SAT Math Multiple Choice Question 174: Answer and Explanation

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Question: 174

9. Mike consumes an average of 1,680 calories per day. Each day he has finals, Mike consumes 12% more calories per day than he usually does. During the last day of finals, he celebrates by consuming an additional 900 calories. Which of the following represents the total number of calories Mike consumes during d days of finals?

  • A. 1.12(1,680d + 900)
  • B. 1.12(1,680d) + 900
  • C. 1.12(1,680 + 900)d
  • D. (1,680 + 0.12d) + 900

Correct Answer: B

Explanation:

B First, calculate what Mike's daily calorie consumption is during finals. 12% of 1,680 is 0.12 × 1,680 = 201.6. During finals Mike consumes 1,680 + 201.6 = 1,881.6 calories per day. Whenever the question includes variables, Plug in. Let d = 2. Over 2 days Mike consumes 2 × 1,881.6 = 3,763.2 calories. He also adds 900 calories at the end of finals. His total consumption over the entire finals period is 3,763.2 + 900 = 4,663.2 calories, so 4,663.2 is the target number. Plug in 2 for d in each of the answer choices. In (A), 1.12[1,680(2) + 900] = 4,771.2, which is not the target number. Eliminate (A). In (B), 1.12[1,680(2)] + 900 = 4,663.2, which is the target. Leave (B), but check the other answer choices just in case. In (C), 1.12(1,680 + 900)(2) = 5,779.2, and in (D), [1,680 + (0.12)(2)] + 900 = 2,580.24. Eliminate both (C) and (D). The correct answer is (B).

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