If the smaller number is half of the bigger number and their product is 72, then find the bigger number.

Appeared in: KGMU 2023

Explanation

The problem requires setting up an algebraic equation from the given statements.
Let the larger number be 'x'. The smaller number is then 'x/2'.
Their product is given as 72, leading to the equation: x * (x/2) = 72.
Solving this equation, we get x² = 144.
Taking the square root, x = 12. Thus, the bigger number is 12.

Option A: If the bigger number is 20, the smaller number would be 10. Their product is 20 * 10 = 200, which is not 72.
Option B: If the bigger number is 14, the smaller number would be 7. Their product is 14 * 7 = 98, which is not 72.
Option D: If the bigger number is 6, the smaller number would be 3. Their product is 6 * 3 = 18, which is not 72. Also, the question asks for the bigger number, and 6 is the smaller number in the correct solution pair (6 and 12).

Visual 1: No visual is required for this type of quantitative aptitude question.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving algebraic word problems as background academic context rather than a clinical decision trigger.
While not a direct clinical question, this tests quantitative aptitude, a fundamental skill for nurses.
Nurses must be proficient in math for tasks like calculating drug dosages, IV drip rates, and interpreting patient data, where errors can have serious consequences.
What if the product was 288? Following the same logic, x²/2 = 288, so x² = 576, and x = 24. The bigger number would be 24.

How to Approach the Question

First, carefully read the word problem to understand the relationships between the unknown quantities.
Assign a variable (like 'x') to one of the unknown quantities, typically the one you are asked to find (the bigger number).
Express the other unknown quantity (the smaller number) in terms of 'x' based on the problem statement (smaller number = x/2).
Formulate an equation using the remaining information (product = 72).
Solve the resulting algebraic equation to find the value of 'x'.
Check your answer by plugging the value back into the original problem to ensure it satisfies all conditions.

Concept Tested & Keywords

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Practise the full KGMU 2023

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