DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 13)

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 :

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