SAT Math Multiple Choice Question 712: Answer and Explanation

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Question: 712

7. The value of y varies with x according to the equation y = kx2, where k > 0. When the value of x increases from 3 to 12, which of the following best describes the behavior of y?

  • A. It increases by 81.
  • B. It increases by 135.
  • C. It is multiplied by 4.
  • D. It is multiplied by 16.

Correct Answer: D

Explanation:

D

Advanced Mathematics (quadratics)

MEDIUM-HARD

Since k can be any number greater than 0, let's pick k = 1 for convenience. If x = 3, then y = (1)(3)2 = 9, and if x = 12, then y = (1)(12)2 = 144. In this case, both statement (B) and statement (D) are true, since 9 + 135 = 144 and 9(16) = 144; therefore, we can eliminate choices (A) and (C). Now let's choose k = 2. If x = 3, then y = (2)(3)2 = 18, and if x = 12, then y = 2(12)2 = 288. Since 18 + 135 ≠ 288, but 18(16) = 288, the correct answer is (D).

Notice, also, that since y varies directly as the square of x, then when x is multiplied by n, y is multiplied by n2. Since x is being multiplied by 4 (to go from 3 to 12), then y must be multiplied by 42 = 16.

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