SAT Math Multiple Choice Question 116: Answer and Explanation

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Question: 116

11. If x2 + 2xy + y2 = 64 and y - x = 12, which of the following could be the value of x ?

  • A. -10
  • B. -4
  • C. 2
  • D. 10

Correct Answer: A

Explanation:

A Factoring the left side of the equation x2 + 2xy + y2 = 64 gives (x + y)2 = 64. Taking the square root of both sides of the equation, we find that x + y = 8 or -8. The other equation provides that y - x = 12, so y = x + 12 . Substitute this value of y into the first equation: either x + (x + 12) = 8, so 2x + 12 = 8, 2x = -4, and x = -2, or else or x + (x + 12) = -8, so 2x + 12 = -8, so 2x = -20, and x = -10. Therefore, x could be either -2 or -10, and only -10 is an option in the answers, so (A) is correct.

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