The sum of two numbers is 75 and their difference is 25. The product of the two numbers is

Appeared in: SGPGI Nursing Officer-2024

Explanation

The problem is solved by setting up two algebraic equations: x + y = 75 (for the sum) and x - y = 25 (for the difference).
Adding the two equations together eliminates the 'y' variable, resulting in 2x = 100, which gives x = 50.
Substituting x = 50 back into the first equation (50 + y = 75) gives y = 25.
The final step is to calculate the product of these two numbers: 50 × 25 = 1250.

Option A: This value is significantly larger than the actual product and likely results from a major calculation error.
Option B: This value might be a result of miscalculation, such as adding the two numbers (75+50) or some other incorrect operation. The product requires multiplication.
Option C: This value might be obtained from an incorrect multiplication, for example, 50 × 80. It does not match the product of the correctly identified numbers (50 and 25).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving a system of linear equations to find the product of two unknown numbers as background academic context rather than a clinical decision trigger.
While this is a math problem, strong numeracy and algebraic skills are fundamental in nursing for accurate medication dosage calculations, especially for titrating IV drips or calculating weight-based drug doses.
Understanding these principles helps prevent medication errors, which are a major patient safety concern.
What if the sum was 100 and the difference was 20? The numbers would be 60 and 40, and the product would be 2400. The same algebraic method applies regardless of the numbers.

How to Approach the Question

First, read the problem carefully to identify the given information (sum and difference) and what needs to be found (the product).
Represent the two unknown numbers with variables, such as 'x' and 'y'.
Translate the word problem into two distinct algebraic equations based on the given sum and difference.
Solve this system of equations. A common method is elimination (adding or subtracting the equations) or substitution.
Once you have found the values for both variables, perform the final operation required by the question, which is to calculate their product.

Concept Tested & Keywords

Concept Tested: Solving a system of linear equations to find the product of two unknown numbers.
Stem keywords: sum of two numbers, difference, product
Lead-in keywords: The product of the two numbers is
Negative lead-in flag: false

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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.