# SAT Math Multiple Choice Question 116: Answer and Explanation

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**Question: 116**

**11.** If x^{2} + 2xy + y^{2} = 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 x^{2} + 2xy + y^{2} = 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.