Problem Solving 1
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Câu 1. Each 3.0-ounce serving of cheddar cheese and each 1.2-ounce serving of tuna provides about 1 microgram of vitamin B12. If a total of 1.7 micrograms of vitamin B12 are consumed from eating x ounces of cheese and y ounces of tuna, which equation best represents this situation?
- A. 3.0x + 1.2y = 1.7
- B. 0.33x + 0.83y = 1.7
- C. 0.83x + 0.33y = 1.7
- D. 1.2x + 3.0y = 1.7
Câu 2. A market researcher selected 200 people at random from a group of people who indicated that they liked a certain book. The 200 people were shown a movie based on the book and then asked whether they liked or disliked the movie. Of those surveyed, 95% said they disliked the movie. Which of the following inferences can appropriately be drawn from this survey result?
- A. At least 95% of people who go see movies will dislike this movie.
- B. At least 95% of people who read books will dislike this movie.
- C. Most people who dislike this book will like this movie.
- D. Most people who like this book will dislike this movie.
Câu 3. A polling agency recently surveyed 1,000 adults who were selected at random from a large city and asked each of the adults, “Are you satisfied with the quality of air in the city?”. Of those surveyed, 78 percent responded that they were satisfied with the quality of air in the city. Based on the results of the survey, which of the following statements must be true? 1. Of all adults in the city, 78 percent are satisfied with the quality of air in the city. 2. If another 1,000 adults selected at random from the city were surveyed, 78 percent of them would report they are satisfied with the quali...
- A. None
- B. II only
- C. I and II only
- D. I and III only
Câu 4. A market researcher selected 200 people at random from a group of people who indicated that they liked a certain book. The 200 people were shown a movie based on the book and then asked whether they liked or disliked the movie. Of those surveyed, 95% said they disliked the movie. Which of the following inferences can appropriately be drawn from this survey result?
- A. At least 95% of people who go see movies will dislike this movie.
- B. At least 95% of people who read books will dislike this movie.
- C. Most people who dislike this book will like this movie.
- D. Most people who like this book will dislike this movie.
Câu 5. At a conference, there are a total of 275 attendees. Each attendee is assigned to either group A, group B, or group C. If one of these attendees is selected at random, the probability of selecting an attendee who is assigned to group A is 0.44 and the probability of selecting an attendee who is assigned to group B is 0.24. How many attendees are assigned to group C?
Câu 6. Where do people get most of their medical information? Source Percent of those surveyed Doctor 63% Internet 13% Magazines/brochures 9% Pharmacy 6% Television 2% Other/none of the above 7% The table above shows a summary of 1,200 responses to a survey question. Based on the table, how many of those surveyed get most of their medical information from either a doctor or the Internet?
- A. 865
- B. 887
- C. 912
- D. 926
Câu 7. The weights, in pounds, for 15 horses in a stable were reported, and the mean, median, range, and standard deviation for the data were found. The horse with the lowest reported weight was found to actually weigh 10 pounds less than its reported weight. What value remains unchanged if the four values are reported using the corrected weight?
- A. Mean
- B. Median
- C. Range
- D. Standard deviation
Câu 8. A partially filled container containing 28 milliliters of water is placed under a leaky faucet that produces one 0.05-milliliter drop of water every 5 seconds. Until the container is full, which of the following can be used to represent the volume v, in milliliters, of water in the container t seconds after it is placed under the faucet, where t is a multiple of 5?
- A. v = 5t
- B. v = 0.25t + 28
- C. v = 0.01t + 28
- D. v = 0.05t + 28
Câu 9. The scatterplot above shows the number of visitors to a railroad museum in Pennsylvania each year from 1968 to 1980, where t is the number of years since 1968 and n is the number of visitors. A line of best fit is also shown. Which of the following could be an equation of the line of best fit shown?
