In a recent survey, 40% houses contained two or more people. Of those houses containing only one person, 25% were having only a male. What is the percentage of all houses, which contain exactly one female and no males?

### Concept & Logic This problem tests logical deduction and set segmentation. By subtracting the percentage of houses with two or more people, you isolate the single-occupancy houses. Since single-occupancy houses can logically only contain either one male or one female, finding the percentage of one directly yields the other. ### Step-by-Step Solution * **Given:** Houses with $2$ or more people = $40\%$. Of single-person houses, $25\%$ contain only a male. * **Calculation / Deduction:** Let the total number of houses surveyed be $100$. Number of houses with two or more people = $40$. Therefore, the number of houses containing only one person = $100 - 40 = 60$. We are told that $25\%$ of these single-occupancy houses contain only a male. Number of houses with exactly one male = $25\%$ of $60 = 0.25 \times 60 = 15$. Since these $60$ houses contain *only one person*, they must either contain a lone male or a lone female. There are no other possibilities. Number of houses with exactly one female and no males = $60 - 15 = 45$. The percentage of all houses is therefore $45\%$. ### Exam Strategy & Shortcut Recognize the binary nature of "one person" houses. If $40\%$ are multi-person, $60\%$ are single-person. If $\frac{1}{4}$ of the $60\%$ are male, then $\frac{3}{4}$ of the $60\%$ must be female. Mentally compute $\frac{3}{4} \times 60 = 45$. Since $45$ is not among the explicit numerical options (15, 40, 75), confidently mark "None of these" immediately without second-guessing. ### Common Pitfall Students often incorrectly apply the $25\%$ to the total $100$ houses instead of the $60$ single-person houses. This leads to calculating $25$ male-only houses and incorrectly deducing female-only houses. Read phrases like "Of those houses..." very carefully to avoid applying percentages to the wrong base. ### Final Answer **Therefore, the correct answer is None of these.**