If an adult ticket cost $3.00 more than a children's ticket, what is the cost of a children's ticket?

  8. In a certain community, the property tax is solely a function of the tax rate and assessed value of the property. If the assessed value of a property is decreased by 25 percent while the tax rate is increased by 25 percent, what is the net effect on the taxes on the property?

9. The average weight of the 8 packages in a certain shipment is 6 pounds. If the heaviest package is removed, the average weight of the remaining packages is 5 pounds. What is the weight, in pounds, of the heaviest package?

 10. A company bought a load of water-damaged copy paper, estimating that 2/3 of the reams could be salvaged, in which case the cost per salvageable ream would be $0.72. If it later turned out that 3/4 of the reams were salvageable, then what was the actual cost per salvageable ream?

 11. How many of the two-element subsets of the set below do NOT contain the pair red and green?

 {red, green, yellow, blue} 

 12. In a certain direct mail center, each of x computers addresses y letters every z minutes. If every computer works without interruption, how many hours are required for the center to address 100,000 letters?

 13. In the Excel Manufacturing Company, 46 percent of the employees are men. If 60 percent of the employees are unionized and 70 percent of these are men, what percent of the non-union employees are women?

 14. An accrediting agency set up a proficiency test for a lab in which 20 percent of the samples were injected with a contaminant. If the lab correctly labeled 80 percent of the contaminated samples but incorrectly labeled 5 percent of the uncontaminated samples, then what percent of the samples labeled by the lab as uncontaminated were actually contaminated?

 15. A study of a city's water-use patterns shows that for every 8x percent increase in the price of water, usage drops by x percent. If the price for water is currently $1.05 per 1,000 cubic feet, by how much should the price per 1,000 cubic feet be raised in order to obtain a reduction in usage of 2 percent?

Answer Key