DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 33)

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Problem 1 :

x² – 20x + k = 0

The quadratic equation above has two real roots. If one of the roots is 2 more than five times of the other root, then, what is the value of k?

Solution :

Problem 2 :

In the ratrional equation above, P, Q and R are constants. Find the value of P + Q + R?

Solution :

Problem 3 :

Two investments were made as shown in the table above. The interest in Account A is compounded once per year. Which of the following is true about the investments?

A) Account A always earns more money per year than Account B.

B) Account A always earns less money per year than Account B.

C) Account A earns more money per year than Account B at first but eventually earns less money per year.

D) Account A earns less money per year than Account B at first but eventually earns more money per year.

Solution :

Problem 4 :

For x > 0, the function f is defined as follows : f(x) equals 201% of x. Which of the following could describe this function?

A) Decreasing exponential

B) Decreasing linear

C) Increasing Exponential

D) Increasing linear

Solution :

Problem 5 :

The scatterplot above shows the size x and the sale price y of 25 houses for sale in Town H. Which of the following could be an equation for a line of best fit for the data?

A) y = 200x + 100

B) y = 100x + 100

C) y = 50x + 100

D) y = 100x

Solution :

Problem 6 :

Triangle ABC above is isosceles with AB = BC, and the ratio of DE to DF is 3 : 2. If the area of triangle ABC is 78, what is the area of triangle ABD?

A) 46.8

B) 54

C) 60

D) 60.25

Solution :

Problem 7 :

P(x) = (x² + ax + 2) – 2(x – b)

In the polynomial P(x) defined above, a and b are constants. If P(x) is divisible by (x – 1) and (x – 3), what is the value of a?

A) –4

B) –2

C) 2

D) 4

Solution :

Problem 8 :

y = x² – 2x

y = x + k

In the system of equations defined above, k is a constant. If the system has no solution, which of the following could be the value of k?

A) 1

B) 0

C) –2

D) –3

Solution :

Problem 9 :

The distance between two parallel lines is defined as the length of the perpendicular segment between them. What is the distance between y = x and y = x – 4?

A) √2

B) 2

C) 2√2

D) 4

Solution :

Problem 10 :

In the xy-plane above, the graph of a quadratic function y = f(x) intersects the x-axis at points O and Q, and has a vertex at point P. If line ℓ passes through points P and Q, what is the y-intercept of line ℓ?

A) 8

B) 10

C) 12

D) 15

Solution :

Problem 11 :

h = 3a + 28.6

A pediatrician uses the model above to estimate the height h of a boy, in inches, in terms of the boy’s age a, in years, between the ages of 2 and 5. Based on the model, what is the estimated increase, in inches, of a boy’s height each year?

A) 3

B) 5.7

C) 9.5

D) 14.3

Solution :

Problem 12 :

The formula above gives the monthly payment m needed to pay off a loan of P dollars at r percent annual interest over N months. Which of the following gives P in terms of m, r, and N?

Solution :

Problem 13 :

If a/b = 2, what is the value of 4b/a?

A) 0

B) 1

C) 2

D) 4

Solution :

Problem 14 :

g(x) = ax² + 24

For the function g defined above, a is a constant and g(4) = 8. What is the value of g(-4)?

A) 8

B) 0

C) -1

D) -8

Solution :

Problem 15 :

b = 2.35 + 0.25x

c = 1.75 + 0.40x

In the equations above, b and c represent the price per pound, in dollars, of beef and chicken, respectively, x weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken?

A) $2.60

B) $2.85

C) $2.95

D) $3.35

Solution :

Problem 16 :

f(x) = 2^{x + 2}

In the function above, which of the following is equivalent to f(a + b)?

A) 2(2^a + 2^b)

B) 4(2^a + 2^b)

C) 4(2^a ⋅ 2^b)

D) 4 + (2^a ⋅ 2^b)

Problem 17 :

The sum of four numbers is 783. One of the numbers, a is 25% more than the sum of the other three numbers. What is the value of a?

A) 348

B) 435

C) 520

D) 585

Solution :

Problem 18 :

Mr. Lee brought reading books to his class. If each student takes 5 books, there will be 15 books left. If 5 students do not take a book and the rest of the students take 7 books each, there will be no books left. How many books were brought to the class ?

A) 140

B) 125

C) 120

D) 104

Solution :