Three pieces of wire, 120 meters, 64 meters and 124 meters long, have to be divided into small pieces of equal length. What is the greatest possible length of each piece?

1. A

   10 metres

2. B

   32 metres

3. C

   12 metres

4. D

   4 metres

Appeared in: DSSSB 13 August 2024

Explanation

• The question requires finding the largest number that can evenly divide 120, 64, and 124. This is a problem of finding the Highest Common Factor (HCF).
• To find the HCF, we can use prime factorization. The prime factors are: 120 = 2³ × 3 × 5; 64 = 2⁶; 124 = 2² × 31.
• The only common prime factor is 2. The lowest power of this common factor across all numbers is 2².
• Therefore, the HCF is 2² = 4. This means the greatest possible equal length for each piece of wire is 4 meters.

Why Other Options Were Wrong

• Option A: 10 is not a factor of 64 or 124. For a length to be a common divisor, it must divide all given lengths without a remainder.
• Option B: 32 is a factor of 64, but not of 120 or 124. It fails the condition of being a common divisor for all three lengths.
• Option C: 12 is a factor of 120, but not of 64 or 124. It cannot be the greatest common length.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Highest Common Factor (HCF) / Greatest Common Divisor (GCD) as background academic context rather than a clinical decision trigger.
• While this is a quantitative aptitude question, the underlying skill of finding common factors is useful in nursing practice.
• It can be applied when dividing bulk medical supplies (like gauze rolls or tubing) into equal, smaller units for multiple patients or procedures, ensuring no wastage.
• This skill is also foundational for dosage calculations, especially when dealing with different concentrations or volumes of medication.

How to Approach the Question

• First, read the question carefully and identify the key phrases: 'divided into... small pieces of equal length' and 'greatest possible length'.
• Recognize that these phrases are asking for the Highest Common Factor (HCF) of the given numbers.
• List the numbers for which you need to find the HCF: 120, 64, and 124.
• Choose a method to find the HCF. Prime factorization is a reliable method. Break down each number into its prime factors.
• Identify the prime factors that are common to all the numbers. Multiply these common factors together, using the lowest power of each common factor.
• The result is the HCF, which is the answer to the question. You can also quickly check your answer by ensuring it divides all three original numbers.

Concept Tested & Keywords

• Concept Tested: Highest Common Factor (HCF) / Greatest Common Divisor (GCD)
• Stem keywords: wire, 120 meters, 64 meters, 124 meters, divided, equal length, greatest possible length
• Lead-in keywords: What is the greatest possible length

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Q5zmLe2a6ygI7iPSdOk2MM

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