SAT CollegeBoard Practice Test (1-8) Ratios and Proportions

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1. (Test1/Q 21/Calculator)

Dreams Recalled during One Week $$\begin{array}{|l|c|c|c|c|} \hline & \text{None }& \text{1 to 4} & 5 \text{ or more} &\text{ Total }\\ \hline \hline \text{Group }\mathrm{X} & 15 & 28 & 57 & 100 \\ \hline \text{Group } \mathrm{Y} & 21 & 11 & 68 & 100 \\ \hline \text{Total} & 36 & 39 & 125 & 200 \\ \hline \end{array}$$ The data in the table above were produced by a sleep researcher studying the number of dreams people recall when asked to record their dreams for one week. Group X consisted of 100 people who observed early bedtimes, and Group Y consisted of 100 people who observed later bedtimes. If a person is chosen at random from those who recalled at least 1 dream, what is the probability that the person belonged to Group Y? A) $\frac{68}{100}$ B) $\frac{79}{100}$ C) $\frac{79}{164}$ D) $\frac{164}{200}$

2. (Test2/Q 2/Calculator)

A quality control manager at a factory selects 7 lightbulbs at random for inspection out of every 400 lightbulbs produced. At this rate, how many lightbulbs will be inspected if the factory produces 20,000 lightbulbs? A) 300 B) 350 C) 400 D) 450

3. (Test2/Q 16/Calculator)

Results on the Bar Exam of Law School Graduates $$\begin{array}{|l|c|c|}\hline & \text{Passed bar exam }& \text{Did not pass bar exam} \\ \hline \text{Took review course }& 18 & 82 \\ \hline \text{ Did not take review course} & 7 & 93 \\ \hline \end{array}$$ The table above summarizes the results of 200 law school graduates who took the bar exam. If one of the surveyed graduates who passed the bar exam is chosen at random for an interview, what is the probability that the person chosen did not take the review course? A) $\frac{18}{25}$ B) $\frac{7}{25}$ C) $\frac{25}{200}$ D) $\frac{7}{200}$

4. (Test $3 / Q 2 /$ Calculator)

$$\begin{array}{|l||c|c||c|}\hline & \text{ Age } & \text{Age}&\text{Total} \\ \text{Gender} & \text{Under 40} & \text{40 or older} & \\ \hline \hline \text{Male }& 12 & 2 & 14 \\ \hline \text{Female} & 8 & 3 & 11 \\ \hline \hline \text{Total }& 20 & 5 & 25 \\ \hline \end{array}$$ The table above shows the distribution of age and gender for 25 people who entered a contest. If the contest winner will be selected at random, what is the probability that the winner will be either a female under age 40 or a male age 40 or older? A) $\frac{4}{25}$ B) $\frac{10}{25}$ C) $\frac{11}{25}$ D) $\frac{16}{25}$

5. (Test $3 / Q 29 /$ Calculator)

$$\begin{array}{|l|c|c|}\hline & \text{Handedness }&\text{Handedness}\\ \hline \text{Gender} & \text{Left} & \text{Right }\\ \hline \text{Female} & & \\ \hline \text{Male} & & \\ \hline \text{Total} & 18 & 122 \\ \hline \end{array}$$ The incomplete table above summarizes the number of left-handed students and right-handed students by gender for the eighth-grade students at Keisel Middle School. There are 5 times as many right-handed female students as there are left-handed female students, and there are 9 times as many right-handed male students as there are left-handed male students. If there is a total of 18 left-handed students and 122 right-handed students in the school, which of the following is closest to the probability that a right-handed student selected at random is female? (Note: Assume that none of the eighth-grade students are both right-handed and left-handed.) A) $0.410$ B) $0.357$ C) $0.333$ D) $0.250$

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6. (Test4/Q 9/Calculator)

Number of Registered Voters in the United States in 2012, in Thousands The table above shows the number of registered voters in 2012 in thousands, in four geographic regions and five age groups. Based on the table, if a registered voter who was 18 to 44 years old in 2012 is chosen at random, which of the following is closest to the probability that the registered voter was from the Midwest region? A) $0.10$ B) $0.25$ C) $0.40$ D) $0.75$

7. (Test5/Q 14/Calculator)

