From 2015 to 2025, the number of households in a town... | SAT Percentages Question, Answer Explained

Math · Problem-Solving and Data AnalysisHard

From $2015$ to $2025$ , the number of households in a town increased by $20\%$ . During the same period, the percent of the town's households that own a dog increased from $40\%$ to $50\%$ . By what percent did the number of households that own a dog increase from $2015$ to $2025$ ?

$10\%$

$25\%$

$30\%$

$50\%$

Show answer and explanation

Answer: D

Let $N$ be the number of households in $2015$ , so $0.40N$ households owned a dog. In $2025$ there were $1.2N$ households, and $0.50(1.2N) = 0.60N$ of them owned a dog. The number of dog-owning households went from $0.40N$ to $0.60N$ , an increase of $\frac{0.20N}{0.40N} = 0.5$ , or $50\%$ .

Choice B would be correct only if the number of households had stayed the same; it ignores the $20\%$ growth in households.

Why the other choices are wrong

A. 10 is the change in percentage points, not the percent increase in dog-owning households.
B. 25% would be right only if the number of households hadn't changed.
C. This adds 10 and 20, but the percent changes multiply: 0.40N becomes 0.60N.

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