DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 246)

Problem 1 :

If p² – q² = x and y = 2pq, which of the following is equivalent to x² + y²?

A)  (p² + q²)²

B)  (p² – q²)²

C)  p⁴ – q⁴

D)  p⁴ + q⁴

Solution :

Problem 2 :

The volume of a right circular cone is 33 cubic feet. What is the volume, in cubic feet, of a right circular cone with half the radius and twice the height of the cone?

A)  16.5

B)  33

C)  49.6

D)  66

Solution :

Problem 3 :

8(p – 1) = 5(p² – 1) – 6(p – 1)

If p > 1, what is the solution of the equation above?

Solution :

Problem 4 :

The expression is equivalent to (3x + 2)/(x + 2)², where a and b are constants and x ≠ 2. What is the value of b?

Solution :

Problem 5 :

In the figure above, line ℓ is parallel to line m. What is the value of k?

Solution :

Problem 6 :

If m + 6 divided by 2 is 4 less than 4m, what is the value of m?

A)  2

B)  3

C)  4

D)  5

Solution :

Problem 7 :

If a line contains the points (0, 0) and (12, 16), then the line will also contain which of the following points?

A)  (2, 3)

B)  (3, 2)

C)  (3, 4)

D)  (4, 3)

Solution :

Problem 8 :

sin x = sin y

In the equation above, x and y are measured in radians. Which of the following could be x in terms of y?

A)  π/2 - y

B)  π/2 + y

C)  y - π/2

D)  π - y

Solution :

Problem 9 :

The equation (2x - b)(7x + b) = 14x² - cx - 16 is true for all values x, where b and c are constants. If b is greater than 0, what is the value of c?

A)  -20

B)  20

C)  28

D)  36

Solution :

Problem 10 :

Battery A runs out of energy after 132 minutes. Battery runs out of energy twice as fast. Battery C runs out of energy three times as fast as Battery B. If used one at a time, what is the total number of minutes that all the three batteries can provide energy for?

Solution :

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