DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 19)

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Problem 1 :

Ten years ago, the age of a father was four times of his son. Ten years hence, the age of the father will be twice that of his son. What is the the present age of the father?

Solution :

Problem 2 :

If |4x − 4| = 112, what is the positive value of x − 1 ?

Solution :

Problem 3 :

What is the diameter of the circle in the xy-plane with equation (x - 5)² + (y - 3)² = 16?

A) 4

B) 8

C) 16

D) 32

Solution :

Problem 4 :

For the exponential function f, the value of f(1) is k, where k is a constant. Which of the following equivalent forms of the function f shows the value of k as the coefficient or the base?

A) f(x) = 50(1.6)^{x + 1}

B) f(x) = 80(1.6)^x

C) f(x) = 128(1.6)^{x - 1}

D) f(x) = 204.8(1.6)^{x - 2}

Solution :

Problem 5 :

A cube has an edge length of 68 inches. A solid sphere with a radius of 34 inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere?

A) 149,796

B) 164,500

C) 190,955

D) 310,800

Solution :

Problem 6 :

A model estimates that at the end of each year from 2015 to 2020, the number of squirrels in a population was 150% more than the number of squirrels in the population at the end of the previous year. The model estimates that at the end of 2016, there were 180 squirrels in the population. Which of the following equations represents this model, where n is the estimated number of squirrels in the population t years after the end of 2015 and t ≤ 5?

A) n = 72(1.5)^t

B) n = 72(2.5)^t

C) n = 180(1.5)^t

D) n = 180(2.5)^t

Solution :

Problem 7 :

The equation above is always true for all values of x except x = -1 and x = -2, where a and b are constants. What is the value of a?

Solution :

Problem 8 :

In the equation above, k is a constant. If the equation has no solution, what is the value of k?

Solution :

Problem 9 :

Which of the following is equal to 10^-2/3?

A) √100

B) ³√100

C) ³√1/100

D) ³√1/100²

Solution :

Problem 10 :

If x + 2y = 2 and x – 2y = 10, what is the value of 2x² – 8y²?

A) 40

B) 30

C) 20

D) 10

Solution :

Problem 11 :

Which of the following numbers is contained in the domain of the function f(x) = 1/(x - 5) - 1/√(x - 5)?

A) 6

B) 5

C) -5

D) -6

Solution :

Problems 12-13 refer to the following information.

The kinetic energy of an object is given by ½mv², where m is the mass of the object v is its velocity.

Problem 12 :

If the kinetic energy of a moving tennis ball is doubled, its velocity must have increased by what factor?

A) 4

B) 2

C) √3

D) √2

Solution :

Problem 13 :

A radioactive element loses 15% of its mass and 20 percent of its velocity. By what percent has its kinetic energy decreased?

A) 32%

B) 36.2%

C) 24.8%

D) 45.6%

Solution :

Problem 14 :

In rectange ABCD above E is on DC, F is on BC, DE = 6 and FC = 1. If angle A is trisected (divided into three equal angles) by AE and AF, what is the length of BF?

A) 5

B) 5√2 - 1

C) 5√3 - 1

D) 6√3 - 1

Solution :

Problem 15 :

x - 3y = 4

2(x - 1) - 6(y + 2) = -6

How many solutions (x, y) are there to the system of equations above?

A) Zero

B) One

C) Two

D) More than two

Solution :

Problem 16 :

Gracie regularly buys six different items at the grocery store. The average price of the items is $30. The prices of five of the items are $7, $25, $36, $40, and $44. What is the price of the sixth item?

Solution :

Problem 17 :

The figure shows the graph of y = f(x). Which of the following could be the graph of y = ½f(x + 1)?

Solution :

Problem 18 :

y = ax + b

5x – 3y = a

In the system of equations above, a and b are constants. If the system has infinitely many solutions, what is b in terms of a?

A) -3

B) -9/5

C) -5/9

D) 9/5

Solution :

Problem 19 :

K = ½mv²

The kinetic energy of an object in motion is given by the equation above, where K is the kinetic energy of the object in joules, m is the mass of the object in kilograms, and v is the speed of the object in meters per second. When the object is moving at a meters per second with a mass of b kilograms, the kinetic energy is 98 joules. What is the kinetic energy in joules, when the object moving at 3a meters per second with a mass of 2b kilograms?

A) 1764

B) 1560

C) 882

D) 441

Solution :

Problem 20 :

If rs²t³u³> 0 and u < 0, which of the following must be true?

A) rt < 0

B) urt < 0

C) r > 0

D) t > 0

Solution :

Problem 21 :

The Maxim Telephone Company charges k cents for the first t minutes of a call and charges for any additional time at the rate of r cents per minute. If a certain customer pays $10, which of the following could be the length of that phone call in minutes?