What is the result of the calculation (65^2 - 55^2) focusing on the tenth digit factor?

Appeared in: AIIMS CRE, SNO-2024

Explanation

The expression (65² - 55²) is a difference of two squares, which can be factored using the identity a² - b² = (a - b)(a + b).
Substituting the values, we get (65 - 55) × (65 + 55), which simplifies to 10 × 120.
The product is 1200.
In the number 1200, the digit in the tens place (the second digit from the right) is 0.

Option A: The digit 1 is in the thousands place of the result (1200), not the tens place.
Option C: The digit 5 is part of the original numbers in the expression (65 and 55) but does not appear in the final calculated result of 1200.
Option D: The number 10 is the result of the first part of the factored calculation (65 - 55). However, it is a two-digit number, not a single digit representing a place value in the final answer.

Visual 1: Infographic: A chart showing place values (Units, Tens, Hundreds, Thousands) for a 4-digit number to visually clarify how to identify the tens digit.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation using algebraic identities and identifying place values in a number as background academic context rather than a clinical decision trigger.
This question tests basic mathematical aptitude, which is a component of many competitive examinations. Strong numeracy skills are essential for various calculations in clinical practice, such as drug dosage calculations, fluid balance charting, and interpreting lab results.
What if? - If the stem changed one defining clue so that 0 no longer matched, reassess the option whose mechanism, classification, or indication now fits the revised presentation.

How to Approach the Question

First, carefully read the question to understand what is being asked. Here, the key is to find the 'tenth digit' (tens place digit) of a calculated result.
Recognize that the expression (65² - 55²) is in the form of a² - b², which is a difference of squares.
Apply the algebraic identity a² - b² = (a - b)(a + b) to simplify the calculation. This is often faster and less prone to error than squaring large numbers directly.
Calculate the result: (65 - 55) × (65 + 55) = 10 × 120 = 1200.
Once you have the final number (1200), identify the digit in the tens place.
Compare your identified digit with the given options to select the correct answer.

Concept Tested & Keywords

Concept Tested: Calculation using algebraic identities and identifying place values in a number.
Stem keywords: calculation, 65^2 - 55^2, tenth digit
Lead-in keywords: What is

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