DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 7)

Problem 1 :

A worker makes $20/hour for the first 40 hours that he works in a week. He will make $30/hour for any hours worked above 40 hours a week. How many total whole number of hours would he have to work, if he makes $1045 in a week?

A)  49

B)  48

C)  9

D)  8 

Solution :

Problem 2 :

Which expression is equivalent to 16x³y² + 14xy?

A)  2xy(8xy + 7)

B)  2xy(8x²y + 7)

C)  14xy(2x²y + 1)

D)  14xy(8x²y + 1)

Solution :

Problem 3 :

In a shipment of 45,000,000 shirts, 4,950,000 are white. What percentage of the shirts are white shirts?

A)  11%

B)  22%

C)  78%

D)  89%

Solution :

Problem 4 :

If 3(x – 8) – 16 = 8(x + 10) + x, what is the value of 6x?

Solution :

Problem 5 :

8(a – 3) – 17 = 9(a – 3)

In the equation above, what is the value of a – 3?

A)  -20

B)  -17

C)  -14

D)  3

Solution :

Problem 6 :

A school classroom with a total of 4,200 floor tiles is divided into a 30 square-foot lab area and an 80 squarefoot seating area. The number of tiles on the entire classroom floor can be represented by the equation 30a + 80b = 4,200. In this context, which of the following does b represent?

A)  The average number of tiles per square foot in the lab area

B)  The total number of tiles in the lab area

C)  The average number of tiles per square foot in the seating area

D)  The total number of tiles in the seating area

Solution :

Problem 7 :

A triangle has a base that is 65% of its height. If the base were decreased by 13 inches, how would the height need to change to keep the same proportions?

A)  It must increase by 13 inches.

B)  It must increase by 20 inches.

C)  It must decrease by 13 inches.

D)  It must decrease by 20 inches.

Solution :

Problem 8 :

What is the value of x?

x^x = 2²⁰⁴⁸

A)  0

B)  40

C)  128

D)  256

Solution :

Problem 9 :

A producer is creating a video with a length of 70 minutes. The video will consist of segments that are 1 minute long and segments that are 3 minutes long. Which equation represents this situation, where x represents the number of 1-minute segments and y represents the number of 3-minute segments?

A)  4xy = 70

B)  4(x + y) = 70

C)  3x + y = 70

D)  x + 3y = 70

Solution :

Problem 10 :

A chemist combines water and acetic acid to make a mixture with a volume of 56 milliliters (mL). The volume of acetic acid in the mixture is 10 mL. What is the volume of water, in mL, in the mixture? (Assume that the volume of the mixture is the sum of the volumes of water and acetic acid before they were mixed.)

Solution :

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