- A. n = 16, 090 + 4, 680t
- B. n = 4, 690 + 16, 090t
- C. n = 16, 090 + 9, 060t
- D. n = 9, 060 + 16, 090t
Câu 10. Near the end of a US cable news show, the host invited viewers to respond to a poll on the show’s website that asked, “Do you support the new federal policy discussed during the show?” At the end of the show, the host reported that 28% responded “Yes,” and 70% responded “No.” Which of the following best explains why the results are unlikely to represent the sentiments of the population of the United States?
- A. The percentages do not add up to 100%, so any possible conclusions from the poll are invalid.
- B. Those who responded to the poll were not a random sample of the population of the United States.
- C. There were not 50% “Yes” responses and 50% “No” responses.
- D. The show did not allow viewers enough time to respond to the poll.
Câu 11. The dot plot represents the 15 values in data set A. Data set B is created by adding 56 to each of the values in data set A. Which of the following correctly compares the medians and the ranges of data sets A and B?
- A. The median of data set B is equal to the median of data set A, and the range of data set B is equal to the range of data set A.
- B. The median of data set B is equal to the median of data set A, and the range of data set B is greater than the range of data set A.
- C. The median of data set B is greater than the median of data set A, and the range of data set B is equal to the range of data set A.
- D. The median of data set B is greater than the median of data set A, and the range of data set B is greater than the range of data set A.
Câu 12. Data set X: 5, 9, 9, 13 Data set Y: 5, 9, 9, 13, 27 The lists give the values in data sets X and Y. Which statement correctly compares the mean of data set X and the mean of data set Y?
- A. The mean of data set X is greater than the mean of data set Y.
- B. The mean of data set X is less than the mean of data set Y.
- C. The means of data set X and data set Y are equal.
- D. There is not enough information to compare the means.
Câu 13. Data set F consists of 55 integers between 170 and 290. Data set G consists of all the integers in data set F as well as the integer 10. Which of the following must be less for data set F than for data set G? I. The mean II. The median
- A. I only
- B. II only
- C. I and II
- D. Neither I nor II
Câu 14. Based on a random sample from a population, a researcher estimated that the mean value of a certain variable for the population is 20.5, with an associated margin of error of 1. Which of the following is the most appropriate conclusion?
- A. It is plausible that the actual mean value of the variable for the population is between 19.5 and 21.5.
- B. It is not possible that the mean value of the variable for the population is less than 19.5 or greater than 21.5.
- C. Every value of the variable in the population is between 19.5 and 21.5.
- D. The mean value of the variable for the population is 20.5.
Câu 15. Data set A: 5, 5, 5, 5, 5, 5, 5, 5, 5 Data set B: 5, 5, 5, 5, 5, 5, 5, 5, 5, 100 Which of the following statements about the means and medians of data set A and data set B is true?
- A. Only the means are different.
- B. Only the medians are different.
- C. Both the means and the medians are different.
- D. Neither the means nor the medians are different.
Câu 16. High school 2008 2009 2010 2011 2012 Foothill 87 80 75 76 70 Valley 44 54 65 76 82 Total 131 134 140 152 152 The table above shows the number of students from two different high schools who completed summer internships in each of five years. No student treated both schools. Which of the following statements are true about the number of students who completed summer internships for the 5 years shown? I. The mean number from Foothill High School is greater than the mean number from Valley High School. II. The median number from Foothill High School is greater than the median number from Valley H...
- A. I only
- B. II only
- C. I and II
- D. Neither I nor II
Câu 17. Candidate Votes Angel Cruz 483 Terry Smith 320 The table shows the results of a poll. A total of 803 voters selected at random were asked which candidate they would vote for in the upcoming election. According to the poll, if 6,424 people vote in the election, by how many votes would Angel Cruz be expected to win?
