DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 22)

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Problem 1 :

The circle shown has center O, circumference 144π, and diameters PR and QS. The length of arc PS is twice the length of arc PQ. What is the length of arc QR?

A) 24π

B) 48π

C) 72π

D) 96π

Solution :

Problem 2 :

A company that provides whale-watching tours takes groups of 21 people at a time. The company’s revenue is 80 dollars per adult and 60 dollars per child. If the company’s revenue for one group consisting of adults and children was 1,440 dollars, how many people in the group were children?

A) 3

B) 9

C) 12

D) 18

Solution :

Problem 3 :

The function his defined by h(x) = 4x + 28. The graph of y = h(x) in the xy-plane has an x-intercept at (a, 0) and a y-intercept at (0, b), where a and b are constants. What is the value of a + b?

A) 21

B) 28

C) 32

D) 35

Solution :

Problem 4 :

One of the factors of 2x³ + 42x² + 208x is (x + b) where b is a positive constant. What is the smallest possible value of b?

Solution :

Problem 5 :

y = -1.5

y = x² + 8x + a

In the given system of equations, a is a positive constant. The system has exactly one real solution. What is the value of a?

Solution :

Problem 6 :

In the figure above, AE = 18, DE = 9 and CD = 15. What is the length of AB?

A) 15

B) 18

C) 21

D) 24

Solution :

Problem 7 :

In the xy-plane above, the equation of circle P is (x - 12)² + y² = 144 and M is the midpoint of PS. What is the area of the shaded region?

A) 72√3

B) 72√3 - 36π

C) 72√3 - 24π

D) 72√3 - 12π

Solution :

Problem 8 :

The scatter plot shows the relationship between body mass and test bite force for lions. The linear model of best fit for the data is also shown. For a body mass of 175 pounds, which of the following best approximates the percent increase from the test bite force to the force that the model predicts?

A) 50%

B) 100%

C) 125%

D) 150%

Solution :

Problem 9 :

In the equation above, a is a positive number. What is the value of x?

A) 12

B) 10

C) –10

D) –12

Solution :

Problem 10 :

A truck leaves City A traveling at an average speed of 40 miles per hour. Three hours later, a car leaves City A, on the same route, traveling at an average speed of 60 miles per hour. How many hours after the car leaves City A will the car catch up to the truck?

A) 4

B) 6

C) 9

D) 12

Solution :

Problem 11 :

The distance d, in meters traveled by a rocket depends on the amount of fuel f, in liters, it burns according to the equation d = (2/3)f. Based on the table above, how many rockets traveled more than 20 meters?

A) One

B) Two

C) Three

D) Four

Solution :

Problem 12 :

A researcher decides to interview a student who attends either State University or Southwest University. Which of the following is closest to the probability that the chosen student is an undergrduate at Southwest University?

A) 0.21

B) 0.25

C) 0.32

D) 0.54

Solution :

Problem 13 :

A grocery store has two recycling machines outside. The first recycle machine took in 240 plastic bottles and 180 metal cans. The second took in 30 percent more plastic bottles but 10 percent less metal cans. The second machine recycled what percent more items than the first (rounded to the nearest percent)?

A) 9%

B) 11%

C) 13%

D) 15%

Solution :

Problem 14 :

Ashley estimates that there are a marbles in a jar. Harry, who knows the actual number of marbles in the jar, b notes that Ashley's estimate is within 15 marbles (inclusive) of the actual number of marbles. Which of the following inequalities represents the relationship between Ashley's estimate and the actual number marbles in the jar?

A) -15 ≤ a - b ≤ 15

B) a ≤ b + 15

C) a ≥ b - 15

D) a + b ≥ 15

Solution :