The HCF and the LCM of two numbers are 33 and 495, respectively. If one of the numbers is 99, what is the other number?

Appeared in: DSSSB October 2024

Explanation

The fundamental principle is that for any two numbers, the product of the numbers is equal to the product of their HCF and LCM.
The formula is: Number 1 × Number 2 = HCF × LCM.
Substituting the given values: 99 × Number 2 = 33 × 495.
Solving for the second number gives: Number 2 = (33 × 495) / 99.
Simplifying the expression, Number 2 = 495 / 3, which equals 165.

Option A: If the other number were 55, the product of the numbers would be 99 × 55 = 5445. The product of the HCF and LCM is 33 × 495 = 16335. Since 5445 is not equal to 16335, this option is incorrect.
Option B: The product of 99 and 116 is 11484, which does not equal the required product of HCF and LCM (16335).
Option D: If both numbers were 99, their HCF would be 99 and their LCM would also be 99. This contradicts the given HCF of 33 and LCM of 495.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Relationship between HCF and LCM of two numbers as background academic context rather than a clinical decision trigger.
While this is a mathematics question, strong numeracy and calculation skills are essential for safe nursing practice.
Nurses perform calculations daily for medication dosages, IV drip rates, fluid balance charts, and interpreting clinical data. A simple math error can have significant consequences for patient safety.
For example, miscalculating a pediatric dose based on weight can lead to underdosing (ineffective treatment) or overdosing (toxicity).

How to Approach the Question

First, identify the key information given in the problem: the HCF (33), the LCM (495), and one of the two numbers (99).
Recall the fundamental relationship between two numbers and their HCF and LCM: The product of the two numbers is equal to the product of their HCF and LCM.
Write down the formula: Number 1 × Number 2 = HCF × LCM.
Substitute the known values into the formula: 99 × Number 2 = 33 × 495.
Rearrange the equation to solve for the unknown number (Number 2).
Perform the calculation carefully: Number 2 = (33 × 495) / 99. Simplify to 495 / 3 to get 165. Match the result with the given options.

Concept Tested & Keywords

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Practise the full DSSSB October 2024

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