SAT Math Multiple Choice Question 959: Answer and Explanation
Note: Figure not drawn to scale.
Figure ABCD is a parallelogram. What is the product of xy?
- A. 2,695
- B. 2,940
- C. 4,704
- D. 6,468
Correct Answer: A
Category: Additional Topics in Math / Geometry
Strategic Advice: Opposite angles of a parallelogram are congruent, and the diagonal acts as a transversal that is cutting two parallel lines (the opposite sides of the parallelogram).
Getting to the Answer: The alternate interior angles formed by the diagonal are congruent. This means x - y = 42 and x + y = 112. Set up a system of equations and solve it. The system is already arranged nicely to use elimination; combining the equations by adding them eliminates the y terms:
Substitute this value into either of the original equations for x to find y: 77 + y = 112, so y = 35. The question asks for the product of x and y, so the correct answer is 77 × 35 = 2,695, which is (A).