SAT Math Multiple Choice Question 489: Answer and Explanation

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Question: 489

9.

A voltage divider is a simple circuit that converts a large voltage into a smaller one. The figure above shows a voltage divider that consists of two resistors that together have a total resistance of 294 ohms. To produce the desired voltage of 330 volts, R2 must be 6 ohms less than twice R1. Solving which of the following systems of equations gives the individual resistances for R1 and R2?

  • A.
  • B.
  • C.
  • D.

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Heart of Algebra / Systems of Linear Equations

Strategic Advice: Take a quick peek at the answers just to see what variables are being used, but don't study the equations. Instead, write your own system using the same variables as given in the answer choices.

Getting to the Answer: One of the equations in the system should represent the sum of the two resistors (R1 + R2), which is equal to 294. This means you can eliminate C and D. The second equation needs to satisfy the condition that R2 is 6 less than twice R1, or R2 = 2R1 - 6. This means (A) is correct.

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