DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 185)

Problem 1 :

6ax² + 60bx + 6a = 0

In the equation above, a and b are constants. What is the greatest value of a/b for which the equation has at least one real solution?

Solution :

Problem 2 :

x^x = 2²⁰⁴⁸

What is the value of x?

A)  0

B)  40

C)  128

D)  256

Solution :

Problem 3 :

In the figure above, four congruent rectangles and a square are put together to form a larger square. The perimeter of each rectangle is 24, and the area of the smaller square is 36. If the dimensions of each rectangle are  a and b as shown above, what is the value of b?

Solution :

Problem 4 :

In the figure above, two congruent circles are tangent to each other and are internally tangent to the larger circle. Line segment AB is the diameter of the larger circle. If the area of each smaller circle is 10, what is the area of the shaded region?

Solution :

Problem 5 :

f(x) = x² – 6x + 12

g(x) = k

In the equations above, f(x) ≥ g(x) for all real numbers x. If k is a constant, what is the value of k?

Solution :

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