which of the following describes a proportional relationship
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ATI TEAS 7

TEAS Practice Math Test

1. Which of the following describes a proportional relationship?

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 dry cleaner charges $3 per shirt, $6 per pair of pants, and an extra $5 per item for mending. Annie drops off 5 shirts and 4 pairs of pants, 2 of which need mending. Assuming the cleaner charges an 8% sales tax, what will be the amount of Annie’s total bill?

Correct answer: C

Rationale: To determine the total cost before tax, calculate: 5 shirts × $3/shirt + 4 pants × $6/pair of pants + 2 items mended × $5/item mended = $49. Now, multiply this amount by 1.08 to include the 8% sales tax: $49 × 1.08 = $52.92. Therefore, Annie's total bill will be $52.92. Choice A, $45.08, is incorrect as it does not include the correct calculation for the total bill. Choice B, $49.00, is wrong because it is the total cost before tax and does not consider the added sales tax. Choice D, $88.20, is incorrect as it does not accurately calculate the total bill including the sales tax.

3. As the number of credit hours a student takes in a semester increases, the amount of tuition, the amount of access fees, and the number of student loans available also increase. Which of the following is the independent variable?

Correct answer: B

Rationale: The correct answer is the number of credit hours. In this scenario, the number of credit hours is the independent variable because it is the factor that is intentionally changed or manipulated. The amount of tuition, access fees, and student loans are dependent variables as they are influenced by the number of credit hours a student takes. The number of credit hours drives the changes in the other factors, making it the independent variable.

4. What defines rational and irrational numbers?

Correct answer: A

Rationale: Rational numbers are those that can be written as a simple fraction, including whole numbers and decimals that either terminate or repeat. Irrational numbers, on the other hand, cannot be expressed as fractions. Choice B is incorrect because not all rational numbers necessarily terminate or repeat. Choice C is incorrect as it oversimplifies the concept of rational and irrational numbers by only considering whole numbers and decimals. Choice D is incorrect as it inaccurately defines rational and irrational numbers solely based on decimals terminating or repeating, excluding the broader category of fractions.

5. How many kiloliters are in 147 liters?

Correct answer: A

Rationale: To convert liters to kiloliters, divide by 1000 since there are 1000 liters in a kiloliter. Therefore, 147 liters = 0.147 kiloliters. Choice B is incorrect as it incorrectly moves the decimal point. Choices C and D are significantly larger than the correct answer, indicating an incorrect conversion factor used.

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