DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 24)

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Problem 1 :

The number a is 110% greater than the number b. The number b is 90% less than 47. What is the value of a?

Solution :

Problem 2 :

There are 55 students in Spanish club. A sample of the Spanish club students was selected at random and asked whether they intend to enroll in a new study program. Of those surveyed, 20% responded that they intend to enroll in the study program. Based on this survey, which of the following is the best estimate of the total number of Spanish club students who intend to enroll in the study program?

A) 11

B) 20

C) 44

D) 55

Solution :

Problem 3 :

Jay walks at a speed of 3 miles per hour and runs at a speed of 5 miles per hour. He walks for w hours and runs for r hours for a combined total of 14 miles. Which equation represents this situation?

Solution :

Problem 4 :

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 5 :

The function F gives the temperature, in degrees Fahrenheit, that corresponds to a temperature of x kelvins. If a temperature increased by 2.10 kelvins, by how much did the temperature increase, in degrees in Fahrenheit?

A) 3.78

B) 35.78

C) 487.89

D) 519.89

Solution :

Problem 6 :

(2x – 2)(x – 7) = 2(x – a)² – b

In the equation above, a and b are constants. If the equation is true for all real values of x, what is the value of b?

Solution :

Problem 7 :

The function f is defined by f(x) = x³ – ax² + bx – 4, where a and b are constants. In the xy-plane, the graph of f intersects the x-axis at the three points (–1, 0), (–2, 0) and (k, 0). What is the value of k?

Solution :

Problem 8 :

The graphs of y = x² and y = mx – 1 are shown in the xy-plane above, where m is the slope of the line. If the graph of y = mx – 1 is tangent to the graph of y = x², what is the value of m?

Solution :

Problem 9 :

x + 16 < 2x + 1 < x + 46

Which of the following is equivalent to the inequality above?

A) |x – 15| < 45

B) |x – 29| ≤ 15

C) |x – 30| < 15

D) |x + 15| < 30

Solution :

Problem 10 :

In the figure above, ΔABC and ΔDBE are similar and AD/AB = 1/3. If the area ΔABC is 45, what is the area of the shaded region?

A) 15

B) 17.5

C) 25

D) 30

Solution :

Problem 11 :

During a trip, Jonathan had driven a total of 75 miles by 6:20 PM and a total of 85 miles by 6:40 PM. He drove at the same rate for the entire trip. At what time had he driven a total of 140 miles?

(A) 7:30 PM

(B) 8:00 PM

(D) 9:00 PM

Solution :

Problem 12 :

The equation above is true for all real values of x ≠ ⅔, where k is a constant. What is the value of k ?

(A) -4

(B) 0

(D) 2

Solution :

Problem 13 :

Which of the following is equivalent to the expression above?

Solution :

Problem 14 :

In the figure above, what is the value of x?

Solution :

Problem 15 :

In the table above, if y = x² + x - 2, what is the value of k?

Solution :

Problem 16 :

In the figure above, the cylindrical and cone-shaped containers have the same height of 12 inches and the same radius of 5 inches. If the cone-shaped container filled with water and then the water is poured into the empty cylindrical container, what will be the depth, in inches, of the water in the cylindrical container?

Solution :

Problem 17 :

In the xy-plane above, the graph of y = 2x² – 19x + 9 intersects the y-axis at P and the x-axis at R. What is the area of rectangle OPQR?

Solution :

Problem 18 :

-6 ≤ x ≤ 20

If the interval above is rewritten in the form |x – a|≤ k, what is the value of k?

Solution :

Problem 19 :

Mr. Trump drove to work in the morning at the average speed of 60 miles per hour. He returned home in the evening along the same route and averaged 45 miles per hour. To the nearest tenth, what is his average speed, in miles per hour, for the entire trip?

Solution :

Problem 20 :

A car has travelled to a destination at a speed S with time taken T. If the distance is now doubled and speed is half of its previous speed, then time taken by the car is

A) T

B) 2T

C) T/2

D) 4T

Solution :