In a survey, 607 general surgeons and orthopedic surgeons indicated their major professional activity. The results are summarized in the table above. If one of the surgeons is selected at random, which of the following is closest to the probability that the selected surgeon is an orthopedic surgeon whose indicated professional activity is research? A) $0.122$ B) $0.196$ C) $0.318$ D) $0.379$

8. (Test5/Q 31/Calculator)

Horsepower and watts are units of measure of power. They are directly proportional such that 5 horsepower is equal to 3730 watts. How much power, in watts, is equal to 2 horsepower? 9. (Test1/Q 6/Calculator) $$\begin{array}{|rl|}\hline 1 \text{decagram }&=10 \text{grams} \\ 1,000 \text{milligrams}&=1\text{gram }\\\hline \end{array}$$ A hospital stores one type of medicine in 2-decagram containers. Based on the information given in the box above, how many 1-milligram doses are there in one 2 -decagram container? A) $0.002$ B) 200 C) 2,000 D) 20,000 10. (Test1/Q $27 /$ Calculator) A square field measures 10 meters by 10 meters. Ten students each mark off a randomly selected region of the field; each region is square and has side lengths of 1 meter, and no two regions overlap. The students count the earthworms contained in the soil to a depth of 5 centimeters beneath the ground's surface in each region. The results are shown in the table below. $$\begin{array}{|c|c|c|c|} \hline \text{Region }& \text{Number of earthworms }& \text{Region} & \text{Number of earthworms} \\ \hline A & 107 & F & 141 \\ \hline B & 147 & G & 150 \\ \hline C & 146 & H & 154 \\ \hline D & 135 & I & 176 \\ \hline E & 149 & J & 166 \\ \hline \end{array}$$ Which of the following is a reasonable approximation of the number of earthworms to a depth of 5 centimeters beneath the ground's surface in the entire field? A) 150 B) 1,500 C) 15,000 D) 150,000 11. (Test1/Q 31/Calculator) Wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour. Based on this information, what is a possible amount of time, in hours, that it could take Wyatt to husk 72 dozen ears of corn? 12. (Test1/Q 34/Calculator) A local television station sells time slots for programs in 30 -minute intervals. If the station operates 24 hours per day, every day of the week, what is the total number of 30 -minute time slots the station can sell for Tuesday and Wednesday? 13. (Test2/Q 4/Calculator) The amount of money a performer earns is directly proportional to the number of people attending the performance. The performer earns $\$ 120$ at a performance where 8 people attend. How much money will the performer earn when 20 people attend a performance? A) $\$ 960$ B) $\$ 480$ C) $\$ 300$ D) $\$ 240$ 14. (Test2/Q 5/Calculator) The amount of money a performer earns is directly proportional to the number of people attending the performance. The performer earns $\$ 120$ at a performance where 8 people attend. The performer uses $43 \%$ of the money earned to pay the costs involved in putting on each performance, The rest of the money earned is the performer's profit. What is the profit the performer makes at a performance where 8 people attend? A) $\$ 51.60$ B) $\$ 57,00$ C) $\$ 68.40$ D) $\$ 77.00$ 15. (Test2/Q $15 /$ Calculator) The distance traveled by Earth in one orbit around the Sun is about $580,000,000$ miles. Earth makes one complete orbit around the Sun in one year. Of the following, which is closest to the average speed of Earth, in miles per hour, as it orbits the Sun? A) 66,000 B) 93,000 C) 210,000 D) 420,000 16. (Test3/Q $19 /$ Calculator) Graphene, which is used in the manufacture of integrated circuits, is so thin that a sheet weighing one ounce can cover up to 7 football fields. If a football field has an area of approximately $1 \frac{1}{3}$ acres, about how many acres could 48 ounces of graphene cover? A) 250 B) 350 C) 450 D) 1,350 17. (Test $4 / Q 20 /$ No Calculator) The mesosphere is the layer of Earth's atmosphere between 50 kilometers and 85 kilometers above Earth's surface. At a distance of 50 kilometers from Earth's surface, the temperature in the mesosphere is $-5^{\circ}$ Celsius, and at a distance of 80 kilometers from Earth's surface, the temperature in the mesosphere is $-80^{\circ}$ Celsius. For every additional 10 kilometers from Earth's surface, the temperature in the mesosphere decreases by $k^{\circ}$ Celsius, where $k$ is a constant. What is the value of $k$ ? 18. (Test4/Q 5/Calculator) The density of an object is equal to the mass of the object divided by the volume of the object. What is the volume, in milliliters, of an object with a mass of 24 grams and a density of 3 grams per milliliter? A) $0.125$ B) 8 C) 21 D) 72

