What least number must be subtracted from 13601 to get a number exactly divisible by 87?

Appeared in: RRB Staff Nurse Ahmedabad-2015

Explanation

The question asks for the smallest number to subtract from 13601 to make it perfectly divisible by 87.
This required number is simply the remainder obtained when 13601 is divided by 87.
The division algorithm states: Dividend = (Divisor × Quotient) + Remainder.
Performing the long division of 13601 by 87 gives a quotient of 156 and a final remainder of 29.
Therefore, 13601 = (87 × 156) + 29.
To make the number divisible by 87, the remainder (29) must be subtracted from the original number.

Option A: This value, 49, is the remainder from the first step of the long division (136 - 87 = 49). It is an intermediate result, not the final remainder for the entire number.
Option B: This is an incorrect value that does not result from any step of the correct division process. It is likely a calculation error.
Option D: This is an incorrect value that does not result from any step of the correct division process. It is likely a calculation error.

Visual 1: Infographic - A step-by-step visual breakdown of the long division of 13601 by 87, clearly showing how the final remainder of 29 is obtained.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Divisibility and Remainders in Arithmetic as background academic context rather than a clinical decision trigger.
Basic arithmetic skills, including division and finding remainders, are foundational for safe nursing practice, especially in medication administration.
Nurses frequently perform dosage calculations, which require precision. For example, calculating infusion rates (mL/hr) or drip rates (gtt/min) involves division.
An error in calculation can lead to underdosing or overdosing a patient, with potentially severe consequences.

How to Approach the Question

First, identify the key numbers in the problem: the dividend (13601) and the divisor (87).
Understand the core question: You need to find the 'least number to be subtracted' to make the dividend 'exactly divisible' by the divisor.
Recognize that this problem is asking for the remainder of a division operation.
Perform the long division of the dividend (13601) by the divisor (87).
The final remainder you calculate is the answer to the question.
To double-check, subtract this remainder from the original dividend and then divide the result by the divisor. The new division should have no remainder.

Concept Tested & Keywords

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Practise the full RRB Staff Nurse Ahmedabad-2015

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