DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 13)

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Problem 1 :

Two nearby trees are perpendicular to the ground, which is flat. One of these trees is 10 feet tall and has a shadow that is 5 feet long. At the same time, the shadow of the other tree is 2 feet long. How tall, in feet, is the other tree?

A) 3

B) 4

C) 8

D) 27

Solution :

Problem 2 :

The length of a rectangle’s diagonal is 5√17 , and the length of the rectangle’s shorter side is 5. What is the length of the rectangle’s longer side?

A) √17

B) 20

C) 15√2

D) 400

Solution :

Problem 3 :

A circle has center O, and points A and B lie on the circle. The measure of arc AB is 45° and the length of arc AB is 3 inches. What is the circumference, in inches, of the circle?

A) 3

B) 6

C) 9

D) 24

Solution :

Problem 4 :

The total cost, in dollars, to rent a surfboard consists of a $25 service fee and a $10 per hour rental fee. A person rents a surfboard for t hours and intends to spend a maximum of dollar $75 to rent the surfboard. Which inequality represents this situation?

A) 10t ≤ 75

B) 10 + 25t ≤ 75

C) 25t ≤ 75

D) 25 + 10t ≤ 75

Solution :

Problem 5 :

The function g is defined by g(x) = x² + 9. For which value of x is g(x) = 25?

A) 4

B) 5

C) 9

D) 13

Solution :

Problem 6 :

A certain township consists of a 5-hectare industrial park and a 24-hectare neighborhood. The total number of trees in the township is 4,529. The equation 5x + 24y = 4,529 represents this situation. Which of the following is the best interpretation of x in this context?

A) The average number of trees per hectare in the industrial park

B) The average number of trees per hectare in the neighborhood

C) The total number of trees in the industrial park

D) The total number of trees in the neighborhood

Solution :

Problem 7 :

Which expression is equivalent to a^11/12?

A) ¹²√a¹³²

B) ¹⁴⁴√a¹³²

C) ¹²¹√a¹³²

D) ¹¹√a¹³²

Solution :

Problem 8 :

A circle has center O, and points R and S lie on the circle. In triangle ORS, the measure of ∠ROS is 88°. What is the measure of ∠RSO, in degrees? (Disregard the degree symbol when entering your answer.)

Solution :

Problem 9 :

In the given equation, c is a positive constant. Which of the following is one of the solutions to the given equation?

Solution :

Problem 10 :

A company opens an account with an initial balance of $36,100.00. The account earns interest, and no additional deposits or withdrawals are made. The account balance is given by an exponential function A, where A(t) is the account balance, in dollars, t years after the account is opened. The account balance after 13 years is $68,071.93. Which equation could define A?

A) A(t) = 36,100.00(1.05)^t

B) A(t) = 31,971.93(1.05)^t

C) A(t) = 31,971.93(0.05)^t

D) A(t) = 36,100.00(0.05)^t

Solution :

Problem 11 :

The scatterplot above shows the ticket price for a school music concert and the profit made when the ticket was sold at different prices. A quadratic model that best fits the data was drawn on the scatterplot. For a ticket price $40, which of the following is closest to the percent decrease from the actual profit to the profit predicted by the curve of best fit?

A) 25%

B) 29%

C) 40%

D) 50%

Solution :

Problem 12 :

In the xy-plane above, OP is perpendicular to PR. What is the value of k?

A) 5

B) 2√10

C) 8

D) 3√5

Solution :

Problem 13 :

A small computer monitor manufacturing company produces 10-inch and 20-inch sized monitors. The table aboveshows how many hours are required on each machine per day in order to produce the monitors. If x represents the number of 10-inch monitors and y represents the number of 20-inch monitors, which of the following systems represents all the constraints that x and y must satisfy?

x ≥ 0

y ≥ 0

x + 2y ≥ 20

2x + 3y ≥ 15

0 ≤ x ≤ 3

0 ≤ y ≤ 5

x + 2y ≤ 20

2x + 3y ≤ 15

x ≥ 0

y ≥ 0

x + 2y ≤ 20

2x + 3y ≤ 15

x ≥ 0

y ≥ 0

x + 2y = 20

2x + 3y = 15

Solution :

Problem 14 :

The triangle above was altered by increasing its base by 20 percent and decreasing its height by k percent. If these alterations decreased the area of the triangle by 16 percent, which of the following is the value of k?

A) 20

B) 25

C) 30

D) 40

Solution :

Problem 15 :

P(x) = x² – 5x + k

In the function above, k is a constant. When a polynomial P(x) is divided by x – 1, the remainder is 3. If P(x) is divided by x + 1, what is the remainder?

A) 3

B) 4

C) 7

D) 13

Solution :

Problem 16 :

The graph of the linear function f passes through the points (a, 1) and (1, b) in the xy-plane. If the slope of the graph of f is 1, which of the following is true?

A) a - b = 1

B) a + b = 1

C) a - b = 2

D) a + b = 2

Solution :

Problem 17 :

Johnny received m text messages on Friday, three less than twice as many text messages on Saturday than on Friday, and five more text messages on Sunday than on Saturday. What is the total number of text messages he received over the three days?

A) 4m + 2

B) 5m - 1

C) 4m - 2

D) 5m + 1

Solution :