SAT Math Multiple Choice Question 118: Answer and Explanation

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Question: 118

13. Cuthbert is conducting a chemistry experiment that calls for a number of chemicals to be mixed in various quantities. The one amount of which he is unsure is grams of potassium, p . If Cuthbert is certain that (3p2 + 14p + 24) - 2(p2 + 7p + 20) = 0, what is one possible value of 3p + 6, the exact number of grams of potassium that Cuthbert would like to use for this experiment?

  • A. 20
  • B. 18
  • C. 12
  • D. 10

Correct Answer: B

Explanation:

B Begin by simplifying the equation given. (3p2 + 14p + 24) - 2(p2 + 7p + 20) = 3p2 + 14p + 24 - 2p2 - 14p - 40 = p2 - 16 = 0. Factoring the left side of the simplified equation, we find that (p - 4)(p + 4) = 16. Solving for p, we find that p = ±4. The value of 3p + 6 must then be either 3(-4) + 6 = -6 or 3(4) + 6 = 18. The latter value is (B).

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