OSSSC Nursing Officer-2023
Non Nursing Subjects
Hard
The greatest 4-digit number exactly divisible by 15, 20 and 25 is?
Appeared in: OSSSC Nursing Officer-2023
Explanation
- To be divisible by 15, 20, and 25, a number must be a multiple of their Least Common Multiple (LCM).
- The prime factorization of the numbers are: 15 = 3 × 5, 20 = 2² × 5, and 25 = 5².
- The LCM is the product of the highest powers of all prime factors: 2² × 3 × 5² = 300.
- The greatest 4-digit number is 9999. To find the largest multiple of 300 within this range, we divide 9999 by 300, which is 33.33.
- Multiplying the integer part of the quotient (33) by the LCM gives the answer: 33 × 300 = 9900.
Why Other Options Were Wrong
- Option A: The number 9990 is not divisible by 20 or 25. A number divisible by 20 must end in 0 and have the preceding digit be even. A number divisible by 25 must have its last two digits be 00, 25, 50, or 75.
- Option C: The number 9995 is not divisible by 15, 20, or 25. It does not end in 0 or 5, so it cannot be divisible by 15. It does not end in 0, so it cannot be divisible by 20.
- Option D: Although 9000 is divisible by 15, 20, and 25 (since 9000 = 30 × 300), it is not the greatest 4-digit number with this property. The question specifically asks for the greatest number, and 9900 is larger.
Related Visual
Clinical Relevance
- Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Finding the greatest n-digit number divisible by a set of numbers using the Least Common Multiple (LCM) as background academic context rather than a clinical decision trigger.
- This question tests basic numeracy, a fundamental skill for nurses, which is crucial for accurate medication dosage calculations, setting IV drip rates, and interpreting patient data.
- Errors in mathematical calculations can have severe patient safety consequences, making proficiency in this area a core competency for healthcare professionals.
- What if? If the question asked for the smallest 5-digit number divisible by 15, 20, and 25, the process would be similar. The LCM is 300. The smallest 5-digit number is 10,000. Divide 10,000 by 300 (33.33), round up to the next whole number (34), and multiply by the LCM: 34 × 300 = 10,200.
How to Approach the Question
- First, identify the core requirement: the number must be 'exactly divisible by 15, 20, and 25'. This indicates that the number must be a common multiple.
- To find the number that satisfies this for all three, calculate their Least Common Multiple (LCM).
- Next, identify the constraint: the number must be the 'greatest 4-digit number'. The range of 4-digit numbers is 1000 to 9999.
- Divide the largest number in the range (9999) by the calculated LCM.
- Take the whole number part (quotient) of the result from the division.
- Multiply this whole number by the LCM. The product is the greatest number in the given range that is divisible by all the specified numbers.
Concept Tested & Keywords
- Concept Tested: Finding the greatest n-digit number divisible by a set of numbers using the Least Common Multiple (LCM).
- Stem keywords: greatest 4-digit number, exactly divisible, 15, 20, 25
- Lead-in keywords: is?
- Negative lead-in flag: false
Question ID
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Practise the full OSSSC Nursing Officer-2023
Attempt every question from this paper in a timed mock, then review the full solution for each one.
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