When a number is divided by 24, the remainder is 16. If the same number is divided by 12, what will be the remainder?

Appeared in: SGPGI Nursing Officer-2024

Explanation

Let the number be N. From the problem, we can write N = 24k + 16, where k is the quotient.
We need to find the remainder when N is divided by 12.
Substitute the expression for N: (24k + 16) / 12.
The term 24k is perfectly divisible by 12 because 24 is a multiple of 12. So, this part gives a remainder of 0.
The problem reduces to finding the remainder of 16 divided by 12.
When 16 is divided by 12, the remainder is 4.

Option B: This is an incorrect calculation. The remainder of 16 divided by 12 is 4, not 6.
Option C: This is an incorrect calculation. The remainder of 16 divided by 12 is 4, not 8.
Option D: This is an incorrect calculation. The remainder of 16 divided by 12 is 4, not 3.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Divisibility and Remainder Theorem as background academic context rather than a clinical decision trigger.
While this is a general aptitude question, strong foundational math skills are critical in nursing.
Nurses frequently use arithmetic for calculating medication dosages, setting IV drip rates, and monitoring fluid balance (intake and output).
Errors in calculation can have serious patient safety consequences, making numeracy a core competency for safe nursing practice.

How to Approach the Question

First, understand the relationship given: Dividend = (Divisor × Quotient) + Remainder.
Represent the unknown number (let's call it N) using the first piece of information: N = 24k + 16.
Now, analyze the second part of the question: what is the remainder when N is divided by 12?
Observe the relationship between the two divisors (24 and 12). Notice that 12 is a factor of 24.
Because the new divisor (12) is a factor of the original divisor (24), the part of the number that was a multiple of 24 (24k) will also be a multiple of 12, leaving no remainder.
Therefore, the new remainder is simply the remainder of the original remainder (16) when divided by the new divisor (12).

Concept Tested & Keywords

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Practise the full SGPGI Nursing Officer-2024

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