When two numbers are separately divided by 33 the remainders are 21 and 28 respectively. If the sum of the two numbers is divided by 33 the remainder will be:

Appeared in: RRB Staff Nurse Delhi-2015

Explanation

The problem utilizes the property that the remainder of a sum of numbers divided by a common divisor is equal to the remainder of the sum of their individual remainders divided by that same divisor.
First, sum the given remainders: 21 + 28 = 49.
Since this sum (49) is greater than the divisor (33), the next step is to find the remainder of 49 when it is divided by 33.
Dividing 49 by 33 gives a quotient of 1 and a remainder of 16, which is the final answer.

Option A: This is an incorrect calculation. The sum of remainders is 49, and the remainder of 49 divided by 33 is 16, not 10.
Option B: This is an incorrect calculation. It does not correspond to the correct application of the remainder theorem.
Option C: This is an incorrect calculation. The sum of remainders is 49, and 49 divided by 33 leaves a remainder of 16, not 14.

Visual 1: Flowchart: Step-by-step process for solving remainder problems. Step 1: Identify the divisor and remainders. Step 2: Sum the remainders. Step 3: Check if the sum is greater than the divisor. Step 4: If yes, divide the sum by the divisor to find the final remainder. If no, the sum is the final remainder.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Modular Arithmetic and Properties of Remainders as background academic context rather than a clinical decision trigger.
This question tests mathematical aptitude and logical reasoning, which are non-clinical skills assessed in nursing entrance exams.
These quantitative skills are foundational for critical nursing tasks like medication dosage calculation, interpreting data from patient charts, and managing fluid intake and output, where precision is essential for patient safety.
What if? If the remainders were 10 and 15, the sum of remainders would be 10 + 15 = 25. Since 25 is less than the divisor 33, the remainder would simply be 25.

How to Approach the Question

First, identify the key components of the problem: the divisor (33) and the two separate remainders (21 and 28).
Recall the fundamental property of remainders: The remainder of the sum of numbers is the same as the remainder of the sum of their individual remainders, when divided by the same divisor.
Apply this property by adding the two given remainders: 21 + 28 = 49.
Compare the result (49) with the divisor (33). Since 49 is larger than 33, an additional step is needed.
Divide the sum of the remainders (49) by the divisor (33) to find the final remainder.
The remainder of 49 ÷ 33 is 16. This is the correct answer.

Concept Tested & Keywords

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