What is the product of all the numbers in the dial of a telephone?

Appeared in: ESIC Nursing Officer 2016 (shift-1)

Explanation

A standard telephone dial includes the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
The term 'product' in mathematics refers to the result of multiplying a set of numbers.
The zero-product property states that if any factor in a multiplication is zero, the entire product is zero.
Since the set of numbers on a telephone dial includes 0, multiplying all the numbers together (0 × 1 × 2 × ... × 9) results in 0.

Option A: This value is incorrect. It seems to be a random large number and does not result from any logical calculation related to the question.
Option B: The product is 1 only if all the numbers being multiplied are 1, or if it's an empty product. This is incorrect because the dial has multiple numbers other than 1, and crucially, it includes 0.
Option C: This value is incorrect. Like the first option, it is a random large number with no mathematical basis in the context of the question.

Visual 1: Image - A clear image of a standard telephone keypad or rotary dial, with all the numbers (0-9) clearly visible. This helps the learner to visually confirm the set of numbers involved in the calculation.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Basic mathematical principles, specifically the zero-product property as background academic context rather than a clinical decision trigger.
This is a general aptitude question, not a clinical one. However, it tests logical reasoning and attention to detail, which are crucial skills for nurses.
Nurses must pay close attention to details in medication dosages, patient charts, and equipment settings. A simple oversight, like misinterpreting a number, can have significant consequences.
What if the question asked for the sum of all the numbers? The calculation would be 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 0 = 45. This highlights the importance of carefully reading the question to understand the specific operation required (product vs. sum).

How to Approach the Question

First, identify the core task in the question. Here, the task is to find the 'product' of numbers on a 'telephone dial'.
Next, list all the numbers present on a standard telephone dial. These are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Recall the mathematical definition of 'product', which means to multiply.
Set up the multiplication: 0 × 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9.
Apply the zero-product property: recognize that multiplying any number by zero results in zero.
Conclude that the presence of '0' in the set makes the final product 0, without needing to calculate the rest of the multiplication. Select the option that matches this result.

Concept Tested & Keywords

Concept Tested: Basic mathematical principles, specifically the zero-product property.
Stem keywords: product, numbers, dial, telephone
Lead-in keywords: What is

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Practise the full ESIC Nursing Officer 2016 (shift-1)

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