DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 7)

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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 :

Problem 11 :

x² – 2ax + y² – 4by = 0

The equation of a circle in the xy-plane with center (2, 4) is shown above. What is the radius of the circle?

A) 4

B) 2√5

C) 5

D) 3√5

Solution :

Problem 12 :

In the xy-plane above, OQ is perpendicular to OP and the length of OQ is 5. What are the coordinates of point Q?

A) (-4, 3)

B) (-4, 5)

C) (-3, 4)

D) (-3, 5)

Solution :

Problem 13 :

The graph of the linear function g intersects points (p, 0) and (0, q) in the xy-plane. If pq < 0, which of the following is true about the graph of g?

A) The graph of g has a positive y-intercept.

B) The graph of g has a negative y-intercept.

C) The graph of g has a positive slope.

D) The graph of g has a negative slope.

Solution :

Problem 14 :

If 5x + y = 13 and 8^x/2^y = 32, what is the value of x?

A) 2.25

B) 4.5

C) 6.5

D) 7.75

Solution :

Problem 15 :

Jackson drives an average of 300 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Jackson would like to reduce his weekly expenditure on gasoline by $8. If gasoline costs $2.50 per gallon, how many average miles should he drive each week?

A) 200 miles

B) 220 miles

C) 240 miles

D) 250 miles

Solution :

Problem 16 :

The amount of water w, in gallons, left in a tank can be modeled by the equation w = 300 - 5t, where t is the number of hours since the tank started leaking. Which of the following is the best interpretation of the number 5 in the equation?

A) The tank is empty after 5 hours

B) The tank loses 5 gallons of water each hour

C) The tank continues to lose water until 5 gallons are left.

D) Each hour, the tank loses 5 less gallons of water than it did the previous hour.

Solution :

Problem 17 :

3x + ky = 8

x + 4y = -1

If (x, y) is a solution to the system of equations above and k is a constant, what is y in terms of k?

Solution :

Problem 18 :

A car has a gas mileage of 32 miles per gallon when it travels at an average speed of 65 miles per hour. If the car travels for t hours at 65 miles per hour, which of the following expressions represents the amount of gas, in gallons, the car has consumed?