DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 231)

Problem 1 :

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 2 :

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 3 :

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 4 :

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 5 :

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 6 :

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 7 :

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 8 :

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 9 :

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 10 :

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 :

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