Which is the smallest number to be subtracted from 7348 to make it exactly divisible by 135?

Appeared in: DSSSB 12 August 2024

Explanation

The question asks for the smallest number to be subtracted from 7348 to make it exactly divisible by 135.
This is a direct application of the Division Algorithm, which states that Dividend = (Divisor × Quotient) + Remainder.
To find this number, we must calculate the remainder of the division 7348 ÷ 135.
Performing the division, we get: 7348 = (135 × 54) + 58.
The remainder is 58. This is the 'excess' amount that prevents perfect division.
Subtracting this remainder (58) from the original number (7348) makes it perfectly divisible by 135 (7290 ÷ 135 = 54).

Option A: Subtracting 52 from 7348 gives 7296. When 7296 is divided by 135, it leaves a remainder of 6, so it is not exactly divisible.
Option C: Subtracting 56 from 7348 gives 7292. When 7292 is divided by 135, it leaves a remainder of 2, so it is not exactly divisible.
Option D: 54 is the quotient of the division (7348 ÷ 135), not the remainder. Subtracting the quotient is a common mistake.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Divisibility and Remainder as background academic context rather than a clinical decision trigger.
Accurate arithmetic is a fundamental non-nursing skill tested in nursing exams and is crucial for safe clinical practice.
Nurses use basic math daily for calculating medication dosages, setting IV infusion rates, and tracking patient fluid balance, where errors can have serious consequences.
What if? If the question asked for the smallest number to be added to make it divisible, the answer would be Divisor - Remainder. In this case, 135 - 58 = 77.

How to Approach the Question

First, identify the key components of the problem: the dividend (the number being divided, 7348) and the divisor (the number to divide by, 135).
Recognize that the phrase 'smallest number to be subtracted to make it exactly divisible' is a direct instruction to find the remainder of a division.
Perform the division: 7348 ÷ 135.
The remainder obtained from this calculation is the answer.
To double-check, subtract the remainder from the original number and divide by the divisor. The result should be a whole number with no remainder.

Concept Tested & Keywords

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Practise the full DSSSB 12 August 2024

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