Question 1 refers to the following table:
Top Three Majors at Greenly Community College
Percentage of Class in Major | |||
History | Engineering | Spanish | |
Freshman | 30 | 25 | 17 |
Sophomore | 33 | 21 | 18 |
Junior | 36 | 22 | 14 |
Senior | 29 | 28 | 19 |
1. Which of the following are the lowest terms for expressing the ratio of the percentage of juniors majoring in Spanish to the percentage of juniors majoring in history?
- 14:36
- 14:22
- 7:11
- 7:18
- 14:18
2. If a restaurant’s salad dressing is made entirely of oil and vinegar at a ratio of 3/4 cup oil to ¼ cup vinegar, how many cups of vinegar are there in 6 cups of salad dressing?
- 1/2
- 1 1/2
- 1 3/4
- 2 1/4
- 2 1/2
3. A classroom has 15 boys and 13 girls. If 10 more girls join the class, what is the ratio of girls to boys?
- 15:23
- 13:15
- 10:15
- 23:15
4. The ratio of left-handed to right-handed ballplayers on the girls’ softball team is 2:3. If there are 12 left-handed players on the team, how many girls are on the roster in all?
- a. 18
- b. 24
- c. 30
- d. 32
5. The ratio of blue food coloring to yellow food coloring used in making green cake frosting is 3 to 2. If 18 drops of blue food coloring are used, how many drops of yellow food coloring are needed?
- a. 2
- b. 6
- c. 8
- d. 12
6. Hunter planted a combination of tomatoes, broccoli, and bell peppers in a ratio of 3:2:1 in his garden. If the garden had a total of 72 plants, how many tomatoes are in his garden?
- 12
- 24
- 32
- 36
7. Which of the following expressions represents the ratio of the circumference of a circle to its area?
- 1:πr^{2}
- 1:πr^{2}/2π
- 1:2πr/r^{2}
- 1:2πr^{1/2}
- 1:r/2
Question 8 is based on the following figure.
8. In the figure, A, B, and C are points on the number line, where O is the origin. What is the ratio of the distance BC to distance AB?
- 3:5
- 8:5
- 8:11
- 3:11
- 8:6
9. Approximately 40,000 obstetricians are registered in the U.S. There are an estimated 440,000 midwives in the country. What is the ratio of midwives to obstetricians?
- 8:1
- 12:1
- 11:1
- 7:1
10. Two-thirds of the students in Mr. Garcia’s class are boys. If there are 27 students in the class, how many of them are girls?
- 1
- 9
- 12
- 20
11. A solution contains 6% calcium. How many milliliters of solution can be made from 50 ml of calcium?
- 833
- 952
- 1054
- 2000
Answers and Explanations
1. D: The percentage of juniors majoring in Spanish is 14. The percentage of juniors majoring in history is 36. The ratio 14:36 in lowest terms is 7:18.
2. B: Determine what the ratio of vinegar to the salad dressing as a whole is. Vinegar is 1/4 of a cup and the salad dressing as a whole is 1/4 cup vinegar plus 3/4 cup oil, or 1 cup. Thus, vinegar is 1/4 of the salad dressing. Therefore, 1/4 of 6 cups is 3/2 or 1 1/2 cups of vinegar.
3. D: First, calculate how many girls there will be after 10 more join the class: 13 + 10 = 23.
Then, express the number of girls compared to boys as a ratio: 23:15.
4. C: The ratio of left- to right-handed players will be proportional to the ratio 2:3. Therefore, 2/3=12/R , so that by cross-multiplying we get 2R = 36 or R = 18 right-handed players. The total number on the roster is therefore 12 + 18 = 30.
5. D: Set up and solve a proportion, as shown below, where is the number of drops of yellow food coloring. To solve the proportion, cross-multiply:
3/2=18/x
3x = 36
x = 12, Choice D.
6. D: A ratio of 3:2:1 gives a whole of 6 (in other words, in each set of 6 plants, there are 3 tomato, 2 broccoli, and 1 bell pepper plants). It takes 12 sets of 6 plants to total 72 plants. To determine how many tomatoes Hunter planted, multiply 3 by 12, for a total of 36, Choice D.
7. E. The area of the circle is πr^{2} while the circumference is 2πr. Taking the ratio of these two expressions and reducing gives: 2πr:πr^{2}=1:r/2.
8. D: Since the figure represents the number line, the distance from point A to point B will be the difference B – A, which is 5 – (-6) = 11. Likewise, the distance from point B to point C will be the difference C – B, which is 8 – 5 = 3. So the ratio of the distances BC to AB will be 3:11.
9. C: To find the ratio, divide the number of midwives by the number of obstetricians. This yields 440,000/40,000 = 11. Therefore, the ratio is 11 to 1.
10. B: You are given the total number of students in the class and the fraction of students who are boys. With this information, you can determine the number of boys by multiplying 2/3 by 27. You will find that there are 18 boys in the class. You can then find the number of girls by subtracting the number of boys from the total number of students: 27 – 18 = 9.
11. A: Set up a ratio of 6/100=50/x , with x equal to the total number of milliliters of solution. Then, solve by cross multiplying: 6x = 5000, or x = 5000/6 = 833, Choice A.