On dividing a number by 329, we get 46 as remainder. On dividing the same number by 47, what will be the remainder?

Appeared in: RRB Nsg. Superintendent-20 July 2019 (Shift-2)

Explanation

The solution relies on the division algorithm: Dividend = (Divisor × Quotient) + Remainder. Let the number be N. We are given N = 329k + 46.
The key insight is that the first divisor (329) is a direct multiple of the second divisor (47), since 329 = 47 × 7.
By substituting this relationship, the equation becomes N = (47 × 7)k + 46. The term (47 × 7k) is perfectly divisible by 47.
Therefore, the remainder of the entire expression when divided by 47 is determined solely by the original remainder, 46.
Since 46 is less than the new divisor 47, it is the final remainder.

Option B: This is an incorrect calculation. It might arise from mistakenly subtracting 2 from the remainder (46 - 2), but there is no mathematical basis for this operation.
Option C: This is an incorrect calculation. There is no standard arithmetic operation in this context that would result in 32.
Option D: This is an incorrect calculation. There is no logical mathematical step that leads to this result in the given problem.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Remainder Theorem and Divisibility as background academic context rather than a clinical decision trigger.
This question tests general aptitude and numerical reasoning skills, which are essential for nurses.
Nurses frequently perform calculations for drug dosages, IV drip rates, and fluid balance, requiring strong mathematical proficiency and logical thinking.
What if the first divisor was 330 instead of 329? In that case, 330 is not a multiple of 47. The problem could not be solved with the given information, as the remainder would depend on the specific value of the quotient 'k'.

How to Approach the Question

First, identify the key numbers from the problem: the first divisor (329), the first remainder (46), and the second divisor (47).
Represent the unknown number using the division algorithm: Number = (First Divisor × Quotient) + First Remainder.
The crucial step is to check the relationship between the two divisors. Divide the first divisor (329) by the second divisor (47).
If the first divisor is a multiple of the second (i.e., the division results in a whole number), the problem becomes simple.
In this case, the new remainder is found by dividing the original remainder (46) by the new divisor (47).
Since 46 is smaller than 47, it cannot be divided further, so 46 itself is the remainder.

Concept Tested & Keywords

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Practise the full RRB Nsg. Superintendent-20 July 2019 (Shift-2)

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