DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 48)

Subscribe to our ▶️ YouTube channel 🔴 for the latest videos, updates, and tips.

Problem 1 :

In the xy-plane, the line determined by the points (c, 11) and (-1, c) intersects the y-axisat y = 5. Which of the following could be the value of c?

A) -3

B) 1

C) 2

D) 4

Solution :

Problem 2 :

The function is g is defined by g(x) = c√x + d, where c and d are constants. In the xy-plane, the graph of y = g(x) passes through the point (16, 0) and g(36) is less than 0. Which of the following must be true?

A) g(0) = 36

B) g(0) = -36

C) c > d

D) c < d

Solution :

Problem 3 :

The quadratic equation ax² + 200x + c = 0 has at least one real solution. What is the greatest possible value of c?

Solution :

Problem 4 :

Which of the following equations represents a circle in the xy-plane that intersects the y-axis at exactly one point?

A) (x - 8)² + (y - 8)² = 16

B) (x - 8)² + (y - 4)² = 16

C) (x - 4)² + (y - 9)² = 16

D) x)² + (y - 9)² = 16

Solution :

Problem 5 :

In triangles ABC and DEF, angles B and E each have measure 27° and angles C and F each have measure 41°. Which additional piece of information is sufficient to determine whether triangle ABC is congruent to triangle upper DEF ?

A) The measure of angle upper A

B) The length of side AB

C) The lengths of sides BC and EF

D) No additional information is necessary.

Solution :

Problem 6 :

Given :

cos (a) = 0.5

sin (b) = 0.39

Find the value of the following expression :

cos (90 - b) sin (b) + sin (90 - a) cos (a)

Solution :

Problem 7 :

(2x - k)(3x² – 48)(5x² – 15x + 7k) = 0

In the equation above, k is a constant and sum of all the solutions of the equation is 5. What is the value of k?

Solution :

Problem 8 :

The figure above shows two squares and a circle. If the length of PS is a, what is the area of the shaded region?

A) a²(π - 2)/4

B) a²(π - 4)/4

C) πa²/4 - 4

D) πa² - 8

Problem 9 :

ax + by – 2 = 0

In the function above, a and b are constants. If the graph of the function has a negative slope and a negative y-intercept, which of the following is true?

A) a = 0

B) a > 0

C) a < 0

D) a ≥ 0

Solution :

Problem 10 :

In the xy-plane above, MATH is a rhombus and line ℓ passes through points A and H. Which of the following is the equation of line ℓ?

A) y = -3x/5 + 6

B) y = -5x/3 + 6

A) y = -3x/5 + 36/5

A) y = -3x/5 + 92/5

Problem 11 :

A) 87/67

B) 67/87

C) 91/73

D) 73/91

Solution :

Problem 12 :

The scatterplot above shows the weekly number of requests received at 7 different government agencies and their processing time per request. Of the labeled points, which represents the government agency that spends the most time processing all of its requests each week?

A) A

B) B

C) C

D) D

Solution :

Problem 13 :

Claire first walked one third of the way from home to her friend’s house for a birthday party. For the rest of the way to her friend’s house, she ran 4 times as fast as she walked. If she took 14 minutes to walk one third of the way, how many minutes did it take her to get from home to her friend’s house?

A) 21

B) 24

C) 28

D) 35

Solution :

Problem 14 :

The xy-plane shows the graphs of a linear function and a quadratic function, where a is a constant. If (r, s) is the point of intersection, what is the value of r?

A) 6

B) 6.5

C) 7

D) 7.5

Solution :

Problem 15 :

A) ⅓

B) 3

C) ½

D) 2

Solution :

Problem 16 :

The quadratic expression 6x² + 11x + 4 can be written as (3x + a)(2x + b), where a and b are integer constants. It can also be written as (3x + c)(2x + d), where c and d are non-integer constants. What is the value of a + c?

Solution :

Problem 17 :

R² – S² = 19

In the equation above, if R and S are positive integers, what is the value of R?

Solution :

Problem 18 :

In reading group A with 90 students, there are 4 boys for every 5 girls. In the other reading group B, there are 3 boys for every 2 girls. If these two groups are combined, the ratio of boys to girls will be 10 : 9. How many students are in the reading group B?

Solution :