DSSSB 13 August 2024
Non Nursing Subjects
Hard
Three positive numbers are in the ratio of 1:2:3, and the sum of their squares is 896. What is the highest number?
Appeared in: DSSSB 13 August 2024
Explanation
- The numbers are represented as x, 2x, and 3x based on the 1:2:3 ratio.
- The sum of their squares is (x)² + (2x)² + (3x)² = x² + 4x² + 9x² = 14x².
- Setting 14x² equal to the given sum, 896, yields x² = 64, so x = 8.
- The highest number is represented by 3x, which calculates to 3 * 8 = 24.
Why Other Options Were Wrong
- Option B: If 26 were the highest number (3x), then x would be 26/3, which is not an integer. The sum of the squares of the resulting numbers (26/3, 52/3, 26) would not equal 896.
- Option C: If 25 were the highest number (3x), then x would be 25/3. The sum of the squares of the numbers (25/3, 50/3, 25) would not result in 896.
- Option D: If 20 were the highest number (3x), then x would be 20/3. The sum of the squares of the numbers (20/3, 40/3, 20) would not equal 896.
Related Visual
Clinical Relevance
- Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Application of Ratios and Proportions in Algebra as background academic context rather than a clinical decision trigger.
- This is a non-nursing question from the General Aptitude section of the exam, designed to test logical and mathematical reasoning skills.
- While not directly clinical, the analytical skills required to solve this problem are the same skills nurses use for critical tasks like calculating medication dosages, titrating IV drips, and interpreting patient data trends.
- What if the ratio was 2:3:4? The equation would become (2x)² + (3x)² + (4x)² = 4x² + 9x² + 16x² = 29x². The value of x and the final numbers would change accordingly.
How to Approach the Question
- First, identify the core components of the problem: a ratio (1:2:3) and a mathematical condition (sum of squares is 896).
- Represent the unknown numbers using a single variable (x) and the given ratio. The numbers become x, 2x, and 3x.
- Translate the mathematical condition into an algebraic equation: (x)² + (2x)² + (3x)² = 896.
- Solve the equation for the variable 'x'.
- Once 'x' is found, use it to calculate the value of the highest number, which is represented by 3x.
- Finally, check your answer against the given options.
Concept Tested & Keywords
- Concept Tested: Application of Ratios and Proportions in Algebra
- Stem keywords: positive numbers, ratio, sum of their squares
- Lead-in keywords: highest number
Question ID
QjytDIdox8ixtAFkZ33c3h
Practise the full DSSSB 13 August 2024
Attempt every question from this paper in a timed mock, then review the full solution for each one.
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