SAT Math Multiple Choice Question 20: Answer and Explanation

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Question: 20

6. The sum of three numbers, a, b, and c, is 400. One of the numbers, a, is 40 percent less than the sum of b and c. What is the value of b + c ?

  • A. 40
  • B. 60
  • C. 150
  • D. 250

Correct Answer: D

Explanation:

DThis is a system of equations question in disguise. First, locate a piece of information in this question that you can work with. "The sum of three numbers, a, b, and c, is 400," seems very straightforward. Write the equation a + b + c = 400. Now the question tells you that "one of the numbers, a, is 40 percent less than the sum of b and c." Translate this piece by piece to get a = (1 - 0.4) (b + c), or a = 0.6(b + c). Distribute the 0.6 to get a = 0.6b + 0.6c. Arrange these variables so they line up with those in the first equation as a - 0.6b - 0.6c = 0. To solve for b + c, stack the equations and multiply the second equation by -1:

a + b + c = 400
-1(a - 0.6b - 0.6c) = 0(-1)

Now solve:

Simplify by dividing both sides by 1.6 to get b + c = 250. The correct answer is (D).

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