On dividing a number by 385, we get 54 as remainder. On dividing the same number by 55, what will be the remainder?

Appeared in: RRB Nsg. Superintendent-20 July 2019 (Shift-1)

Explanation

The problem uses the division algorithm: Dividend = (Divisor × Quotient) + Remainder. Initially, this is expressed as Number = (385 × k) + 54.
The key insight is that the first divisor (385) is a direct multiple of the second divisor (55), since 385 = 55 × 7.
By substituting this relationship, the equation becomes Number = (55 × 7k) + 54.
The term (55 × 7k) is perfectly divisible by 55, leaving a remainder of 0.
Therefore, the final remainder is determined solely by the original remainder, 54, as it is less than the new divisor, 55.

Option B: The value 50 is an incorrect calculation. It does not follow from the logic of the remainder theorem.
Option C: The value 48 is an incorrect calculation. It might result from an arithmetic error or misunderstanding the problem.
Option D: The value 52 is an incorrect calculation. It does not align with the principles of divisibility applied here.

Visual 1: Flowchart - A flowchart showing the logical steps: 1. Write the equation for the first division. 2. Check if the first divisor is a multiple of the second. 3. If yes, substitute and simplify. 4. The new remainder is the original remainder.

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 is a general aptitude question testing mathematical reasoning, not a clinical nursing concept.
Numerical proficiency is essential for nurses for tasks like medication dosage calculation, IV drip rate monitoring, and interpreting lab results, making aptitude tests a part of many nursing entrance exams.
What if the first divisor (385) was NOT a multiple of the second (e.g., 60)? In that case, the remainder cannot be determined from the given information alone.

How to Approach the Question

First, identify the components of the problem: the initial divisor (385), the initial remainder (54), and the new divisor (55).
Represent the unknown number using the division algorithm: Number = 385k + 54.
Next, check for a relationship between the two divisors. Divide the larger divisor (385) by the smaller one (55).
Recognize that 385 is a multiple of 55 (385 = 55 × 7). This is the crucial shortcut.
Since the first divisor is a multiple of the second, the new remainder is found by dividing the first remainder (54) by the new divisor (55).
As 54 is smaller than 55, the remainder of this division is 54 itself.

Concept Tested & Keywords

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Practise the full RRB Nsg. Superintendent-20 July 2019 (Shift-1)

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