DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 36)

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Problem 1 :

The population of Greenville increased by 7% from 2015 to 2016. If the 2016 population is k times the 2015 population, what is the value of k?

A) 0.07

B) 0.7

C) 1.07

D) 1.7

Solution :

Problem 2 :

f(x) = a ⋅ b^x

f(n - 1) = f(n) + 0.72f(n - 1)

What is the value of b?

Solution :

Problem 3 :

177 feet²/minute is equivalent to how many yards²/hour? (1 yard = 3 feet)

Solution :

Problem 4 :

h(x) = -2(x - 3)² + 50

In the xy-plane, the graph of the quadratic function h(x) intersects the x-axis at the points (a, 0) and (b, 0), where a and b are cosntants. What is the value of a + b?

A) -10

B) -6

C) 6

D) 10

Solution :

Problem 5 :

The function f(x) = -8(x - a)(x - b) is defined by the given equation, where a and b are distinct constants. When a < x < b, the value of f(x) is positive. The graph of y = f(x) in the xy-plane contains the point (r, s), where r and s are constants. If s = 10, which of the following could be true?

I. r < a

II. r > b

III. a < r < b

A) I only

B) II only

C) III Only

D) II and III only

Solution :

Problem 6 :

In the given equation, c is a constant. Which of the following is one of the solutions to the given equation?

Solution :

Problem 7 :

x – 29 = (x – a)(x – 29)

Which of the following are solutions to the given equation, where a is a constant and a is greater 30?

I. a

II. a + 1

III. 29

A) I and II only

B) I and III only

C) II and III only

D) I, II and III

Solution :

Problem 8 :

A rectangle is inscribed in a circle, such that each vertex of the rectangle lies on the circumference of the circle. The diagonal of the rectangle is twice the length of the shortest side of the rectangle. The area of the rectangle is 1089√3 square units. What is the length, in units, of the diameter of the circle?

Solution :

Problem 9 :

The function f is defined by f(x) = ax² + bx + c, where a, b and c are constants. The graph of y = f(x) in the xy-plane passes through the points (7, 0) and (-3, 0). If a is an integer greater than 1, which of the following could be the value of a + b?

A) -6

B) -3

C) 4

D) 5

Solution :

Problem 10 :

In a set of four consecutive odd integers, where the integers are ordered from least to greatest, the first integer is represented by x. The product of 12 and the fourth odd integer is at most 26 less than the sum of the first and third odd integers. Which inequality represents this situation?

A) 12(x + 6) ≤ x + (x + 4) – 26

B) 12(x + 6) ≥ 26 – [x + (x + 4)]

C) 12(x + 6) ≤ x + (x + 3) – 26

D) 12(x + 6) ≥ 26 - [x + (x + 3)]

Solution :

Problem 11 :

5G + 45R = 380

At a school fair, students can win colored tokens that are worth a different number of points depending on the color. One student won G green tokens and R red tokens worth a total of 380 points. The given equation represents this situation. How many more points is a red token worth than a green token?

Solution :

Problem 12 :

If 2^x = 4^y = 8^z and 1/2x + 1/4y + 1/4z = 4, then the value of x is

A) 7/19

B) 7/23

C) 7/17

D) 7/16

Solution :

Problem 13 :

If the median of the observations 7, 11, 2x – 1, 2x + 1, 23 and 29 written in ascending order is 18, the value of x is

A) 9

B) 6

C) 12

D) 15

Solution :

Problem 14 :

In an xy-plane, a line with the equation 2y = c for some constant c intersects a parabola at exactly one point. If the parabola has equation y = -2x² + 9x, what is the value of c?

Solution :

Problem 15 :

For a group of 25 or more people, a museum charges $21 per person for the first 25 people and $14 for each additional person. Which function f gives the total charge, in dollars, for a group with n people, where n ≥ 25?

A) f(n) = 14n + 175

B) f(n) = 14n + 525

C) f(n) = 14n - 350

D) f(n) = 14n + 21

Solution :

Problem 16 :

A) 3

B) 5

C) 7

D) 9

Solution :

Problem 17 :

In the figure above, the radius of the circle is 12. If the length of the chord AB is 18. What is the distance between the chord and diameter?

A) 2√10

B) 3√7

C) 4√5

D) 6√2

Solution :

Problem 18 :

x² + y² = 8

y = √(2x)

In the system of equations above, what is the value of y?

Solution :

Problem 19 :

The Sky Telephone Company charges a cents for the first 3 minutes of a call and charges r cents for each additional minute. If Jackson uses t minutes, where t > 3, how much, in dollars, is his call?

A) a + rt

B) a + r(t – 3)

C) 0.01[a + r(t – 3)]

D) 0.01(a + rt – 3)

Solution :

Problem 20 :

If Sally drives m miles from her house to her office in f hours, and drives back to her house in g hours, what is her average speed of the entire trip, in miles per hour?