DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 221)

Problem 1 :

C(x) = 200x + 150

R(x) = -0.5x² + 600x + 100

In the equations above, a company produces x units of a product per month, where C(x) represents the total cost and R(x) represents the total revenue for the month. The profit is the difference ween revenue and the cost where P(x) = R(x) – C(x). For what value of x will the company create the maximum profit for the month?

A)  200

B)  400

C)  600

D)  1200

Solution :

Problem 2 :

x³ – 3x + k = (x – 1)(ax² + bx + c)

In the equation above, a, b, c and k are constants. If the equation is true for all values of x, what is the value of c?

A)  4

B)  2

C)  –2

D)  –4

Solution :

Problem 3 :

A car traveled at an average speed of p miles per hour for h hours and consumed fuel at a rate of m miles per gallon. How many gallons of fuel did the car use for the trip?

Solution :

Problem 4 :

f(x) = (x + a)² – 36

In the function f above, a is a constant. If sum of the zeros of the function is -10, which of the following is the product of the zeros of the function?

A)  –36

B)  –26

C)  –11

D)  26

Solution :

Problem 5 :

In the cylinder above, r is the radius of the base and h is the height of the cylinder. If the volume of the cylinder is equal to the surface area of the cylinder, which of the following is true about the cylinder?

Solution :

Problem 6 :

If y = kx, where k is a constant, and y = 24 when x = 6, what is the value of y when x = 5 ?

A)  6

B)  15

C)  20

D)  23

Solution :

Problem 7 :

In the figure above, lines ℓ and m are parallel and lines s and t are parallel. If the measure of ∠1 is 35°, what is the measure of ∠2 ?

A)  35°

B)  55°

C)  70°

D)  145°

Solution :

Problem 8 :

For what value of n is |n - 1| + 1 equal to 0?

A)  0

B)  1

C)  2

D)  There is no such value of n.

Solution :

Problem 9 :

The number of rooftops with solar panel installations in 5 cities is shown in the graph above. If the total number of installations is 27,500, what is an appropriate label for the vertical axis of the graph?

A)  Number of installations (in tens)

B)  Number of installations (in hundreds)

C)  Number of installations (in thousands)

D)  Number of installations (in tens of thousands)

Solution :

Problem 10 :

Based on the histogram above, of the following, which is closest to the average (arithmetic mean) number of seeds per apple?

A)  4

B)  5

C)  6

D)  7

Solution :

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