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

Appeared in: RRB Staff Nurse Mumbai-2015

Explanation

The question asks for the number that, when subtracted from 13601, results in a number perfectly divisible by 87.
This is a classic division problem where the number to be subtracted is the remainder of the division 13601 ÷ 87.
Performing the long division: 13601 = (87 × 156) + 29.
The remainder is 29.
Subtracting the remainder (29) from the original number (13601) leaves 13572, which is exactly divisible by 87 (13572 ÷ 87 = 156).

Option A: 49 is the remainder from the first step of the long division (136 ÷ 87), not the final remainder for the entire number 13601.
Option B: 23 is an incorrect value, likely resulting from a calculation error during the long division process.
Option D: 31 is an incorrect value, likely resulting from a miscalculation in the final step of the division, such as 551 - 520 instead of 551 - 522.

Visual 1: Flowchart: A flowchart illustrating the process of finding the number to subtract for exact divisibility. It would show the steps: 1. Perform division. 2. Identify the remainder. 3. The remainder is the answer.

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.
While this is a mathematics question, strong numeracy skills are fundamental in nursing for accurate medication dosage calculations, IV drip rate monitoring, and interpreting patient data.
Errors in basic arithmetic can have serious patient safety consequences. This type of question reinforces the need for precision in calculations.
What if the question asked what number must be added? You would find the remainder (29) and then calculate the difference between the divisor and the remainder (87 - 29 = 58). So, 58 would be the number to add.

How to Approach the Question

First, understand the question. It's asking what to remove from 13601 to make it a perfect multiple of 87.
Recognize that the number to be 'subtracted' for exact divisibility is always the remainder of the division.
Set up the long division problem: 13601 ÷ 87.
Carefully perform each step of the division to find the quotient and, more importantly, the final remainder.
The final remainder you calculate is the answer.
Compare your result with the given options to find the correct choice.

Concept Tested & Keywords

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Practise the full RRB Staff Nurse Mumbai-2015

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