Which number among the following options is NOT divisible by 9?

Appeared in: NCL (Northern Coalfields Limited)-NO

Explanation

The core concept is the divisibility rule for 9, which states a number is divisible by 9 if the sum of its digits is divisible by 9.
For the number 30,365, the sum of its digits is 3 + 0 + 3 + 6 + 5 = 17.
Since 17 is not a multiple of 9 (17 ÷ 9 = 1 with a remainder of 8), the number 30,365 is not divisible by 9.
This makes it the correct answer as the question asks which number is NOT divisible by 9.

Option A: The number 31,491 is divisible by 9. The sum of its digits (3+1+4+9+1) is 18, which is a multiple of 9 (18 ÷ 9 = 2).
Option C: The number 28,476 is divisible by 9. The sum of its digits (2+8+4+7+6) is 27, which is a multiple of 9 (27 ÷ 9 = 3).
Option D: The number 29,646 is divisible by 9. The sum of its digits (2+9+6+4+6) is 27, which is a multiple of 9 (27 ÷ 9 = 3).

Visual 1: Infographic - A simple chart showing the divisibility rules for common numbers (2, 3, 4, 5, 6, 9, 10). This provides a quick reference for similar questions.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Divisibility Rules in Mathematics as background academic context rather than a clinical decision trigger.
This question tests basic numeracy, a fundamental skill required for nursing and other professional entrance exams.
While not a direct clinical scenario, mathematical accuracy is critical in nursing for tasks like medication dosage calculation, IV drip rate monitoring, and interpreting lab results.
What if the question asked for a number divisible by 3? The same principle applies: sum the digits and check if the sum is divisible by 3. In this case, 31491, 28476, and 29646 would all be correct answers as their digit sums (18, 27, 27) are divisible by 3.

How to Approach the Question

First, identify the keyword 'NOT' in the question. This means you are looking for the exception among the options.
Recall the divisibility rule for the number 9: A number is divisible by 9 if the sum of all its digits is a multiple of 9.
Systematically calculate the sum of the digits for each of the four options provided.
Check if each sum is divisible by 9.
The option whose sum of digits is not divisible by 9 is the correct answer.

Concept Tested & Keywords

Concept Tested: Divisibility Rules in Mathematics
Stem keywords: divisible by 9, number
Lead-in keywords: NOT
Negative lead-in flag: The question asks to identify the number that is NOT divisible by 9.

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Practise the full NCL (Northern Coalfields Limited)-NO

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