Find value 102 x 102 – 98 x 98.

Appeared in: AIIMS Rishikesh & Jodhpur NO - 2017

Explanation

The expression 102 x 102 – 98 x 98 is in the form of a² - b².
The algebraic identity for the difference of squares is a² - b² = (a - b)(a + b).
By substituting a = 102 and b = 98, we get (102 - 98) × (102 + 98).
This simplifies to 4 × 200.
The final calculation is 4 × 200 = 800.

Option A: 700 is an incorrect calculation. It might result from a miscalculation, such as incorrectly calculating the sum or difference in the formula.
Option B: 1000 is an incorrect calculation. This could arise from an error like multiplying 4 by 250 instead of 200.
Option D: 1200 is an incorrect calculation. This might result from an error such as multiplying 4 by 300 instead of 200.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Algebraic Identities (Difference of Squares) as background academic context rather than a clinical decision trigger.
While not a clinical question, proficiency in quick mental calculations and recognizing mathematical patterns is a valuable skill for nurses.
It aids in tasks like medication dosage calculations, titrating IV drips, and interpreting patient data charts quickly and accurately.
What if the numbers were 55 and 45? The same logic applies: (55-45)(55+45) = 10 * 100 = 1000. Recognizing the pattern is key.

How to Approach the Question

First, examine the mathematical expression: 102 × 102 – 98 × 98.
Recognize that this expression fits the pattern of a² - b², a common algebraic identity.
Identify 'a' as 102 and 'b' as 98.
Recall or apply the formula for the difference of squares: a² - b² = (a - b)(a + b).
Substitute the values into the formula: (102 - 98) × (102 + 98).
Perform the simpler calculations inside the parentheses: (4) × (200).

Concept Tested & Keywords

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