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NORCET-11 Prelims

Medium

The sum of two numbers is 115 and their difference is 21. What are the two numbers?

Appeared in: NORCET-11 Prelims

Explanation

Let the numbers be x and y.
x + y = 115 and x - y = 21.
Adding both equations gives 2x = 136, so x = 68.
Substitute x = 68 into x + y = 115 to get y = 47.
68 and 47 are the only pair that satisfy both conditions.

Why Other Options Were Wrong

Option B: 67 and 48 add up to 115, but their difference is 19, not 21.
Option C: 69 and 46 add up to 115, but their difference is 23, not 21.
Option D: 65 and 50 add up to 115, but their difference is 15, not 21.

Related Visual

Steps to solve two equations with two unknowns sum and difference method.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving simultaneous equations for two unknowns (sum and difference) as background academic context rather than a clinical decision trigger.
Nurses may need to solve basic algebraic equations for medication calculations or dosage adjustments.
What if? If the sum was 120 and the difference was 20, the numbers would be 70 and 50.

How to Approach the Question

Identify the two equations from the stem (sum and difference).
Add the equations to eliminate one variable.
Solve for the first variable.
Substitute back to find the second variable.
Check which option matches both conditions.

Concept Tested & Keywords

Concept Tested: Solving simultaneous equations for two unknowns (sum and difference)
Stem keywords: sum, difference, two numbers, 115, 21
Lead-in keywords: What are the two numbers

Question ID

QmQOB6bQuOPveP7LtPGRHL

Reference Book

E6 NursingResearch Suresh Sharma 5e Part 2 p. 213-215

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