SAT Math Multiple Choice Question 674: Answer and Explanation

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Question: 674

14. A culture of bacteria initially contained p cells, where p > 100. After one hour, this population decreased by Images. In the second and third hours, however, the population increased by 40% and 50%, respectively. At the end of those first three hours, what was the population of the culture?

  • A. 1.3p
  • B. 1.4p
  • C. 1.5p
  • D. 1.6p

Correct Answer: B

Explanation:

B

Advanced Mathematics (exponential growth) MEDIUM

We might begin by plugging in a number for p. Let's say p = 120 cells to start. We are told that after one hour the population decreased by Images. Since Images of 120 is 40, the population decreased by 40 and the population was then 120 - 40 = 80 cells. In the second hour, the population increased by 40%. Increasing a number by 40% is equivalent to it by 1.40 (because it becomes 140% of what it was), so the population was then 80(1.40) = 112 cells. In the third hour, the population increased by 50%, so it became 112(1.50) = 168 cells.

Substituting p = 120 into each of the answer choices yields (A) 1.3p = 1.3(120) = 156, (B) 1.4p = 1.4(120) = 168, (C) 1.5p = 1.5(120) = 180, and (D) 1.6p = 1.6(120) = 192. Therefore the answer is (B).

Alternately, you can solve this problem algebraically: p(2/3)(1.40)(1.50) = 1.40p.

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