A site slopes 15 feet over a horizontal distance of 300 feet. What is the percentage of slope?
Correct Answer
C) 5%
Why this is correct: Slope percentage is (Rise / Run) * 100. Here, the rise (vertical change) is 15 feet, and the run (horizontal distance) is 300 feet. Calculation: (15 / 300) = 0.05. Multiply by 100 to get 5%. Why the other choices are wrong: 15% would be the result if you used (15/100)*100 or misapplied the formula. 20% is incorrect (e.g., 15/75). 2% would be the result of (15/750)*100. Exam tip: Slope % = (Vertical Change / Horizontal Distance) * 100. Keep units consistent.
Why This Is the Correct Answer
Option B (5%) is correct because slope percentage is calculated using the formula (rise ÷ run) × 100. With a rise of 15 feet over a horizontal distance (run) of 300 feet, the calculation is (15 ÷ 300) × 100 = 0.05 × 100 = 5%. This represents a relatively gentle slope that would typically not pose significant development challenges. The decimal 0.05 converted to percentage form equals 5%.
Why the Other Options Are Wrong
Option A: 15%
Option A (15%) is incorrect because it represents the rise value without proper calculation. This common error occurs when someone mistakenly uses just the rise number (15) as the percentage, forgetting to divide by the run distance and properly calculate the ratio.
Option B: 20%
Option B (20%) is incorrect and appears to be a distractor with no logical basis in the given measurements. This percentage would require a much steeper slope than what the given measurements indicate, possibly resulting from completely incorrect calculations.
Option D: 2%
Option D (2%) is incorrect because it represents an error in the basic division calculation. This would result from incorrectly calculating 15 ÷ 300 as 0.02 instead of 0.05, possibly from a mathematical error or misreading the numbers.
Rise Over Run Times 100
Remember 'ROR-100': Rise Over Run times 100. Think of it as 'climbing stairs' - you go UP (rise) a certain amount for every step FORWARD (run), then multiply by 100 to get the percentage grade.
How to use: When you see a slope calculation question, immediately identify the rise (vertical change) and run (horizontal distance), then apply ROR-100: divide rise by run and multiply by 100 for the percentage.
Exam Tip
Always double-check that you're dividing the smaller number (rise) by the larger number (run) in typical slope problems, and don't forget to multiply by 100 to convert the decimal to a percentage.
Common Mistakes to Avoid
- -Using the rise number directly as the percentage without dividing by run
- -Forgetting to multiply by 100 to convert decimal to percentage
- -Confusing rise and run in the calculation
Concept Deep Dive
Analysis
This question tests the fundamental concept of calculating slope percentage, which is essential for real estate appraisers when evaluating topographical conditions of properties. Slope percentage is a critical factor in determining land usability, drainage patterns, construction costs, and overall property value. The calculation requires understanding the relationship between vertical rise and horizontal run, expressed as a percentage. This measurement helps appraisers assess whether a site is suitable for development, requires special engineering considerations, or has limitations that affect marketability.
Background Knowledge
Slope percentage is calculated as the ratio of vertical rise to horizontal run, multiplied by 100 to express as a percentage. This measurement is crucial in real estate appraisal for assessing site conditions, drainage, accessibility, and development potential. Understanding slope calculations helps appraisers determine appropriate adjustments for topographical conditions when comparing properties.
Real-World Application
Appraisers use slope calculations when evaluating hillside properties, determining if lots are suitable for septic systems (which require specific slope ranges), assessing drainage patterns, and estimating additional construction costs for sloped sites that may require retaining walls or special foundations.
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