The s a t® Practice Test #6 Math Test—Calculator

Questions 17 through 19 refer to the following information

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Questions 17 through 19 refer to the following information.

When designing a stairway, an architect can use the riser‑tread formula

2 h plus d equals 25, where h is the riser height, in inches, and d is the tread depth, in inches. For any given stairway, the riser heights are the same and the tread depths are the same for all steps in that stairway.

The number of steps in a stairway is the number of its risers. For example, there are 5 steps in the stairway in the following figure. The total rise of a stairway is the sum of the riser heights as shown in the figure.

Begin skippable figure description.

The figure presents a drawing of the side view of a stairway that has 5 steps. The height of the stairway is labeled “total rise.” The height of each step is labeled “riser height, h,” and the width of each step is labeled “tread depth, d.” Note: the figure is not drawn to scale.

End skippable figure description.

Question 17.

Based on the given information, which of the following expresses the riser height in terms of the tread depth?

A. h equals one‑half, times, open parenthesis, 25 plus d, close parenthesis

B. h equals one‑half, times, open parenthesis, 25 minus d, close parenthesis

C. h equals negative one‑half, times, open parenthesis, 25 plus d, close parenthesis

D. h equals negative one‑half, times, open parenthesis, 25 minus d, close parenthesis

Question 18.

Some building codes require that, for indoor stairways, the tread depth must be at least 9 inches and the riser height must be at least 5 inches. According to the riser‑tread formula (refer to the given information), which of the following inequalities represents the set of all possible values for the riser height that meets this code requirement?

A. 0 is less than or equal to h, which is less than or equal to 5

B. h is greater than or equal to 5

C. 5 is less than or equal to h, which is less than or equal to 8

8 is less than or equal to h, which is less than or equal to 16

Question 19.

An architect wants to use the riser‑tread formula (refer to the given information) to design a stairway with a total rise of 9 feet, a riser height between 7 and 8 inches, and an odd number of steps. With the architect’s constraints, which of the following must be the tread depth, in inches, of the stairway? (1 foot equals 12 inches.)

A. 7.2

B. 9.5

C. 10.6

D. 15

Question 20.

What is the sum of the solutions to

open parenthesis, x minus 6, close parenthesis, times, open parenthesis, x plus 0.7, close parenthesis, equals 0?

A. negative 6.7

B. negative 5.3

C. 5.3

D. 6.7

Question 21.

A study was done on the weights of different types of fish in a pond. A random sample of fish were caught and marked in order to ensure that none were weighed more than once. The sample contained 150 largemouth bass, of which 30% weighed more than 2 pounds. Which of the following conclusions is best supported by the sample data?

A. The majority of all fish in the pond weigh less than 2 pounds.

B. The average weight of all fish in the pond is approximately 2 pounds.

C. Approximately 30% of all fish in the pond weigh more than 2 pounds.

D. Approximately 30% of all largemouth bass in the pond weigh more than 2 pounds.

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