DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 2)

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Problem 1 :

A random sample of 5,000 students out of 60,000 undergraduate students at a university were surveyed about a potential change to the registration system. According to the survey results, 75% of the respondents did not support the existing registration system, with a 4% margin of error. Which of the following represents a reasonable total number of students who did not support the existing registration system ?

A) 1,250

B) 3,750

C) 13,800

D) 43,800

Solution :

Problem 2 :

After a hot air balloon is launched from a plateau 1,000 meters above sea level, it rises at a constant rate of 750 meters per minute. Which of the following best describes the function used to model the balloon’s distance above sea level over time ?

A) Increasing linear

B) Increasing exponential

C) Decreasing linear

D) Decreasing exponential

Solution :

Problem 3 :

What is the x-intercept of the function f(x) = (22)^x – 1 when it is graphed in the xy-plane, where y = f(x) ?

A) (-1, 0)

B) (0, 0)

C) (21, 0)

D) (22, 0)

Solution :

Problem 4 :

In parallelogram ABCD shown above, the length of AB is one-third the length of AD. The perimeter of the parallelogram is 64. What is the length of AB ?

A) 8

B) 16

C) 24

D) 32

Solution :

Problem 5 :

A triangle with an area of 18 square units has a base of (m + 5) units and a height of m units. What is the value of m ?

A) 4

B) 9

C) 13

D) 36

Solution :

Problem 6 :

If x⁸y⁷ = 333 and x⁷y⁶ = 3, what is the value of xy?

Solution :

Problem 7 :

The graph of a system of a linear equation and a nonlinear equation is shown. What is the solution (x, y) to this system?

A) (0, 0)

B) (0, 4)

C) (4, 5)

D) (5, 0)

Solution :

The solution to the given system is point of intersection of the two graphs.

At the point of intersection, the x-coordinate is 4 and the y-coordinate is 5. Then the solution for the given system is (4, 5).

The correct answer choice for this question is (C).

Problem 8 :

On the first day of a semester, a film club has 90 members. Each day after the first day of the semester, 10 new members join the film club. If no members leave the film club, how many total members will the film club have 4 days after the first day of the semester?

A) 400

B) 130

C) 94

D) 90

Solution :

Let y be the number of members and x be the number of days. We can write a linear equation base on the given information we have.

y = (x - 1)10 + 90

where x ≥ 1.

We have to find the number of members 4 days after the first day. That is, we have to find the number of numbers on the 5^th day (1 + 4 = 5). Then, we have plug in 5 for x and find the value of y.

y = (5 - 1)10 + 90

y = 4 ⋅ 10 + 90

y = 40 + 90

y = 130

The film club will have 130 members after 4 days after the first day of the semester.

The correct answer choice for this question is (B).

Problem 9 :

The graph of the linear function f is shown, where y = f(x). What is the y-intercept of the graph of f ?

A) (0, 0)

B) (0, -16/11)

C) (0, -8)

D) (0, 8)

Solution :

To find the y-intercept of the graph, we have to see at what value, the graph of the given function intersects y-axis. In the above figure, the graph of f(x) intersects y-axis at 8. And, always the x-coordinate of y-intercept is 0. Then, the y-intercept of f(x) is (0, 8).

The correct answer choice for this question is (D).

Problem 10 :

s + 7r = 27

r = 3

What is the solution (r, s) to the given system of equations?

A) (6, 3)

B) (3, 6)

C) (3, 27)

D) (27, 3)

Solution :

In the given system of equations, we have the value of r in the second equation, that is 3. Substitute r = 3 into the first equation to find the value of s.

s + 7(3) = 27

s + 21 = 27

Subtract 21 from both sides.

s = 6

(r, s) = (3, 6)

The correct answer choice for this question is (B).

Problem 11 :

Stephen wins the lottery and decides to donate 30% of his winnings to charity. Then he decides to give 20% of what he has left to his mother. What percent of his winnings does stephen have left for himself?

A) 67%

B) 56%

C) 54%

D) 50%

Solution :

Problem 12 :

The perimeter of an equilateral triangle with sides of length s is p. What is the perimeter of a square with sides of length 3s, in terms of p?

A) p²

B) 12p

A) 4p

A) 3p

Solution :

Problem 13 :

If a + b = c, which of the following is equal to a² + b²?

A) c + 2ab

B) c²

C) c² - ab

D) c² - 2ab

Solution :

Problem 14 :

If m/n = 2/3, what is the value of 2n/m + 5?

Solution :

Problem 15 :

If k is an integer cosntant greater than 1, which of the following values of x satisfies the inequality

x/3 + 1 ≥ k

A) k - 3

B) k

C) 3k - 4

D) 3k - 2

Solution :

Problem 16 :

-377x + k = 377x + k

If k is a constant, how many solutions does the given equation have?

A) No solution

B) One solution

C) Two solutions

D) Infinite solutions

Solution :

Problem 17 :

The graph of the linear equation passes through the points (-21, -89/2) and (12, 65/2). The graph also passes through the point (27/4, a). What is the value of a?

Solution :

Problem 18 :

The figure below shows a square and a right triangle. What is the area of shaded region?

A) x(x + y)/2

B) (x² + y²)/2

C) xy

D) 2xy

Solution :

Problem 19 :

|x| < 1, which of the following is the greatest?

A) 2

B) 1 – x

C) 1 + x

D) 2x

Solution :

Problem 20 :

Sam drove to work at an average speed of 50 miles per hour from her house and then returned along the same route at an average speed of 40 miles per hour. If the entire trip took her 2.25 hours, what is the entire distance, in miles, for the round trip?

A) 90

B) 100

C) 120

D) 125

Solution :