DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 18)

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Problem 1 :

Given that

What is the value of x + y + z?

Answer :

Problem 2 :

The function p is defined by p(n) = 7n³. What is the value of n when p(n) is equal to 56?

A) 2

B) ⁸⁄₃

C) 7

D) 8

Solution :

Problem 3 :

The equation E(t) = 5(1.8)^t gives the estimated number of employees at a restaurant, where t is the number of years since the restaurant opened. Which of the following is the best interpretation of the number 5 in this context?

A) The estimated number of employees when the restaurant opened

B) The increase in the estimated number of employees each year

C) The number of years the restaurant has been open

D) The percent increase in the estimated number of employees each year

Solution :

Problem 4 :

Each year, the value of an investment increases by 0.49% of its value the previous year. Which of the following functions best models how the value of the investment changes over time?

A) Decreasing exponential

B) Decreasing linear

C) Increasing exponential

D) Increasing linear

Solution :

Problem 5 :

Solution :

Problem 6 :

An event planner is planning a party. It costs the event planner a onetime fee of $35 to rent the venue and $10.25 per attendee. The event planner has a budget of $200. What is the greatest number of attendees possible without exceeding the budget?

Solution :

Problem 7 :

x² – 4x + 2 = 0

If a and b are the roots of the equation above, what is the value of (a + 1)(b + 1)?

A) 5

B) 6

C) 7

D) 10

Solution :

Problem 8 :

If a⁵ = 10 and a⁷ = 2/p, which of the following is an expression for p?

A) 2a²

B) 5/a²

C) 1/5a²

D) a²/100

Solution :

Problem 9 :

A movie theater sold n tickets today. Some of these were adult tickets and the rest were child tickets. An adult ticket costs twelve dollars and a child ticket costs eight dollars. If the theater sold $2000 worth of tickets and the number of child tickets sold is c, which of the following could be the value of n?

A) n = 2000/c

B) n = (500 - 4c)/3

C) n = (500 - c)/3

D) n = (500 + c)/3

Solution :

Problem 10 :

f(x) = x(x + 2)(x – 3)

In the function f(x) above, which of the following about the graph of f in the xy-plane could not be true?

A) The graph of f rises to the right as x approaches positive infinity.

B) The function f falls to the left as x approaches negative infinity.

C) The function f has three distinct real zeros.

D) The graph of f has a negative y-intercept.

Solution :

Problem 11 :

In the xy-plane above, the graphs of f(x) and g(x) are shown. The graph of g(x) is the result of a translation of f(x). If f(x) = x²(x - 2), which of the following is an equation of g(x)?

A) g(x) = (x - 2)³ + 2(x - 2) - 2

B) g(x) = (x + 2)³ - 2(x + 2)² - 2

C) g(x) = (x - 2)³ - 2(x - 2)² - 2

D) g(x) = (x + 2)³ - 2(x + 2)² - 2

Solution :

Problem 12 :

(3x + 2y)²

If the expression above can be written as

ax² + bxy + cy²,

where a, b and c are constants, find the value of

a + b + c

Solution :

Problem 13 :

What is one possible value of x for which the function g above is undefined?

Solution :

Problem 14 :

At a certain pizza restaurant, 8 ounces of cheese is enough for 2/3 of a pizza. Given that there are 16 ounces in a pound, how many pizzas can be produced with 12 pounds of cheese?

Solution :

Problem 15 :

y - 3x ≤ 4

y + 2x ≥ 45

In the xy-plane, a point with coordinates (h, k) lies in the solution set of the system of inequalities above. What is the minimum possible value of h?

Solution :

Problem 16 :

Call center A handle 20% fewer calls than call center B. Call center B handles 20% fewer calls than call center C. If call center A handles 1,200 calls, how many calls does call center C handle?

Solution :

Problem 17 :

The circle graph above shows the distribution of the subjects in a certain high school. If there are 136 more students taking algebra than geometry, how many more students are taking geometry than calculus?

A) 36

B) 40

C) 42

D) 84

Solution :

Problem 18 :

A farmer can plow a field in k days. How many days will it take two farmers working at the same rate to plow a field in two times larger?

A) 2k

B) k

C) k/2

D) k/4

Solution :

Problem 19 :

In the figure above, a rectangle is inscribed in a part of a circle. If the length of AD is 4 and the length of DC is 3, what is the area of the shaded region?

A) 25π - 12

B) (25π - 12)/2

C) (25π - 24)/2

D) (25π - 48)/4

Solution :

Problem 20 :

How does the graph of f(x) = (x + 2)(x – 4) compare with the graph of g(x) = x²?.

A) The graph of g(x) is moved to the left 1 unit and up 9 units.

B) The graph of g(x) is moved to the right 1 unit and down 8 units.

C) The graph of g(x) is moved to the left 1 unit and down 9 units.

D) The graph of g(x) is moved to the right 1 unit and down 9 units.

Solution :

Problem 21 :

In the figure above, the right regular pyramid has a square base and all four triangular faces are congruent. If AB = 4 and the total surface area of the pyramid is 56, what is the length of DE?

A) 4

B) 5

C) 5√2

D) 6

Solution :