Digital SAT Math Questions and Answers (Part - 7)

Question 1 :

At a retail store, a sales person can choose between two salary options. The first option is a monthly salary of $2,800. The second option is a monthly salary of $1,500 and a $12 commission on each dress shirt sold. Which of the following inequalities gives the number of dress shirts x that must be sold in a month for the salary offered by the second option to exceed the one offered by the first?

A)  x > 108

B)  x ≥ 108

C)  x > 109

D)  x ≥ 109

Answer :

Question 2 :

The table above shows the number of coffee shops in seven different towns. Removing which of the following towns from the data would bring the mean number of coffee shops and the median number of coffee shops for the six remaning towns closest together in value?

A)  Town A

B)  Town B

C)  Town C

D)  Town D

Answer :

Question 3 :

A store owner increases the price of a pillow by 35 percent, but a customer uses a coupon to buy the pillow at 35 percent off the already increased price. If the original price of the pillow was p dollars, which of the following represents the final price in terms of p?

A)  (1.35)(0.65)p

B)  (1.35)(1.65)p

C)  (0.35)(1.65)p

D)  1.35p – 0.35p  

Answer :

Question 4 :

The side of a tire is shown above. The surface area S of the tire is given by S = π²(R² – r²), where R is the outer radius and r is the inner radius. Which of the following expresses the outer radius in terms of the surface area and the inner radius?

Answer :

Question 5 :

A coal-processing plant can process 90 tons of coal per minute. Three trucks can deliver 135 tons of coal per hour. What is the minimum number of trucks necessary to keep up with the plant?

A) 40

B) 80

C)  100

D)  120

Answer :

Question 6 :

A circle in the xy-plane with center (4, 0) passes through the point (7, 4). Which of the following is the equation of the circle?

A)  (x – 4)² + y² = 9

B)  (x – 4)² + y² = 25

C)  (x – 4)² + y² = 5

D)  (x + 4)² + y² = 5

Answer :

Question 7 :

The graph of the function f is shown in the xy-plane above. Which of the following is the average rate of change between x = -3 and x = 6?

A)  2/9

B)  8/9

C)  2

D)  It cannot be determined from the given information

Answer :

Question 8 :

Emily traveled 60 miles on the highway and 16 miles on the local roads to reach her destination. On the highway, she traveled 30 miles faster than on the local roads. If her speed on local roads is 20 miles per hour, then what was her average speed, in miles per hour, during her entire trip?

A)  24

B)  25

C)  35

D)  38

Answer :

Question 9 :

For O.K theatre tickets, a ticket for an adult is 5 dollars more than a ticket for a child. If a group of 6 adults and 10 children pay a total of 142 dollars, what is the cost, in dollars, of a ticket for one adult and one child?

A)  19

B)  18

C)  17

D)  16

Answer :

Question 10 :

The scatterplot above shows the distance traveled in hours for 10 taxi drivers and the line of best fit for the data. Which of the following is closest to the average speed, in miles per hour, for the drivers?

A)  54

B)  59

C)  65

D)  68   

Answer :

Question 11 :

Which of the following is an equation of a circle in the xy-plane with center (2, -3) and a circumference of 20π?

A)  (x + 2)² + (y – 3)² = 20

B)  (x – 2)² + (y + 3)² = 20

C)  (x – 2)² + (y + 3)² = 100

D)  (x + 2)² + (y – 3)² = 400

Answer :

Question 12 :

f(x) = x³ + 2

g(x) = 2x

The functions f and g are defined above. If f(b) = 29, what is the value of g(b)?

Answer :

Question 13 :

Researchers are attempting to model the growth of the recovering hawskbill turtle population in East Africa. They estimate the population to be 200 in the first year. In the second year, they record the population of 600 turtles. How much greater would the estimated population be in the third year, if the turtle population growth were exponential rather than linear?

A)  800

B)  1000

C)  1200

D)  1800

Answer :

Question 14 :

The scatterplot above shows the relationship between the speed of the driver and the amount of the fine, in dollars, for 15 speeding tickets issued by a local police department. The line of best fit is also shown. Which of the following is the best interpretation of the slope of the line of best fit in the context of this problem?

A)  The estimated increase in the speed of the driver, in miles per hour, for every 10 dollar increase in the fine.

B) The estimated fine increase, in dollars, for every 10 miles per hour over the speed limit.

C)  The estimated increase in the speed of the driver, in miles per hour, for every one dollar increase in the fine.

D)  The estimated fine increase, in dollars, for every miles per hour over the speed limit.

Answer :

Question 15 :

A parabola is shown in the xy-plane above, which of the following equations correctly represents the parabola by displaying the x-intercepts of the parabola as constants or coefficients?

A)  y = (x + 1.5)² – 20.25

B)  y = (x – 1.5)² – 20.25

C)  y = (x + 6)(x – 3)

D)  y = (x – 6)(x + 3)

Answer :

Question 16 :

For a polynomial p(x), the value of p(-5) = 0. Which of the following must be true about p(x)?

A)  (x – 5) is a factor of p(x).

B)  (x + 5) is a factor of p(x).

C)  x is a factor of p(x).

D)  When p(x) is divided by (x + 5), the remainder is -5.

Answer :

Question 17 :

The figure above shows the graph of the piece-wise function f defined for -4 ≤ x ≤ 5. For which of the following values of x is f(x) < |f(x)|?

A)  -3

B)  -1.3

C)  2.5

D)  3.7

Answer :

Question 18 :

If a and b are positive integers and a² – b² = 24, which of the following could be the smallest value of a?

A)  4

B)  5

C)  7

D)  8

Answer :

Question 19 :

The graph of y = ⅓(x)(x - 6) is shown in the xy-plane above. Which of the following are the coordinates of vertex P?

A)  (3, -2)

B)  (2, -4)

C)  (3, -3)

D)  (3, -4.5)

Answer :

Question 20 :

In right triangle ABC above, if BC = 10 and ∠C = 30°, what is the approximate perimeter of the triangle?

A)  20

B)  23.7

C)  25.8

D)  27.2

Answer :

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