BSF Staff Nurse - 2015
Non Nursing Subjects
Easy
The LCM and HCF of two numbers are 150 and 5 respectively. If one number is 25, then other number is?
Appeared in: BSF Staff Nurse - 2015
Explanation
- The fundamental principle in this problem is that the product of two numbers is equal to the product of their Least Common Multiple (LCM) and Highest Common Factor (HCF).
- The formula is: Number 1 × Number 2 = LCM × HCF.
- Given values are: LCM = 150, HCF = 5, and one number = 25.
- Substituting the values: 25 × Number 2 = 150 × 5.
- The product of the LCM and HCF is 150 × 5 = 750.
- To find the other number, we divide this product by the known number: 750 ÷ 25 = 30.
Why Other Options Were Wrong
- Option B: This is an incorrect calculation. If the other number were 24, the product of the two numbers would be 25 × 24 = 600, which does not equal the product of the LCM and HCF (750).
- Option C: This is an incorrect calculation. If the other number were 28, the product of the two numbers would be 25 × 28 = 700, which is not equal to the product of the LCM and HCF (750).
- Option D: This is an incorrect calculation. If the other number were 20, the product of the two numbers would be 25 × 20 = 500, which does not equal the product of the LCM and HCF (750).
Related Visual
Clinical Relevance
- Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Relationship between LCM, HCF, and the product of two numbers as background academic context rather than a clinical decision trigger.
- This question tests basic mathematical aptitude, which is a component of the general intelligence section in many nursing and other competitive examinations.
- Strong numerical skills are essential for nurses for tasks like medication dosage calculation, IV drip rate monitoring, and interpreting patient data charts.
- What if the LCM was 300 and the HCF was 10? Keeping one number at 25, the other number would be (300 × 10) / 25 = 3000 / 25 = 120. The formula remains the same regardless of the values.
How to Approach the Question
- First, identify the type of question. This is a direct application of a standard mathematical formula involving LCM and HCF.
- Recall the key formula: Product of two numbers = Product of their LCM and HCF.
- List all the values provided in the question: LCM = 150, HCF = 5, and one of the numbers = 25.
- Substitute these values into the formula: 25 × (Second Number) = 150 × 5.
- Solve the equation for the unknown 'Second Number'.
- Perform the calculation: (150 × 5) / 25 = 750 / 25 = 30.
Concept Tested & Keywords
- Concept Tested: Relationship between LCM, HCF, and the product of two numbers
- Stem keywords: LCM, HCF, two numbers
- Lead-in keywords: then other number is?
Question ID
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Attempt every question from this paper in a timed mock, then review the full solution for each one.
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