Percentages SAT question

Choice C is correct. It's given that the population of City A increased by $7\%$ from $2015$ to $2016$. Therefore, the population of City A in $2016$ includes $100\%$ of the population of City A in $2015$ plus an additional $7\%$ of the population of City A in $2015$. This means that the population of City A in $2016$ is $107\%$ of the population in $2015$. Thus, the population of City A in $2016$ is $\frac{107}{100}$, or $1.07$, times the $2015$ population. Therefore, the value of $k$ is $1.07$.

Choice A is incorrect. This would be the value of $k$ if the population in $2016$ was $7\%$ of the population in $2015$.

Choice B is incorrect. This would be the value of $k$ if the population in $2016$ was $70\%$ of the population in $2015$.

Choice D is incorrect. This would be the value of $k$ if the population increased by $70\%$, not $7\%$, from $2015$ to $2016$.