DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 17)

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Problem 1 :

A certain of pair used shoes can be repaired for $12.50 and will last for one year. A pair of the same kind of shoes can be purchased new for $28.00 and will last for two years. The average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes?

A) 3%

B) 5%

C) 12%

D) 15%

Solution :

Problem 2 :

A certain town has an area of 4.36 square miles. What is the area, in square yards, of this town? (1 mile = 1,760 yards)

A) 404

B) 7,674

C) 710,459

D) 13,505,536

Solution :

Problem 3 :

For line h, the table shows three values of x and their corresponding values of y. Line k is the result of translating line h down 5 units in the xy-plane. What is the x-intercept of line k?

A) (-26/3, 0)

B) (-9/2, 0)

C) (-11/3, 0)

D) (-17/6, 0)

Solution :

Problem 4 :

In the xy -plane, the graph of the equation y = -x² + 9x - 100 intersects the line y = c at exactly one point. What is the value of c?

Solution :

Problem 5 :

2x + 3y = 7

10x + 15y = 35

For each real number r, which of the following points lies on the graph of each equation in the xy-plane for the given system?

Solution :

Problem 6 :

The perimeter of an equilateral triangle is 624 centimeters. The height of this triangle is k√3 centimeters, where k is a constant. What is the value of k?

Solution :

Problem 7 :

8x² + 112px + 8y² - 64py = -448p²

In the xy-plane, the graph of the given equation is a circle. The length of the radius of the circle is np, where n and p are positive constants. What is the value of n?

Solution :

Problem 8 :

10x – 4x(k – 2) = 4x

In the equation above, k is a constant. If the equation has infinitely many solutions, what is the value of k?

A) 2

B) 7/2

C) 9/2

D) 11/2

Solution :

Problem 9 :

If (x + y)² = 10 and (x – y)² = 4, what is the value of xy?

Solution :

Problem 10 :

f(x/3) = x² - 2x + k

In the equation above, k is a constant. If f(2) = 20, what is the value of f(-2)?

Solution :

Problem 11 :

In the figure above, the area of square ABCD is 36 and M is the midpoint of AD. What is the area of ΔABE?

Solution :

Problem 12 :

In the xy-plane above, the slope of line ℓ is 2 and the slope of line m is 1. Lines ℓ and m intersect at point P. What is the area of ΔPQR?

Solution :

Problem 13 :

At a movie theatre, an adult ticket costs $10 and a bag of popcorn costs $6. If a group of adults bought tickets to a movie and 4 bags of popcorn, what expression could be used to determine how much in total the group spent, in dollars?

A) 10x + 6, where x is the number of adults

B) 10x + 24, where x is the number of adults

C) 16x, where x is the number of adults

D) 6x + 10, where x is the number of bags of popcorn purchased

Solution :

Problem 14 :

In the figure above AB = AC and c = 50°. What is the value of a?

A) 65

B) 70

C) 75

D) 80

Solution :

Problem 15 :

Barbara has x dolls in her doll collection. If Barbara has half as many dolls as Tanya does and Tanya has y dolls, which of the following equations must be true?

A) y = x + 2

B) y = ½x

C) y = 2x

D) xy = 2

Solution :