What should be added to each of the numbers 2, 4, and 7 so that the resulting numbers are in continued proportion?

Appeared in: UP NHM CHO 7 Sept 2022(shift-1st)

Explanation

For three numbers a, b, and c to be in continued proportion, the relationship b² = a * c must hold true.
Let 'x' be the number to be added. The new set of numbers becomes (2 + x), (4 + x), and (7 + x).
Applying the rule of continued proportion gives the equation: (4 + x)² = (2 + x)(7 + x).
Expanding and simplifying the equation (16 + 8x + x² = 14 + 9x + x²) leads to the solution x = 2.
Verification confirms the answer: adding 2 gives the numbers 4, 6, and 9. Here, 6² (36) is equal to 4 × 9 (36), satisfying the condition.

Option A: If 1 is added, the numbers become 3, 5, and 8. The proportion check fails because 5² (25) is not equal to 3 × 8 (24).
Option B: If 3 is added, the numbers become 5, 7, and 10. The proportion check fails because 7² (49) is not equal to 5 × 10 (50).
Option D: If 4 is added, the numbers become 6, 8, and 11. The proportion check fails because 8² (64) is not equal to 6 × 11 (66).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the mathematical concept of continued proportion as background academic context rather than a clinical decision trigger.
This is a general aptitude question testing mathematical reasoning, not a clinical concept.
While this specific concept of 'continued proportion' has no direct application in daily nursing tasks, proficiency in basic algebra is fundamental for accurate medication dosage calculations, IV drip rate adjustments, and interpreting certain lab results.
What if the question involved calculating a medication dose based on a ratio? The nurse would use similar principles of setting up and solving a proportion (e.g., dose on hand / volume on hand = dose desired / x volume) to ensure patient safety.

How to Approach the Question

First, identify the key mathematical term in the question, which is 'continued proportion'.
Recall the definition: three numbers a, b, and c are in continued proportion if a/b = b/c, or more simply, b² = ac.
Introduce a variable, 'x', to represent the unknown number that needs to be added.
Formulate the new numbers in terms of x: (2+x), (4+x), and (7+x).
Substitute these expressions into the continued proportion formula: (4+x)² = (2+x)(7+x).
Solve the resulting algebraic equation for x.

Concept Tested & Keywords

Concept Tested: This question tests the mathematical concept of continued proportion.
Stem keywords: numbers, 2, 4, and 7, continued proportion
Lead-in keywords: What should be added

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E6 Nursing Fundamentals Potter Perry 12e Part 3 p. 141-143

E6 Nursing Fundamentals Taylor p. 917-919

Practise the full UP NHM CHO 7 Sept 2022(shift-1st)

Attempt every question from this paper in a timed mock, then review the full solution for each one.