DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 59)

Problem 1 :

f(x) = a(x - 3)² + b(x - 3)²

If f(10) = m and f(-4) = n, what is the value of

109(113)^{m - n} + 229(97)^{n - m}?

Solution :

Problem 2 :

Solution :

Problem 3 :

The given quartic function 54x⁴ + 219x² + 105 has factors in the form (k)(ax² + b)(cx² + d). If a, b, c, d and k are integers, what is the smallest possible value of ab?

Solution :

Problem 4 :

If y⁴ = 80 and z⁵ = 32, what is the value of y⁸ ⋅ z^-5?

A)  50

B)  64

C)  160

D)  200

Solution :

Problem 5 :

A rectangular prism has a height of 50 centimeters (cm). The base of the prism is a square and the surface area of the prism is S cm². If the prism is divided into two identical rectangular prisms by making a cut parallel to the square base, each resulting prism has a surface area of (³¹⁄₅₆)S cm². What is the side length, in cm, of each square base?

A)  5

B)  6

C)  12

D)  24

Solution :

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