DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 45)

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

Problem 1 :

What is the value of k, if the given equation has only one solution?

Solution :

Problem 2 :

A square map has side lengths of 120 inches. One inch on the map represents 9 miles. On a smaller version of the map, the side lengths are 40% smaller than the larger map. What is the actual distance represented by 1 inch on the smaller map?

Solution :

Problem 3 :

A value is decreased by 20%. By what percent has the decreased value to be increased , so that the resulting value will be equal to the original value?

Solution :

Problem 4 :

The quadratic function f(x) = (x - 16)² + d can be written as f(x) = (x - 10)(x + c). What is the value of d?

Solution :

Problem 5 :

A square of area 2 is inscribed in a square of area 3, creating four congruent triangles, as shown below. What is the ratio of the shorter leg to the longer leg in the shaded right triangle?

Solution :

Problem 6 :

In the figure above, if the volume of the cube is 64, what is the length of diagonal PQ?

A) 4

B) 4√2

C) 4√3

D) 8√2

Solution :

Problem 7 :

In the equation above, k is a constant. If v is tripled and r is halved, which of the following is true?

A) F is tripled

B) F is multiplied by 8

C) F is multiplied by 12

D) F is multiplied by 18

Solution :

Problem 8 :

In an isosceles triangle with a height 10 and a base 10, a square is inscribed with side x along the base of the triangle as shown above, What is the area of the square?

A) 16

B) 25

C) 26.25

D) 36

Solution :

Problem 9 :

|k – 3| = 10

|m + 3| = 6

If the system of equations above, what is the greatest value of k – m?

A) 10

B) 16

C) 22

D) 24

Solution :

Problem 10 :

In the rectangle above, tan∠BAP = 1/3 and tan∠CDP = 2/5. What is the value of BP/CP?

Solution :

Problem 11 :

A circle in the xy-plane has its center (-1, 1). Line t is tangent to this circle at the point (5, -4). Which of the following points also lies on line t?

A) (0, 6/5)

B) (4, 7)

C) (10, 2)

D) (11, 1)

Solution :

Problem 12 :

In the xy-plane above, the function f is defined by f(x) = 2x³ + 3x² + ax + b, where a and b are constants. If the graph of f intersects the x-axis at three points, what is the value of a?

A) 11

B) 5

C) -5

D) -11

Solution :

Problem 13 :

g(x) = f(x – 3) – 10

If the slope of the linear function f is 2/5, what is the slope of the function g shown above?

A) -2/5

B) -5/2

C) 2/5

D) 5/2

Solution :

Problem 14 :

A certain dancing group does not receive applicants whose height is less than 5 feet or more than 6 feet. Which of the following inequalities can be used to determine the height h, in feet, of applicants who are not accepted in the gorup?

A) |h – 5| > 6

B) |h – 6| > 5

C) |h – 5.5| < 0.5

D) |h – 5.5| > 0.5

Solution :

Problem 15 :

a^-2 + 3a^-1 – 10 = 0

In the equation above, a > 0. What is the value of a?

A) ½

B) 2

C) 3

D) 4

Solution :

Problem 16 :

The sum of two irrational numbers multiplied by the larger one is 70 and their difference is multiplied by the smaller one is 12. The two numbers are

A) 3√2, 2√3

B) 5√2, 3√5

C) 2√3, 3√3

D) 2√2, 5√2

Solution :

Problem 17 :

Square A has side length that is 166 times the side length of square B. The area of square A is k times the area of square B. What is the value of k?

Solution :

Problem 18 :

A right square prism has a height of 14 units. The volume of the prism is 2016 cubic units. What is the length, in units, of an edge of the base?

Solution :

Problem 19 :

In triangle XYZ, angle Z is a right angle and the length of YZ is 24 units. If tan X = 12/35, what is the perimeter, in units, of triangle XYZ?

A) 188

B) 168

C) 84

D) 71

Solution :

Problem 20 :

In triangle XYZ, angle Y is a right angle, the measure of angle Z is 33°, and the length of YZ is 26 units. If the area, in square units, of triangle XYZ can be represented by the expression ktan 33°, where k is a constant, what is the value of k?