DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 155)

Problem 1 :

x² + y² – 2x – 2y = 7

y = k

In the system of equations above, k is a constant. For which of the following values of k, does the system of equations have exactly two real solutions?

A)  k = 6

B)  k = 5

C)  k = 4

D)  k = 3

Solution :

Problem 2 :

In the right triangle ABC above, AC = 10 and the value of sin A = 0.4. What is the length of DC?

A)  1.6

B)  2.4

C)  2.5

D)  2.8

Solution :

Problem 3 :

In the xy-plane above, the area of triangle PRS is 10. What is the value of k?

A)  4

B)  5

C)  6

D)  7

Solution :

Problem 4 :

In the figure above, OP and OS are radii and the length of AC of rectangle ABCO is 10. If the measure of angle is ACO is 60°, which of the following is the closest to the area of the shaded region?

A)  30

B)  32

C)  35

D)  40

Solution :

Problem 5 :

(a + b)x² + (a – 2b)x + k = (k – 1)x² + 5x + 3

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

A)  2

B)  3

C)  5

D)  8

Solution :

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