On dividing a number by 427, we get 60 as remainder. On dividing the same number by 61, what will be the rema… - RRB Nsg. Superintendent-21 July 2019 (Shift-2nd)

RRB Nsg. Superintendent-21 July 2019 (Shift-2nd)

Non Nursing Subjects

Medium

Appeared in: RRB Nsg. Superintendent-21 July 2019 (Shift-2nd)

Explanation

The core principle is that if a number N leaves a remainder R when divided by D, it can be expressed as N = D*q + R.
The first divisor (427) is a direct multiple of the second divisor (61), since 427 = 61 × 7.
Because of this relationship, the original equation N = 427q + 60 can be rewritten as N = (61 × 7)q + 60.
This simplifies to N = 61(7q) + 60, which shows that when N is divided by 61, the term 61(7q) is perfectly divisible, leaving the original remainder of 60.
Since the remainder (60) is less than the new divisor (61), the remainder is 60 itself.

Option B: This is an incorrect value. It does not follow from any correct mathematical procedure related to the problem.
Option C: This is an incorrect value. It may arise from a miscalculation or misunderstanding of the remainder theorem.
Option D: This is an incorrect value. It has no mathematical basis in the context of this specific remainder problem.

Visual 1: Flowchart: A flowchart illustrating the shortcut for solving remainder problems. It would start with the question 'Is Divisor 1 a multiple of Divisor 2?'. If yes, it leads to 'Divide Remainder 1 by Divisor 2'. If no, it leads to 'Shortcut does not apply'.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the application of the Remainder Theorem in number theory, a fundamental concept in basic mathematics as background academic context rather than a clinical decision trigger.
This question does not test a clinical concept but evaluates mathematical aptitude, which is a component of the general intelligence section in nursing entrance exams.
Strong analytical and problem-solving skills are essential for nurses for tasks like medication dosage calculations, interpreting lab results, and managing patient data.
What if the second divisor was 59 instead of 61? In that case, 427 is not a multiple of 59. The shortcut would not apply, and the answer could not be determined from the given information.

How to Approach the Question

First, identify the components of the problem: Divisor 1 (D1 = 427), Remainder 1 (R1 = 60), and Divisor 2 (D2 = 61).
The key step is to check the relationship between the two divisors. Ask yourself: 'Is D1 divisible by D2?'.
Perform the division: 427 ÷ 61 = 7. Since it divides evenly, you can use the shortcut.
The shortcut states that the new remainder is the remainder obtained by dividing the first remainder (R1) by the second divisor (D2).
Apply the shortcut: Find the remainder of 60 ÷ 61.
Since 60 is smaller than 61, the remainder is 60. Select the corresponding option.

Concept Tested & Keywords

Concept Tested: This question tests the application of the Remainder Theorem in number theory, a fundamental concept in basic mathematics.
Stem keywords: dividing a number, 427, 60 as remainder, dividing by 61
Lead-in keywords: what will be the remainder

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