- A. 163
- B. 1,304
- C. 3,864
- D. 5,621
Câu 18. During the first 8.00 seconds after a car started moving, its speed increased to 11.0 meters per second. From 8.00 seconds to 14.0 seconds after the car started moving, its speed increased from 11.0 meters per second to 23.0 meters per second. To the nearest hundredth, what is the positive difference between the average rate of change of the speed of the car, in meters per second per second, during the first 8.00 seconds after the car started moving and the average rate of change of the speed of the car, in meters per second per second, from 8.00 seconds to 14.0 seconds after the car started m...
Câu 19. According to the 2010 Census, the adult population aged 18 years or greater of the United States in 2010 was 234,564,071. In 2010, a survey was conducted among a randomly chosen sample of adults aged 18 years or greater in the United States about their preference to live in a warm climate or a cool climate. The table below displays a summary of the survey results. Climate Preferences Warm Cool No preference Total 18-35 years old 295 168 45 508 36-50 years old 246 123 41 410 51-65 years old 238 117 48 403 Greater than 65 years old 137 78 64 279 Total 916 486 198 1,600 Which of the following is...
- A. 4%
- B. 5%
- C. 10%
- D. 18%
Câu 20. To estimate the proportion of a population that has a certain characteristic, a random sample was selected from the population. Based on the sample, it is estimated that the proportion of the population that has the characteristic is 0.49, with an associated margin of error of 0.04. Based on this estimate and margin of error, which of the following is the most appropriate conclusion about the proportion of the population that has the characteristic?
- A. It is plausible that the proportion is between 0.45 and 0.53.
- B. It is plausible that the proportion is less than 0.45.
- C. The proportion is exactly 0.49.
- D. It is plausible that the proportion is greater than 0.53.
Câu 21. Percent of residents who earned a bachelor’s degree or higher: State Percent of residents State A 21.9% State B 27.9% State C 25.9% State D 19.4% State E 30.1% State F 36.4% State G 35.5% A survey was given to residents of all 50 states asking if they had earned a bachelor’s degree or higher. The results from 7 of the states are given in the table above. The median percent of residents who earned a bachelor’s degree or higher for all 50 states was 26.95%. What is the difference between the median percent of residents who earned a bachelor’s degree or higher for these 7 states and the median fo...
- A. 0.05%
- B. 0.95%
- C. 1.22%
- D. 7.45%
Câu 22. In State X, Mr. Camp’s eighth-grade class consisting of 26 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average eighth-grade class size in the state is 26. If the students in Mr. Camp’s class are representative of students in the state’s eighth-grade classes and there are 1,800 eighth-grade classes in the state, which of the following best estimates the number of eighth-grade students in the state who have fewer than two siblings?
- A. 16,200
- B. 23,400
- C. 30,600
- D. 46,800
Câu 23. The table below shows the distribution of US states according to whether they have a state-level sales tax and a state-level income tax. 2013 State-level taxes state sales tax no state sales tax state income tax 39 4 no state income tax 6 1 To the nearest tenth of a percent, what percent of states with a state-level sales tax do not have a state-level income tax?
- A. 6.0%
- B. 12.0%
- C. 13.3%
- D. 14.0%
Câu 24. The scatterplot above shows the size x and the sale price y of 25 houses for sale in Town H. Which of the following could be an equation for a line of best fit for the data?
- A. y = 200x + 100
- B. y = 100x + 100
- C. y = 50x + 100
- D. y = 100x
Câu 25. 1 Star 2 Stars 3 Stars 4 Stars Total Employee A 16 49 72 8 145 Employee B 4 10 22 34 70 Employee C 8 56 45 16 125 Employee D 22 42 84 12 160 Total 50 157 223 70 500 A supervisor at a call center reviewed 500 calls taken by four employees and rated the employees’ performance on each call on a scale from 1 star to 4 stars. The ratings for each employee are shown in the table above. According to the table, to the nearest whole percent, what percent of Employee A’s calls received a rating of 1 star?
- A. 3%
- B. 11%
- C. 16%
- D. 32%
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