DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 78)

Problem 1 :

In the given figure, O is the center of the circle. What is the area of the shaded region?

A)  144 - 8π

B)  72 - 18π

C)  149 - 7π

D)  92 - 4π

Solution :

Problem 2 :

The expression 6x⁴ + 17x² + 7 can be written as (3x² + a)(2x² + b), where a and b are positive integers, or as (3x² + c)(2x² + d), where c and d are positive nonintegers. What is the value of a + c?

Solution :

Problem 3 :

A data set of 27 different numbers has a a mean of 33 and a median of 33. A new data set is created by adding 7 to each number in the original data set that is greater than the median and subtracting 7 from each number in the original data set that is less than the median. Which of the following measures does NOT have the same value in both the original and new data sets?

A)  Median

B)  Mean

C)  Sum of the numbers

D)  Standard deviation

Solution :

Problem 4 :

What is the largest possible value of the constant c such that x + c is a factor of 3x³ + 15x² – 378x?

Solution :

Problem 5 :

(3x + p)(5x² – 45)(2x² – 16x + 6p) = 0

In the given equation, p is a constant. The sum of the solutions to the equation is 20/3. What is the value of p?

Solution :

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