DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 8)

Subscribe to our ▶️ YouTube channel 🔴 for the latest videos, updates, and tips.

Problem 1 :

If ᵃ⁄₃ = 10 − 7b and a ≠ 0, which of the following correctly expresses b in terms of a?

Solution :

Problem 2 :

In the xy-plane, the equation (x – 7)² + (y + 7)² = 64 defines circle O, and the equation (x – 7)² + (y + 7)² = c defines circle P. If the two circles have the same center, and the radius of circle P is three less than the radius of circle O, what is the value of constant c?

Solution :

Problem 3 :

A school has received a donation of $20,000 for the purchase of new laptops. If each laptop costs $149, no tax is charged, and the laptop manufacturer offers a 7.5% discount on orders of at least 100 laptops, what is the maximum number of laptops the school can purchase with the donation?

A) 124

B) 134

C) 145

D) 146

Solution :

Problem 4 :

3x² – y – 26 = 0

y = –3x + 10

The point (a, b) is an intersection of the system of equations above when graphed in the xy-plane. What is a possible value of a?

A) -4

B) 6

C) 20

D) 26

Solution :

Problem 5 :

How many values for y satisfy the following equation?

–6(4y + 2) = 3(4 – 8y)

A) Zero

B) Exactly one

C) Exactly two

D) Infinitely many

Solution :

Problem 6 :

The length of each edge of a box is 29 inches. Each side of the box is in the shape of a square. The box does not have a lid. What is the exterior surface area, in square inches, of this box without a lid?

Solution :

Problem 7 :

Five Eretmochelys imbricata, a type of sea turtle, each have a nest. The table shows an original data set of the number of eggs that each turtle laid in its nest.

A sixth nest with 121 eggs is added to create a new data set. Which of the following correctly compares the means of the two data sets?

A) The mean of the original data set is greater than the mean of the new data set.

B) The mean of the original data set is less than the mean of the new data set.

C) The means of both data sets are equal.

D) There is not enough information to compare the means.

Solution :

Problem 8 :

Which expression is equivalent to 42a/k + 42ak, where k > 0?

A) 84a/k

B) 84ak²/k

C) 42a(k + 1)/k

D) 42a(k² + 1)/k

Solution :

Problem 9 :

A manager is responsible for ordering supplies for a shaved ice shop. The shop’s inventory starts with 4,500 paper cups, and the manager estimates that 70 of these paper cups are used each day. Based on this
estimate, in how many days will the supply of paper cups reach 1,700?

A) 20

B) 40

C) 60

D) 80

Solution :

Problem 10 :

Which expression is equivalent to

(x² + 11)² + (x - 5)(x + 5)?

A) x⁴ + 23x² - 14

B) x⁴ + 23x² + 96

C) x⁴ + 12x² + 121

D) x⁴ + x² + 146

Solution :

Problem 11 :

In the xy-plane above, ABCDEF is a regular hexagon with a side of 2. What is the x-coordinate of E?

A) 5

B) 6

C) 7

D) 8

Solution :

Problem 12 :

sin (2x - π/12) = cos (x + π/12)

In the equation above, the angle measures are in radians. Which of the following could be the value of x?

A) π/12

B) π/8

C) π/6

D) π/4

Solution :

Problem 13 :

For a polynomial p(x), the value of p(2) and p(-1) is 0. Which of the following could not be true about p(x)?

A) x - 2 is a factor of p(x).

B) x + 1 is a factor of p(x).

C) x² - x - 2 is a factor of p(x).

D) (x - 2) + (x + 1) is a factor of p(x).

Solution :

Problem 14 :

The graph of f(x) = (x - a)(x - 3), where a is a constant, is shown in the xy-plane above. If the y-intercept of the graph is 3, what is the minimum value of f?

A) -1

B) -1.5

C) -2

D) -2.5

Solution :

Problem 15 :

In the xy-plane above, the base of a rectangle is on the x-axis and the upper vertices are on the parabola y = 10 - 2x². Which of the following represents the area of the rectangle?

A) 10a - 2a³

B) 2a³ - 10a

C) 20a - 4a³

D) 4a³ - 20a

Solution :

Problem 16 :

A food manufacturer fills containers of seasoning with various spices, pepper and salt. The amount of pepper p, in milligrams, used in the seasoning can be modeled by the equation

where s is the amount of salt, in milligrams, in the seasoning. According to the model, how many milligrams of pepper are added for every 1 milligram increase in the amount of salt?

Solution :

Problem 17 :

The incomplete table above shows the results of a survey that asked a group of doctors and lawyers how many vacations they take each year. If a doctor from the surveyed group is chosen at random, the probability that the doctor takes at least 1 vacation each year is 4/5. How many people from the surveyed group take at least 2 vacations each year?

Solution :

Problem 18 :

A boutique shop is selling handmade necklaces. The cost per necklace C can be determined by the equation above, where n is the number of necklaces made.

(a) What is the cost of making 6 necklaces now?

(b) If the shop sells each necklace for $150, how many necklaces should be made so that the shop makes a total profit of $564 after all of them are sold?

Solution :