1.

In 2015 the populations of City X and City Y were equal. From 2010 to 2015, the population of City X increased by 20% and the population of City Y decreased by 10%. If the population of City X was 120,000 in 2010, what was the population of City Y in 2010?

Answer»

60000
90000
160000
240000

Solution : It’s given that the population of City X was 120,000 in 2010, and that it INCREASED by 20% from 2010 to 2015. Therefore, the population of City X in 2015 was 120,000 (1 + 0.20) = 144,000.It’s also given that the population of City Y DECREASED by 10% from 2010 to 2015. If y represents the population of City Y in 2010, then y(1 − 0.10) = 144,000. Solving this EQUATION for y yields y =`(144,000)/(1-0.10)`. SIMPLIFYING the denominator yields `(144,000)/(0.90)`, or 160,000.
Choice A is incorrect. If the population of City Y in 2010 was 60,000, then the population of City Y in 2015 would have been 60,000(0.90) = 54,000, which is not equal to the City X population in 2015 of 144,000. Choice B is incorrect because 90,000(0.90) = 81,000, which is not equal to the City X population in 2015 of 144,000. Choice D is incorrect because 240,000(0.90) = 216,000, which is not equal to the City X population in 2015 of 144,000.


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