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Problem-Solving and Data Analysis / Percentages Difficulty: Medium

The population of City A increased by $7 percent sign$ from $2015$ to $2016$ . If the $2016$ population is $k$ times the $2015$ population, what is the value of $k$ ?

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Explanation

Choice C is correct. It's given that the population of City A increased by $7 percent sign$ from $20 15$ to $20 16$ . Therefore, the population of City A in $20 16$ includes $100 percent sign$ of the population of City A in $20 15$ plus an additional $7 percent sign$ of the population of City A in $20 15$ . This means that the population of City A in $20 16$ is $107 percent sign$ of the population in $20 15$ . Thus, the population of City A in $20 16$ is $StartFraction 107 Over 100 EndFraction$ , or $1.07$ , times the $20 15$ population. Therefore, the value of $k$ is $1.07$ .

Choice A is incorrect. This would be the value of $k$ if the population in $20 16$ was $7 percent sign$ of the population in $20 15$ .

Choice B is incorrect. This would be the value of $k$ if the population in $20 16$ was $70 percent sign$ of the population in $20 15$ .

Choice D is incorrect. This would be the value of $k$ if the population increased by $70 percent sign$ , not $7 percent sign$ , from $20 15$ to $20 16$ .