which of the following describes a proportional relationship

ATI TEAS 7

TEAS Practice Math Test

1. Which of the following describes a proportional relationship?

A. Johnathan opens a savings account with an initial deposit of $150 and deposits $125 per month
B. Bruce pays his employees $12 per hour worked during the month of December, as well as a $250 bonus
C. Alvin pays $28 per month for his phone service plus $0.07 for each long-distance minute used
D. Kevin drives 65 miles per hour

Correct answer: A

Rationale: A proportional relationship is one in which two quantities vary directly with each other. In choice A, the amount deposited per month is directly proportional to the initial deposit. The relationship can be represented as y = 125x + 150, where x is the number of months and y is the total amount in the account. Choices B and C involve additional fixed amounts or variable costs that do not maintain a constant ratio, making them non-proportional relationships. Choice D refers to a constant speed of driving, which is not a proportional relationship as it does not involve varying quantities that change in direct proportion.

2. A patient is prescribed 5 mg of medication per kilogram of body weight. If the patient weighs 60 kg, how many milligrams of medication should the patient receive?

A. 100 mg
B. 150 mg
C. 300 mg
D. 400 mg

Correct answer: C

Rationale: The correct calculation to determine the medication dosage for a patient weighing 60 kg is: 5 mg/kg x 60 kg = 300 mg. Therefore, the patient should receive 300 mg of medication. Choice A (100 mg) is incorrect as it does not account for the patient's weight. Choice B (150 mg) is incorrect as it miscalculates the dosage. Choice D (400 mg) is incorrect as it overestimates the dosage based on the patient's weight.

3. Juan wishes to compare the percentages of time he spends on different tasks during the workday. Which of the following representations is the most appropriate choice for displaying the data?

A. Line plot
B. Bar graph
C. Line graph
D. Pie chart

Correct answer: D

Rationale: A pie chart is the most appropriate choice for displaying the percentages of time spent on different tasks during the workday because it visually represents parts of a whole. In this case, each task's percentage represents a part of the entire workday, making a pie chart an ideal way to compare these percentages. Line plots, bar graphs, and line graphs are not suitable for showing percentages of a whole; they are more commonly used for tracking trends, comparing values, or showing relationships between variables but do not efficiently represent parts of a whole like a pie chart does.

4. "is" in math means what?

A. Equals
B. Multiply
C. Subtract
D. Add

Correct answer: A

Rationale: In mathematics, "is" signifies equality, meaning that the values or expressions on both sides of the equation are the same. For example, in the equation 2+2=4, the phrase "2 + 2 is 4" indicates that the sum of 2 and 2 equals 4. "Multiply" refers to the operation of combining two numbers to obtain a product. For instance, in the expression 3×4, we multiply 3 by 4 to get 12. "Subtract" means to take one number away from another, resulting in a difference. For example, in 5−2, we subtract 2 from 5 to get 3. "Add" refers to the operation of combining two numbers to get a sum. For example, in 2+3, we add 2 and 3 to get 5.

5. University Q has an extremely competitive nursing program. Historically, 3/4 of the students in each incoming class major in nursing, but only 1/3 of those who major in nursing actually complete the program. If this year’s incoming class has 100 students, how many students will complete the nursing program?

A. 75
B. 20
C. 25
D. 5

Correct answer: C

Rationale: Out of 100 students, 3/4 major in nursing, which is 75 students (100 * 3/4 = 75). Among these 75 students, only 1/3 will complete the program. Therefore, 1/3 of 75 is 25. Hence, 25 students will complete the nursing program. Choice A (75) is incorrect because this represents the number of students majoring in nursing, not completing the program. Choices B (20) and D (5) are incorrect as they do not align with the calculation based on the given fractions and total number of students.