DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 254)

Problem 1 :

If the square of a is equal to the cube of b, where a ≥ 0 and b ≥ 0, for what value of x is √a^x equal to b?

Solution :

Problem 2 :

The scatterplot shows the relationship between the number of sandwiches sold on a given day, y, at a restaurant and the number of days after February 1, x. The average rate of change, in sandwiches per day, of the number of sandwiches the retaurant sold on February 4 to the number of sandwiches the retaurant sold on February 8 is equal to a. The average rate of change, in sandwiches per day, of the number of sandwiches the restaurant sold on February 7 to the number of sandwiches the restaurant sold on February 11 is equal to b. The number b is p% greater than the number a. What is the value of p, rounded to the nearest hundredth?      

Solution :

Problem 3 :

The function f is defined by f(x) = ax² + bx + c, where a, b, and c are constants and 2 < b < 5. The graph of y = f(x) in the xy-plane is a parabola where f(–12) = f(7). If b is an integer, what could be the value of b – a? 

Solution :

Problem 4 :

The value of a video game console increased by 285% from the end of 2015 to the end of 2016. The value of the console then decreased by 21% from the end of 2016 to the end of 2017. Finally, the value of the console increased by 63% from the end of 2017 to the end of 2018. What was the net percentage increase in the value of the video game console from the end of 2015 to the end of 2018?(Round to the nearest hundredth of a percent)

Solution :

Problem 5 :

The functions f and g are defined by the given equations, where 2 ≤ x ≤ 8. Which of the following equations displays, as a constant or coefficient, the minimum value of the function it defines, where 2 ≤ x ≤ 8?

I.  f(x)  =  0.0625(0.5)(2)^{x + 2}

II.  g(x)  =  1500(0.2)^{x - 3}    

A)  I only

B)  II only

C)  I and II

D)  Neither I nor II

Solution :

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