DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 9)

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Problem 1 :

Four values of x and their corresponding values of g(x) are shown in the table above for the linear function g. The equation g(x) = cx + d defines function g, and c and d are constants. What is the value of c + d?

A) -23

B) 69

C) 92

D) 115

Solution :

Problem 2 :

114, 109, 106, 111

A data set consists of 5 positive integers greater than 101. What is the value of the smallest integer in the data set if the mean of the entire data set is an integer that is less than the mean of the four integers from the data set shown above?

Solution :

Problem 3 :

A teacher awards points to a class based on completed assignments. He gives 5 points per assignment for the first 50 completed assignments and 3 points for each additional completed assignment beyond 50. When a ≥ 50, which function g gives the total number of points earned by the class for a completed assignments?

A) g(a) = 3a + 5

B) g(a) = 3a + 100

C) g(a) = 3a + 250

D) g(a) = 8a – 150

Solution :

Problem 4 :

A parabola represents the graph of the function f in the
xy-plane, where y = f(x). If the vertex of the parabola is (5, –4) and one of the x-intercepts is (–1.5, 0), what is the other x-intercept?

A) (-6.5, 0)

B) (1.5, 0)

C) (3.5, 0)

D) (11.5, 0)

Solution :

Problem 5 :

In triangles ABC and XYZ, AB = 22, XY = 11, and angles A and X both measure 77°. Which of the following pieces of information, if any, would be enough to prove that the two triangles are similar to each other?

I. Angle B measures 40°

II. Angle Y measures 50°

III. Angle Z measures 63°

A) No additional information is necessary.

B) Angle measures alone do not provide enough information.

C) I and II together provide enough information.

D) I and III together provide enough information.

Solution :

Problem 6 :

The table shown summarizes the number of employees at each of the 17 restaurants in a town.

Which of the following could be the median number of employees for the restaurants in this town?

A) 2

B) 9

C) 15

D) 21

Solution :

Problem 7 :

For the exponential function f, the value of f(0) is c, where c is a constant. Of the following equations that define the function f, which equation shows the value of c as the coefficient or the base?

A) f(x) = 22(1.5)^{x + 1}

B) f(x) = 33(1.5)^x

C) f(x) = 49.5(1.5)^{x - 1}

D) f(x) = 74.25(1.5)^{x - 2}

Solution :

Problem 8 :

The function f(t) = 40,000(2)^t^/790 gives the number of bacteria in a population t minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?

A) 2

B) 790

C) 1,580

D) 40,000

Solution :

Problem 9 :

x² + 10x + 12 = 0

The two roots of the equation above are a + √b and a - √b, where a and b are integers and b > 0. What is the value of a - b?

Solution :

Problem 10 :

Points Q and R lie on a circle with center P. The radius of this circle is 9 inches. Triangle PQR has a perimeter of 31 inches. What is the length, in inches, of QR ?

A) 13√2

B) 13

C) 9√2

D) 9

Solution :

Problem 11 :

If f(x + 1) = 5x + k and f(3) = 8, what is the value of f(5)?

Solution :

Problem 12 :

In rectangle ABCD above, AD = 12, AB = 6 and EG = 4. What is the area of ΔEFG?

Solution :

Problem 13 :

3x – ay = 3

ax – by = 4

In the system of equations above, a and b are non zero constants. If the system has infinitely many solutions, what is the value of b?

Solution :

Problem 14 :

In the figure above, AD = 4 and BD = 3. What is the value of sin C?

Solution :

Problem 15 :

Mina can do a job in 2 hours, and Ruth can do the same job in 4 hours. If they work together, how long will it take them to do the job?

A) 50 minutes

B) 60 minutes

C) 80 minutes

D) 100 minutes

Solution :

Problem 16 :

The time it takes a clock pendulum to repeat its motion is called its period. The formula above shows the relationship between T, the period of the pendulum, in seconds, and L, the length of the pendulum, in meters. Which of the following is closest to L when T is 8?

A) 14.4

B) 15.9

C) 16.3

D) 17.1

Solution :

Problem 17 :

The number of girls in a class is three more than four times the number of boys. If there is a total of 33 students in the class, how many boys are there ?

A) 6

B) 8

C) 10

D) 27

Solution :

Problem 18 :

Taylor has a bank account earning 5 percent interest compounded annually. If her initially deposit was $1,000 and she makes a withdrawal of $200 after 3 years, which of the following represents the total amount in her account after 7 years?

A) 1,000(1.05)⁷ - 200

B) 1,000(1.05)³ + 800(1.05)⁴

C) 1,000(1.05)³ - 200(1.05)⁴

D) 1,000(1.05)⁷ - 200(1.05)⁴

Solution :

Problem 19 :

Alex and Brian weigh a total of 300 pounds. Alex and James weigh a total of 280 pounds. James and Brian weigh a total of 350 pounds. How many pounds do Alex, Brian and James weigh altogether?

A) 425

B) 445

C) 450

D) 465

Solution :

Problem 20 :

Squares of side length 2 are removed from the corners of an 8 by 11 piece of paper shown above by cutting along the dashed lines. The sides of the paper are then folded up to create a rectangular box with an opn top. How many cubes of side length 1 are needed to completely fill this box?

Solution :