DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 3)

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Problem 1 :

The table above shows the exponential growth of a type of yeast over time s, in seconds. There are c total yeast colonies on the count plate. What is the equation that represents this relationship, assuming that no yeast was added or removed after counting began?

A) c = (1 + 3)^s

B) c = (1 + 5)^s

C) c = 3(1 + 5)^s

D) c = 5(1 + 3)^s

Solution :

Problem 2 :

The equations 12x = y and 24x + 7 = 2y intersect at how many points when graphed in the xy-plane?

A) 0

B) 1

C) 2

D) 7

Solution :

Problem 3 :

Several tiles labeled with either an A or a B are placed in a bag, and tiles are worth a different point value depending on the label. The equation 15a + 10b = 100 represents the situation when a of the A tiles and b of the B tiles are drawn from the bag for a total of 100 points. How many points would be earned by drawing one A tile and one B tile from the bag?

Solution :

Problem 4 :

The amount of money remaining in a scholarship fund is reduced by one-fourth every year. The amount of money in the fund is represented by d and the number of years by y. If the fund starts with $10,000, which equation below represents this situation after y years?

Solution :

Problem 5 :

What is the diameter, in millimeters (mm), of a cylinder
with a volume of 144π mm³ and a height of 4 mm?

A) 6

B) 9

C) 12

D) 36

Solution :

Given : Volume of the cylinder is 144π mm³.

Formula to find volume of a cylinder is πr²h, where r is the radius and h is height of the cylinder.

Then, we have

πr²h = 144π

Divide both sides by π.

r²h = 144

Substitute h = 4.

r²(4) = 144

Divide both sides by 4.

r² = 36

Taking square root on both sides,

r = 6

Diameter = 2 x radius

= 2 x 6 mm

= 12 mm

The correct answer choice is (C).

Problem 6 :

If n³ = x and n⁴ = 20x, where n > 0, what the value of x?

Solution :

n³ = x ----(1)

n⁴ = 20x ----(2)

Let's take (2).

n⁴ = 20x

n^{3 + 1}= 20x

n³ ⋅ n¹= 20x

n³ ⋅ n= 20x

Substitute n³ = x, from (1).

x ⋅ n= 20x

Divide both sides by x.

n = 20

Substitute n = 20 in (1).

20³ = x

20 ⋅ 20 ⋅ 20 = x

8000 = x

Problem 8 :

The table shows selected values from function f.

Which of the following is the best description of function f ?

A) Decreasing linear

B) Increasing linear

C) Decreasing exponential

D) Increasing exponential

Solution :

In the table above, the value of x increases at a constant rate by 1. Correspondingly, f(x) increases at a constant rate by 1. In a function, if both x and f(x) increase at a constant rate (not necessarily in the same rate), then it is increasing linear.

The correct answer choice is (B).

Problem 9 :

The graph of a system of linear equations is shown. The solution to the system is (x, y). What is the value of x?

Solution :

The solution to the given system of linear equations is point of intersection of the two lines. Since the two lines intersect at the point (4, 1), the solution is (4, 1).

(x, y) = (4, 1)

Therefore, the value of x is 4.

Problem 10 :

23, 27, 27, 32, 35, 36, 52

What is the range of the 7 scores shown?

Solution :

Formula :

Range = Largest Value - Smallest Value

In the given data, the largest value is 52 and the smallest value is 23.

Range = 52 - 23

= 29

Problem 11 :

y = 2x² – ax + b

In the equation above, a and b are constants and the graph of the equation has a vertex at point (3, –6). What is the value of b?

Solution :

Problem 12 :

A landscaper is designing a regular hexagonal garden. If the area of the garden will be 150√3 square feet, what will be the perimeter, in feet, of the garden?

Solution :

Problem 13 :

The elastic potential in joules is the energy stored in a spring when it is stretched. The elastic potential energy is directly proportional to the square of the distance that the spring has been stretched from its original length. When a spring is stretched a distance of 0.5 meter, the elastic potential energy is 12 joules. If the sping is stretched 0.25 meter, what is the elastic potential energy, in joules, stored in the spring?

Solution :

Problem 14 :

Point O is the center of the circle in the figure above. What is the value of x?

Solution :

Problem 15 :

The circle in the figure above has center O and radius 10. If BC is perpendicular to AD, what is the length of AC?

Solution :

Problem 16 :

Lidia lives on a street that runs west and east. Her office is to the east and the town library is to the west of her house. Both are on the same street as her house. At 9.00 a.m., she left her home and drove at an average speed of 30 mph for 6 minutes to her office. When she arrived at the office, she realized she has forgotten to pick up a book at the library. Immediately, she drove to the library at anaverage speed of 36 mph for 8 minutes. After 3 minutes at the library, she drove directly to her office. What is the distance, in miles, from her house to the tow library?

Solution :