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

Appeared in: SGPGI Nursing Officer-2024

Explanation

For three numbers a, b, and c to be in continued proportion, the square of the middle term must equal the product of the other two terms (b² = ac).
Let 'x' be the number to be added. The new numbers are (2+x), (4+x), and (7+x).
The equation becomes (4+x)² = (2+x)(7+x).
Expanding the equation gives 16 + 8x + x² = 14 + 9x + x².
Solving this equation for x yields x = 2.
Verification: If we add 2, the numbers become 4, 6, and 9. Here, 6² = 36 and 4 × 9 = 36, confirming the proportion.

Option A: If 1 is added, the numbers become 3, 5, and 8. Checking for proportion: 5² = 25, while 3 × 8 = 24. Since 25 is not equal to 24, this option is incorrect.
Option B: If 3 is added, the numbers become 5, 7, and 10. Checking for proportion: 7² = 49, while 5 × 10 = 50. Since 49 is not equal to 50, this option is incorrect.
Option D: If 4 is added, the numbers become 6, 8, and 11. Checking for proportion: 8² = 64, while 6 × 11 = 66. Since 64 is not equal to 66, this option is incorrect.

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 mathematics question testing algebraic skills, not a clinical concept.
Proficiency in basic math is essential for various calculations in nursing, such as drug dosage, IV drip rates, and interpreting patient data.
While this specific concept of continued proportion is not directly applied in daily practice, the underlying problem-solving and algebraic skills are transferable and fundamental.

How to Approach the Question

First, identify the key mathematical concept 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, which simplifies to b² = ac.
Translate the word problem into an algebraic equation. Let 'x' be the unknown number to be added. The new numbers are (2+x), (4+x), and (7+x).
Substitute these new numbers into the proportion formula: (4+x)² = (2+x)(7+x).
Solve the resulting algebraic equation for 'x'.
Finally, verify your answer by plugging the value of 'x' back into the numbers and checking if the proportion holds true.

Concept Tested & Keywords

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

QJK67ghLNmox_8nebbb183

Practise the full SGPGI Nursing Officer-2024

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