DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 14)

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Problem 1 :

Each face of a fair 14-sided die is labeled with a number from 1 through 14, with a different number appearing on each face. If the die is rolled one time, what is the probability of rolling a 2?

A) 1/14

B) 2/14

C) 12/14

D) 13/14

Solution :

Problem 2 :

A printer produces posters at a constant rate of 42 posters per minute. At what rate, in posters per hour, does the printer produce the posters?

Solution :

Problem 3 :

The function f is defined by the equation

f(x + 2) = 7x + 2

What is the value of f(x) when x = 4 ?

Solution :

Problem 4 :

A teacher is creating an assignment worth 70 points. The assignment will consist of questions worth 1 point and questions worth 3 points. Which equation represents this situation, where x represents the number of 1-point questions and y represents the number of 3-point questions?

A) 4xy = 70

B) 4(x + y) = 70

C) 3x + y = 70

D) x + 3y = 70

Solution :

Problem 5 :

y = -3x

4x + y = 15

The solution to the given system of equations is (x, y). What is the value of x?

A) 1

B) 5

C) 15

D) 45

Solution :

Problem 6 :

Function f is defined by f(x) = (x + 6)(x + 5)(x + 1). Function g is defined by g(x) = f(x - 1). The graph of y = g(x) in the xy-plane has x-intercepts at (a, 0), (b, 0), and (c, 0), where a, b, and c are distinct constants. What is the value of a + b + c ?

A) -15

B) -9

C) 11

D) 15

Solution :

Problem 7 :

A wire with a length of 106 inches is cut into two parts. One part has a length of x inches, and the other part has a length of y inches. The value of x is 6 more than 4 times the value of y. What is the value of x?

A) 25

B) 28

C) 56

D) 86

Solution :

Problem 8 :

13 is p% of 25. What is the value of p?

Solution :

Problem 9 :

A landscaper uses a hose that puts 88x ounces of water in a bucket in 5y minutes. Which expression represents the number of ounces of water the hose puts in the bucket in 9y minutes at this rate?

A) 9x/440

B) 440x/9

C) 5x/792

D) 792x/5

Solution :

Problem 10 :

4x - 9y = 9y + 5

hy = 2 + 4x

In the given system of equations, h is a constant. If the system has no solution, what is the value of h?

A) -9

B) 0

C) 9

D) 18

Solution :

Problem 11 :

f(x) = a(x – b)² + 10

In the xy-plane, the graph of the function f above has x-intercepts at –2 and 6. What is the value of a?

A) –5

B) – 5/8

C) 5/8

D) 5

Solution :

Problem 12 :

2x – 3y = 1

ax + by = c

In the system of equations above, a, b and c are constants. For which of the following values of a, b and c does the system have only one solution?

A) a = 2, b = –3 and c = 1

B) a = 4, b = –6 and c = 5

C) a = 6, b = –9 and c = 5

D) a = 10, b = 10 and c = 1

Solution :

Problem 13 :

In the xy-plane above, what are the coordinates of point M?

A) (2, 0)

B) (3, 0)

C) (4, 0)

D) (5, 0)

Solution :

Problem 14 :

Based on the equation above, if there is an increase of 27 in F, how much is the increase in C?

A) 9

B) 15

C) 27

D) 59

Solution :

Problem 15 :

The equation is true for all values of x except 1 and 2, where a and b are constants. What is the value of a?

A) –4

B) –2

C) 3

D) 4

Solution :

Problem 16 :

Four values for the functions f and g are shown in the table above. If g(m) = 6, what is the value of f(m)?

Solution :

Problem 17 :

x² - 5x + c = 0

In the quadratic equation above, c is a constant. If the equation has two solutions for x, one of which is -3, what is the value of the other solution?

Solution :