Select the set in which the numbers are related in the same way as are the numbers of the following set. 8, 9, 145

Appeared in: NORCET -4 , 2023

Explanation

The question requires identifying a set of numbers with the same mathematical relationship as the given set (8, 9, 145).
The pattern is: (First Number)² + (Second Number)² = Third Number.
For the given set: 8² + 9² = 64 + 81 = 145.
The correct option (6, 7, 85) follows this pattern: 6² + 7² = 36 + 49 = 85.

Option A: The sum of the squares of the first two numbers (10² + 11² = 100 + 121) is 221, not 121.
Option B: The sum of the squares of the first two numbers (7² + 8² = 49 + 64) is 113, not 117.
Option C: The sum of the squares of the first two numbers (6² + 8² = 36 + 64) is 100, not 104.

Visual 1: Infographic: A simple visual showing the formula a² + b² = c, with the numbers from the question (8, 9, 145) and the correct answer (6, 7, 85) plugged in to demonstrate the pattern.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Number Analogy and Pattern Recognition as background academic context rather than a clinical decision trigger.
This question tests logical and mathematical reasoning, which are essential skills for nurses.
Nurses use these skills daily for tasks like calculating drug dosages, interpreting lab results, and making critical decisions based on changing patient data.
What if the pattern was a² - b² = c? In that case, none of the given options would be correct, and a different set would need to be found.

How to Approach the Question

First, analyze the relationship between the numbers in the given set (8, 9, 145).
Consider common mathematical operations: addition, subtraction, multiplication, division, squares, cubes, etc.
Test the hypothesis that the sum of the squares of the first two numbers equals the third: 8² + 9² = 64 + 81 = 145. This confirms the pattern.
Apply this confirmed pattern (a² + b² = c) to each of the answer options.
Calculate the result for each option and compare it to the third number in its set.
Select the option where the calculation matches the third number.

Concept Tested & Keywords

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Practise the full NORCET -4 , 2023

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