DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 29)

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Problem 1 :

Number a is increased by the product of b and c. The result is divided by c and then decreased by b. Finally, that result is multiplied by c. Which of the following is the final result?

Solution :

Problem 2 :

Jenny had m magazines to sell for her soccer team fundraiser. She sold j magazines on her own and her sister sold nine less than twice the amount Jenny sold. How many magazines remained unsold in terms of m and j?

A) 3j - 9 - m

B) 3j + 9 - m

C) m - 3j - 9

D) m - 3j + 9

Solution :

Problem 3 :

If (x, y) is the solution to the system of the equations above, what is the value of x + y?

A) 2

B) 4

C) 6

D) 8

Solution :

Problem 4 :

In the figure above AB = BC. What is the value of x?

A) 113

B) 118

C) 123

D) 127

Solution :

Problem 5 :

(x²y -2xy² + 3xy) - 2(xy - xy² + x²y)

Which of the following is equivalent to the above expression?

A) 2x²y + xy

B) -x²y + xy

C) -x²y + 4xy² + xy

D) 2x²y + 4xy² + xy

Solution :

Problem 6 :

When the graph of y = x² is moved to the right 3 units and down 4 units, which of the following is the equation of the resulting graph?

A) y = (x – 1)(x – 5)

B) y = (x + 1)(x – 4)

C) y = (x – 2)(x – 4)

D) y = (x + 2)(x – 2)

Solution :

Problem 7 :

For a quadratic function f(x) = x² + bx + c in the xy-plane, f(2) = f(6) = 4, what is the value of c?

A) 4

B) 8

C) 12

D) 16

Solution :

Problem 8 :

y = (x – 5)²

y = k

In the system of equations above, k is a constant. If the system has two points of intersection and the distance between these two points is 10, what is the value of k?

A) 20

B) 25

C) 30

D) 35

Solution :

Problem 9 :

x² + 6x + 2 = 0

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

A) 9

B) 10.5

C) 11

D) 12

Solution :

Problem 10 :

For a polynomial p(x), the remainder when p(x) is divided by (x – 1) is 2 and the remainder when p(x) is divided by (x + 1) is –4. If p(x) is divided by (x² – 1), what is the remainder?

A) 2x + 1

B) 3x – 1

C) 4x + 1

D) 3x + 1

Solution :

Problem 11 :

A certain business is marketing its product and has determined that, when it raised the selling price of its product, its sales went down. The number of units sold, P, is modeled by the equation P = 1200 - 20s, where s is the selling price, in dollars. Based on this model, what is the decrease in selling price from 700 units sold to 900 units sold?

A) 5

B) 10

C) 15

D) 20

Solution :

Problem 12 :

(x² + y²)² - (x² - y²)²

Which of the following is equivalent to the expression above?

A) x⁴ - y⁴

B) 2(x² + y²)

A) 2x²y²

A) 4x²y²

Solution :

Problem 13 :

Kimberly earns k dollars per week. At this rate how many weeks will it take her to earn p dollars?

A) p/k

B) k/p

C) kp

D) 10p/k

Solution :

Problem 14 :

If 2a/b = 5, what is the value of 5b/a?

A) 2

B) 4

C) 10

D) 12.5

Solution :

Problem 15 :

2x + by = 10

ax + 4y = 15

In the system of equations above, a and b are constants and a = 2b. If the system has no solution, which of the following could be a possible value of a?

A) -2

B) 1/2

C) 4

D) 8

Solution :

Problem 16 :

If k = (x + 1)(x - 1)/3 and k ≠ 0, what does 3x² equal in terms of k?

A) 3k

B) 9k

C) 3k + 1

D) 9k + 3

Solution :

Problem 17 :

The average (arithmetic mean) of three positive numbers a, b and c is 15. When the greatest of these numbers is subtracted from sum of the other two, the result is 5. If a < b < c, what is the value of a + b?

A) 20

B) 25

C) 30

D) 40

Solution :