On dividing a number by 511, we get 72 as remainder. On dividing the same number by 73, what will be the remainder?

Appeared in: RRB Nsg. Superintendent-20 July 2019 (Shift-3rd)

Explanation

The problem is based on the division algorithm: Dividend = (Divisor × Quotient) + Remainder.
The first statement gives the equation: Number (N) = (511 × k) + 72, where k is the quotient.
The key is to recognize that the first divisor (511) is a direct multiple of the second divisor (73), as 511 = 73 × 7.
Substituting this, the equation becomes N = (73 × 7 × k) + 72. This can be rewritten as N = 73 × (7k) + 72.
When this new form of N is divided by 73, the term '73 × (7k)' is perfectly divisible, leaving the final remainder as 72.

Option A: A remainder must always be less than the divisor. Since the divisor is 73, a remainder of 74 is not possible.
Option B: Similar to the previous option, a remainder of 75 is impossible when dividing by 73, as the remainder cannot be greater than the divisor.
Option D: A remainder of 73 when dividing by 73 is not possible. If the remainder were 73, it would mean the number is perfectly divisible by 73, and the actual remainder would be 0.

Visual 1: Flowchart - A flowchart illustrating the step-by-step process: 1. Set up the initial equation using the division algorithm. 2. Check if Divisor 1 is a multiple of Divisor 2. 3. Substitute and rearrange the equation. 4. Identify the new 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 quantitative aptitude question and does not have direct clinical relevance.
However, strong numerical and logical reasoning skills are essential for nurses for tasks like medication dosage calculation, IV drip rate monitoring, and interpreting patient data and lab values.
What if the first divisor was not a multiple of the second? If 512 was the divisor instead of 511, the shortcut would not apply, and a different method (like using the Chinese Remainder Theorem or finding a general form of the number) would be needed.

How to Approach the Question

First, represent the given information using the division algorithm formula: Dividend = (Divisor × Quotient) + Remainder.
Let the number be N and the quotient be k. The first condition translates to N = 511k + 72.
Next, examine the relationship between the two divisors (511 and 73). Check if the first divisor is a multiple of the second.
Calculate 511 ÷ 73. You will find that 511 = 73 × 7.
Substitute this relationship into the original equation and rearrange it to be in the form of division by 73.
The resulting equation, N = 73(7k) + 72, clearly shows that when N is divided by 73, the remainder is 72.

Concept Tested & Keywords

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Practise the full RRB Nsg. Superintendent-20 July 2019 (Shift-3rd)

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