Choose the number that is most different and does not fit in the series

3, 10, 29, 66, 127,219,345,514

Appeared in: JSSH Staff Nurse - 2019

Explanation

The series follows the mathematical pattern: (Position of the number)³ + 2.
For the 6th position, the calculation should be 6³ + 2 = 216 + 2 = 218.
The number given in the series for the 6th position is 219, which deviates from the established pattern, making it the incorrect term.

Option A: This number correctly follows the pattern for the 5th position (5³ + 2 = 125 + 2 = 127).
Option C: This number correctly follows the pattern for the 3rd position (3³ + 2 = 27 + 2 = 29).
Option D: This number correctly follows the pattern for the 7th position (7³ + 2 = 343 + 2 = 345).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Identifying the outlier in a number series based on a mathematical pattern (cubic function) as background academic context rather than a clinical decision trigger.
Logical reasoning and pattern recognition are essential skills for problem-solving in various professional fields, including nursing.
In a clinical setting, these skills are crucial for tasks like interpreting lab data, identifying trends in a patient's vital signs, and recognizing early signs of deterioration.
Mastering pattern recognition helps in making quick, accurate decisions based on available data, which is fundamental to patient safety and effective care.

How to Approach the Question

First, observe the series and try to identify a simple relationship between consecutive numbers (e.g., addition, subtraction, multiplication).
If a simple arithmetic pattern is not apparent, consider more complex relationships involving squares (n²) or cubes (n³) of the term's position (n).
Test a hypothesis. For this series, the numbers increase rapidly, suggesting a cubic pattern. Let's test the rule n³ + k. For the first term (n=1), 1³ + k = 3, which means k = 2.
Verify the hypothesized rule (n³ + 2) for all terms in the sequence.
Systematically apply the rule to each position: 1³+2=3, 2³+2=10, 3³+2=29, and so on.
Identify the term that does not conform to the rule. In this case, the 6th term should be 6³+2=218, but it is given as 219. This is the outlier.

Concept Tested & Keywords

Concept Tested: Identifying the outlier in a number series based on a mathematical pattern (cubic function).
Stem keywords: number series, different, does not fit, 3, 10, 29, 66, 127, 219, 345, 514
Lead-in keywords: most different, does not fit
Negative lead-in flag: NOT changes the reasoning strategy; look for the exception or incorrect statement rather than the true statement.

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