DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 245)

Problem 1 :

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 2 :

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 3 :

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 4 :

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 5 :

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 6 :

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 7 :

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 8 :

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?

Solution :

Problem 9 :

x² - x = 4

What are the solutions x to the quadratic equation above?

Solution :

Problem 10 :

If y⁸ = m and y⁹ = ⅔, what is the value of y in terms of m?

Solution :

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