DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 21)

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Problem 1 :

The area of a certain town is 6.32 square miles. Which of the following is the area of the same town, in square yards? (1 mile = 1760 yards)

A) 648

B) 1052

C) 10,524

D) 19,576,832

Solution :

Problem 2 :

In the figure, line m is parallel to line n, and line t intersects both lines. What is the value of x?

A) 33

B) 57

C) 123

D) 147

Solution :

Problem 3 :

A small business owner budgets $2,200 to purchaseThe owner must purchase candles. The owner must purchase a minimum of 200 candles to maintain the discounted pricing. If the owner pays $4.90 per candle to purchase small candles and $11.60 per candle to purchase large candles, what is the maximum number of large candles the owner can purchase to stay within the budget and maintain the discounted pricing?

Solution :

Problem 4 :

In the linear function f, f(0) = 8 and f(1) = 12. Which equation defines f?

A) f(x) = 12x + 8

B) f(x) = 4x

C) f(x) = 4x + 12

D) f(x) = 4x + 8

Solution :

Problem 5 :

The function f(w) = 6w² gives the area of a rectangle, in square feet (ft²), if its rectangle, in square feet (ft²), if its width is w ft and its length is 6 times its width. Which of the following is the best interpretation of f(14) = 1,176?

A) If the width of the rectangle is 14 ft, then the area of the rectangle is 1,176 ft².

B) If the width of the rectangle is 14 ft, then the length of the rectangle is 1,176 ft.

C) If the width of the rectangle is 1,176 ft, then the length of the rectangle is 14 ft.

D) If the width of the rectangle is 1,176 ft, then the area of the rectangle is 14 ft².

Solution :

Problem 6 :

f(x) = 4x² - 50x + 126

The given equation defines the function f. For what value of x does f(x) reach its minimum?

Solution :

Problem 7 :

In the xy-plane above, the area of ΔOPR is 24. What is the slope of OP?

A) 4/3

B) 3/4

C) 2/3

D) 1/2

Solution :

Problem 8 :

The cylinder was altered by increasing its radius of the base by 10 percent and decreasing its height by k percent. If these alterations decreased the volume of the cylinder by 8 percent, which of the following is closest to the value of k?

A) 10

B) 12

C) 24

D) 32

Solution :

Problem 9 :

h = -16t² + 80t + 108

The equation above gives the height h, in feet, of a ball t seconds after it is thrown straight up with an initial velocity of 80 feet per second. Which of the following is true for the interval from 3 to 5 seconds?

A) The ball is moving upward at an average rate of 48 feet per second.

B) The ball is moving upward at an average rate of 96 feet per second.

C) The ball is moving downward at an average rate of 48 feet per second.

D) The ball is moving downward at an average rate of 96 feet per second.

Solution :

Problem 10 :

In the figure above, sin (a°) = cos (b°) and BC = 10. If a = 2x – 16 and b = 3x – 9, which of the following is the area of triangle ABC?

A) 25√3/2

B) 25√5/2

C) 25/2

D) 25√3

Solution :

Problem 11 :

x² + y² - 4x + 4y - 8 = 0

The graph of the equation above in the xy-plane is a circle. If the center of the circle is translated 2 units up and the radius is increased by 2, which of the following is an equation of the resulting circle?

A) (x - 2)² + y² = 18

B) (x - 2)² + (y + 4)² = 36

C) (x - 2)² + y² = 36

D) (x - 2)² + (y - 2)² = 36

Solution :

Problem 12 :

The value of stock is going up by 200% every hour. Which of the following best describes the relationship time (in hours) and the value of the stock?

A) Increasing linear

B) Decreasing linear

C) Exponential growth

D) Exponential decay

Solution :

Problem 13 :

A sports equipment manufacturer produced 3,600 footballs and 2,200 basketballs during the fall. In the winter, it produced 3,060 footballs and a certain number of basketballs. If the manufacturer decreased the production of basketballs by the same percentage as it did foir footballs, how many basketballs did it produce in the winter?

A) 1,810

B) 1,870

C) 1,920

D) 1,950

Solution :

Problem 14 :

If x/5 = k/y, where k is a constant, and y = 3 when x = 10, what is the value of y when x = 2?

A) 10

B) 12

C) 15

D) 18

Solution :

Problem 15 :

The number of books in a warehouse can be found using the expression 4,000 + bd, where b is the number of boxes of books the warehouse receives each day over a period of d days. What is the best interpretation of 100 in the expression?

A) The number of books in each box

B) The number of books received each day

C) The number of boxes received that contain books

D) The number of days it takes to receive each box

Solution :

Problem 16 :

Of the following four scenarios, which one would result in exponential decay of the total amount of money kept in safe?

A) The owner withdraws a third of the money remaining in the safe every month.

B) The owner withdraws 100 dollars every month from the safe.

C) The owner withdraws 10% of the original amount of money in the safe of every month.

D) The owner empties the account in five moths by withdrawing an equal amount of money each month.

Solution :

Problem 17 :

In the figure above, measure of ∠ADB = 60°, measure of ∠ACD = 30°, and CD = 10√3. What is the length of AB?

Solution :

Problem 18 :

f(x) = x⁵ + k²x³ + 3kx – 11

In the function above, k is a positive constant. If x – 1 is a factor of f(x), what is the value of k?

Solution :

Problem 19 :

Ashley and Beth drove from city A to city B in exactly 5 hours, not taking rest stops. Ashley drove up to the area located halfway between the two cities at the average speed of 40 miles per hour and then Beth drove the other half at an average speed of 60 miles per hour. How many hours did Beth drive on their trip?

A) 1

B) 2

C) 3

D) 4

Solution :

Problem 20 :

The combined weight of Adam and Bradley is 165 pounds. The combined weight of Bradley and Chris is 185 pounds. The combined weight of Chris and Adam is 175 pounds. How many pounds of does Bradley weigh?

A) 80

B) 85

C) 87.5

D) 92.5

Solution :