In 2008, Zinah earned 14% more than in 2007, and in 2009 Zinah earned 4% more than in 2008. If Zinah earned y times as much in 2009 as in 2007, what is the value of y?
Correct answer: D. 1.1856
- A. 0.5600
- B. 1.0056
- C. 1.1800
- D. 1.1856
Explanation
Choice D is correct. It's given that in 2008 Zinah earned 14% more than in 2007. Let h represent the amount Zinah earned in 2007 and let j represent the amount that Zinah earned in 2008. This situation can be represented by the equation j = (1 + 14/100)h, or j =1.14 h. It's also given that in 2009 Zinah earned 4% more than in 2008. Let k represent the amount Zinah earned in 2009. This situation can be represented by the equation k = (1 + 4/100)j, or k = 1.04j. Substituting 1.14h for j in the equation k =1.04 j yields k = (1.04)(1.14h), or k =1.1856 h. If Zinah earned y times as much in 2009 as in 2007, then the value of y is 1.1856.
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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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