PSAT Math Multiple-Choice Practice Test 42: Problem Solving and Data Analysis

1. A subway map is drawn to scale so that 1 inch on the map corresponds to 2 miles of actual distance on the track. The subway train travels at a constant average rate of 30 miles per hour. How many minutes will a journey on the subway take if the track distance as portrayed on the map is 3 inches?

2. An electronic reader typically costs $100. However, the price is heavily discounted due to both a coupon and a sale that have the same percent off the regular price. If the price using both the coupon discount and the sale discount is $49, what is the percent off the regular price that the coupon and the sale each provide independently

3. If n percent of 80 is 20, what is n percent of 220

4. If 132 men and 168 women are living in a dormitory, what percent of the total dormitory residents are men

5. If 1 Canadian dollar can be exchanged for 0.80 U.S. dollars and vice versa, how many Canadian dollars can a traveler receive in exchange for 120 U.S. dollars

6. David is developing a fitness plan and wants to get his weight to a level that will be considered healthy in terms of the body mass index (BMI) calculation. The currently recommended BMI is between 18.6 and 24.9. To calculate BMI using inches and pounds, David takes his weight in pounds and divides it by the square of his height in inches. Then he multiplies the entire result by 703. David is 6 feet, 3 inches tall and currently weighs 260 pounds. To the nearest whole pound, what is the least number of whole pounds he needs to lose in order for his BMI to be within the healthy range

Questions 7-9 refer to the following information.
A marine biologist has conducted research into the population of blue whales over the past few decades. The estimated global blue whale population is plotted against the given year in the graph below:

7. From 1940 until 1970, the best-fit equation for the values of the blue whale population has which general characteristic?

8. A worldwide treaty prohibiting commercial whaling (i.e., the hunting of whales) was passed at some point between 1930 and 2010. Based on the data, what is the year when this treaty most likely went into effect

9. Another scientist is reviewing the results of the marine biologist's observations and assessing the impact of measurement error on such an ambitious project. The scientist is considering two possible sources of measurement error: (1) random error from any factor that would affect the scientist's measurements and (2) systematic error from a problem in the overall setup of the data-gathering project. Which of the following would be the best way that the marine biologist's measurement error could have been minimized

Questions 10-11 refer to the following information.
The graph below gives the current GPA of every one of the 389 students at County High School.

10. Which of these values of the GPA for the students portrayed in the graph is between 2 and 3?

Mean

Median

Mode

11. The school administrators have decided that too much grade inflation occurs at the school. They believe the average GPA is skewed too high by teachers giving too many A's and B's and by not enough students receiving C's, D's, and F's. If the administrators want to ensure that grade inflation is minimized, which of these quantities would be important to bring close to 2.0

Questions 12-13 refer to the following information.
In a recent election in a European country, the political parties divided the vote among the Social Democrats, the Christian Democrats, the Socialists, and the Green Party.

12. If women provided 60% of the total votes for the Green, Socialist, and Christian Democrat parties and if males and females each represent 50% of the country's voters, what percent of the Social Democrat vote was from men?

13. The country's constitution states that in order for a party to come to power, it must have a majority of the votes. The constitution also states that the seats in the parliament are allocated proportionally to each party based on the percentage of votes each party received. So if no one political party receives a majority of the vote, a coalition party will have to be formed from 2 or more parties to give a governing majority. Which of the following combinations of political parties from this election would NOT result in a governing coalition

Questions 14-15 refer to the following information.
300 patients at a hospital were categorized based on whether they had high or low cholesterol and on whether they had high or low blood pressure. The results are tabulated in the table below.
High Cholesterol
Low Cholesterol
Total
High Blood Pressure
40
30
70
Low Blood Pressure
50
180
230
Total
90
210
300

14. What is the probability that one of the 230 low blood pressure patients has high cholesterol?

15. What is the percent chance that one of the 300 patients will have at least one of the conditions—high cholesterol or high blood pressure

Questions 16-17 refer to the following information.
A researcher surveyed several residents in a town about the types of vehicles the residents own. The results are shown in the table below.
Car
Van
Truck/SUV
Total
Gas
104
31
43
178
Hybrid
10
1
m
n
Electric
6
3
0
9
Total
120
35
45
200

16. Jennifer and Bill were members of the group surveyed. They have a car and a van in their garage. What is the probability that both of the vehicles in their garage are hybrids?

17. What are the values of m and n in the table above