DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 239)

Problem 1 :

The scatterplot above shows the ticket price for a school music concert and the profit made when the ticket was sold at different prices. A quadratic model that best fits the data was drawn on the scatterplot. For a ticket price $40, which of the following is closest to the percent decrease from the actual profit to the profit predicted by the curve of best fit?

A)  25%

B)  29%

C)  40%

D)  50%

Solution :

Problem 2 :

In the xy-plane above, OP is perpendicular to PR. What is the value of k?

A)  5

B)  2√10

C)  8

D)  3√5

Solution :

Problem 3 :

A small computer monitor manufacturing company produces 10-inch and 20-inch sized monitors. The table aboveshows how many hours are required on each machine per day in order to produce the monitors. If x represents the number of 10-inch monitors and y represents the number of 20-inch monitors, which of the following systems represents all the constraints that x and y must satisfy?

A)

x ≥ 0

y ≥ 0

x + 2y ≥ 20

2x + 3y ≥ 15

B)

0 ≤ x ≤ 3

0 ≤ y ≤ 5

x + 2y ≤ 20

2x + 3y ≤ 15

C)

x ≥ 0

y ≥ 0

x + 2y ≤ 20

2x + 3y ≤ 15

D)

x ≥ 0

y ≥ 0

x + 2y = 20

2x + 3y = 15

Solution :

Problem 4 :

The triangle above was altered by increasing its base by 20 percent and decreasing its height by k percent. If these alterations decreased the area of the triangle by 16 percent, which of the following is the value of k?

A)  20

B)  25

C)  30

D)  40

Solution :

Problem 5 :

P(x) = x² – 5x + k

In the function above, k is a constant. When a polynomial P(x) is divided by x – 1, the remainder is 3. If P(x) is divided by x + 1, what is the remainder?

A)  3

B)  4

C)  7

D)  13

Solution :

Problem 6 :

The graph of the linear function f passes through the points (a, 1) and (1, b) in the xy-plane. If the slope of the graph of f is 1, which of the following is true?

A)  a - b = 1

B)  a + b = 1

C)  a - b = 2

D)  a + b = 2

Solution :

Problem 7 :

Johnny received m text messages on Friday, three less than twice as many text messages on Saturday than on Friday, and five more text messages on Sunday than on Saturday. What is the total number of text messages he received over the three days?

A)  4m + 2

B)  5m - 1

C)  4m - 2

D)  5m + 1

Solution :

Problem 8 :

If point (7, b) is in Quadrant I and point (a, -3) is in Quadrant III, in which Quadrant is the point (a, b)?

A)  Quadrant I

B)  Quadrant II

C)  Quadrant III

D)  Quadrant IV

Solution :

Problem 9 :

On the number line above, if BC = 2AB, what is the value of x?

Solution :

Problem 10 :

If a = 4, b = -3 and c = 7, evaluate the following expression

Solution :

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