The number of 3-digit numbers divisible by 6 is ______

Appeared in: UPUMS Nsg.Officer-2024

Explanation

The problem asks for the count of all 3-digit numbers (100-999) that are divisible by 6.
These numbers form an Arithmetic Progression (AP) with a common difference of 6.
The first term (a) is 102, and the last term (l) is 996.
Using the AP formula for the number of terms, n = ((l - a) / d) + 1, we get ((996 - 102) / 6) + 1.
The calculation simplifies to (894 / 6) + 1, which is 149 + 1 = 150.

Option A: This value represents the total count of numbers divisible by 6 from 1 to 999 (i.e., 996 ÷ 6 = 166). It fails to exclude the 1-digit and 2-digit numbers.
Option B: This is a result of a calculation error. For instance, incorrectly identifying the last term as 998 and the first as 102 would lead to a non-integer result, but a slight miscalculation could lead to 151.
Option D: This is a common error where the '+1' in the arithmetic progression formula is forgotten. It represents the number of intervals between the terms, not the total number of terms.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Arithmetic Progression and Divisibility Rules as background academic context rather than a clinical decision trigger.
While this is a general aptitude question, strong numeracy is a core nursing competency.
Nurses must accurately calculate medication dosages, IV fluid rates, and patient intake/output. A small math error can have significant patient safety consequences.
What if? If a nurse miscalculates a dosage by a factor similar to the error in option D (forgetting a step), it could lead to under-dosing or over-dosing a patient, potentially causing therapeutic failure or toxicity.

How to Approach the Question

First, identify the core mathematical concept being tested: counting numbers in a specific range with a specific property (divisibility). This points to an Arithmetic Progression.
Determine the range of numbers. '3-digit numbers' means from 100 to 999.
Find the first number in this range that satisfies the condition. The first 3-digit number divisible by 6 is 102.
Find the last number in the range that satisfies the condition. The last 3-digit number divisible by 6 is 996.
Apply the formula for the number of terms in an AP: n = ((Last Term - First Term) / Common Difference) + 1.
Substitute the values and calculate carefully: n = ((996 - 102) / 6) + 1. Be sure not to forget the '+1' at the end.

Concept Tested & Keywords

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Practise the full UPUMS Nsg.Officer-2024

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