19. (Test $4 / \mathrm{Q} 7 /$ Calculator)

The table above represents the 50 movies that had the greatest ticket sales in 2012 , categorized by movie type and Motion Picture Association of America (MPAA) rating. What proportion of the movies are comedies with a PG-13 rating? A) $\frac{2}{25}$ B) $\frac{9}{50}$ C) $\frac{2}{11}$ D) $\frac{11}{25}$

20. (Test $4 / Q 33 /$ Calculator)

The pes, a Roman measure of length, is approximately equal to $11.65$ inches. It is also equivalent to 16 smaller Roman units called digits. Based on these relationships, 75 Roman digits is equivalent to how many feet, to the nearest hundredth? (12 inches = 1 foot)

21. (Test $4 / Q$ 34/Calculator)

In a study of bat migration habits, 240 male bats and 160 female bats have been tagged. If 100 more female bats are tagged, how many more male bats must be tagged so that $\frac{3}{5}$ of the total number of bats in the study are male?

22. (Test $6 / Q 26 /$ Calculator)

A gear ratio $r s$ is the ratio of the number of teeth of two connected gears. The ratio of the number of revolutions per minute (rpm) of two gear wheels is s:r. In the diagram below, Gear $A$ is turned by a motor. The turning of Gear A causes Gears B and C to turn as well. If Gear $A$ is rotated by the motor at a rate of $100 \mathrm{rpm}$, what is the number of revolutions per minute for Gear C? A) 50 B) 110 C) 200 D) 1,000

23. (Test7/Q 31/Calculator)

In 1854 , during the California gold rush, each ounce of gold was worth $\$ 20$, and the largest known mass of gold found in California was worth $\$ 62,400$ in that year. What was the weight, in pounds, of this mass of gold? (16 ounces $=1$ pound)

24. (Test $8 / Q 16 /$ Calculator)

Number of Adults Contracting Colds $$\begin{array}{|l|c|c|c|}\hline & \text{Cold} & \text{No cold} & \text{Total} \\ \hline \text{Vitamin C} & 21 & 129 & 150 \\ \hline \text{Sugar pill} & 33 & 117 & 150 \\ \hline \text{Total} & 54 & 246 & 300 \\ \hline \end{array}$$ The table shows the results of a research study that investigated the therapeutic value of vitamin $\mathrm{C}$ in preventing colds. A random sample of 300 adults received either a vitamin C pill or a sugar pill each day during a 2-week period, and the adults reported whether they contracted a cold during that time period. What proportion of adults who received a sugar pill reported contracting a cold? A) $\frac{11}{18}$ B) $\frac{11}{50}$ C) $\frac{9}{50}$ D) $\frac{11}{100}$

25. (Test8/Q 31/Calculator)

There are two atoms of hydrogen and one atom of oxygen in one molecule of water. How many atoms of hydrogen are there in 51 molecules of water?

26. (Test6/Q 9/Calculator)

The total area of a coastal city is 92.1 square miles, of which 11.3 square miles is water. If the city had a population of 621,000 people in the year 2010, which of the following is closest to the population density, in people per square mile of land area, of the city at that time? A) 6,740 B) 7,690 C) 55,000 D) 76,000

Answer

1 C $\quad$ Explanation
2 B $\quad$ Explanation
3 B $\quad$ Explanation
4 B $\quad$ Explanation
5 A $\quad$ Explanation
6 B $\quad$ Explanation
7 A $\quad$ Explanation
8 1492 $\quad$ Explanation
9 D $\quad$ Explanation
10 C $\quad$ Explanation
11 [4,6] $\quad$ Explanation
12 96 $\quad$ Explanation
13 C $\quad$ Explanation
14 C $\quad$ Explanation
15 A $\quad$ Explanation
16 C $\quad$ Explanation
17 25 $\quad$ Explanation
18 B $\quad$ Explanation
19 A $\quad$ Explanation
20 4.55 $\quad$ Explanation
21 150 $\quad$ Explanation
22 C $\quad$ Explanation
23 195 $\quad$ Explanation
24 B $\quad$ Explanation
25 102 $\quad$ Explanation
26 B $\quad$ Explanation