DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 39)

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Problem 1 :

Two hundred grams of a metal alloy that is 0.3% silver is combined with another metal alloy that is 0.8% silver. If the combined metal alloy has 3.45 grams of silver in it, how many grams to the nearest gram of the 0.8% silver alloy was used?

Solution :

Problem 2 :

In the given equation, b and c are constants and contains the points (2, 0) and (0, √(110). What is the greatest value of x that will cause y to be zero?

Solution :

Problem 3 :

In the equation above, what is the value of k?

Solution :

Problem 4 :

If -40 ≤ x ≤ 90 and -30 ≤ y ≤ 20, then what is the greatest possible value of x - y?

Solution :

Problem 5 :

In the xy-plane, what is the y-coordinate of the point of intersection of the graphs of y = (x - 1)2 and y = 2x - 3?

Solution :

Problem 6 :

The coordinates of three points are as follows :

F(1, 0), G(0, 0), H(-1, y)

What is the measure of angle FGH?

A) 26π

B) 27π

C) 31π/2

D) 29π/2

Solution :

Problem 7 :

For the equation 6rx² + 60sx + 6r = 0, what is the largest ratio of r/s for there to be at least one real solution?

Solution :

Problem 8 :

The following equation has one real solution; solve for c.

Solution :

Problem 9 :

When f(a – 7) = 1, what is the value of a?

Solution :

Problem 10 :

In triangle ABC, angle A = 90b, angle B = 53a and angle C = 37a, where a and b are constants. Which of the following is true?

A) Cos C < Sin B

B) Cos C = Sin B

C) Cos C > Sin B

D) Not enough information given to provide a relationship between Cos C and sin B

Solution :

Problem 11 :

There are 20 black marbles and 16 white marbles in a container and no others. How many black marbles must be removed from the container so that the probability of randomly selecting a black marble from the container is 1/3?

A) 8

B) 12

C) 16

D) 20

Solution :

Problem 12 :

The graph above shows the test scores of 30 students. Based on the histogram above, what is the median score of the test?

A) 80

B) 70.5

C) 70

D) 40

Solution :

Problem 13 :

The graphs of f(x) = (x – 2)² and g(x) are shown in the xy-plane above. If the graphs intersect at point (5, 9), which of the following is the equation of g(x)?

Solution :

Problem 14 :

A) 3

B) 6

C) 9

D) 12

Solution :

Problem 15 :

In the xy-plane above, the point Q is on the line y = 2x/3. If the area of rectangle OPQR is 54, what is the value of b?

A) 3

B) 6

C) 9

D) 12

Solution :

Problem 16 :

In triangle RST above, point W (not shown) lies on RT. What is the value of cos(∠RSW) – sin(∠WST)?

Solution :

Problem 17 :

64x² – (16a + 4b)x + ab = 0

In the given equation, a and b are positive constants. The sum of the solutions to the equation is k(4a + b), where k is a constant. What is the value of k?

Solution :

Problem 18 :

The value of collectible comic book increased by 167% from the end of 2011 to the end of 2012 and then decreased by 16% from the end of 2012 to the end of 2013. What was the net percentage increase in the value of the collectible comic book from the end of 2011 to the end of 2013?

A) 124.28%

B) 140.28%

C) 151.00%

D) 209.72%

Solution :

Problem 19 :

The expression above is equivalent to ax^b, where a and b are constants and x > 1. What is the value of a + b?

Solution :

Problem 20 :

In the figure above, PR is tangent to circle O at point P and the length of PR is 12. If the value of sin∠R is 0.6, what is the radius of the circle?

A) 9

B) 12

C) 16

D) 20

Solution :

Problem 21 :

In the figure above, AB and CD are parallel. What is the value of x – y?

A) 50

B) 55

C) 60

D) 65

Solution :

Problem 22 :

The graph of the function f in the xy-plane is a parabola that has a maximum at point (5, 10). If the graph has one x-intercept at (1, 0), what is the other x-intercept of f?

A) (-1, 0)

B) (8, 0)

C) (9, 0)

D) (10, 0)

Solution :

Problem 23 :

The relationship between the temperature F, in degrees Farenheit and the temperature C, in degrees Celsius is given by the formula above. A student uses the approximate formula F = 2C + 30 to convert from degrees Celsius to degrees Farenheit. For what temperature in degrees Celsius does the student’s appoximate formula give the correct temperature in degrees Farenheit?

A) 0

B) 5

C) 10

D) 15

Solution :