Three of the following four number pairs are alike in a certain way and one is different. Find the odd one out!

Appeared in: UPUMS Nsg.Officer-2024

Explanation

The pair 30:40 is the odd one out because it does not follow the logical pattern present in the other three pairs.
The pattern is that each pair is in the form n × (n+1) : (n+1) × (n+2).
For 30:40, while 30 = 5 × 6, the second number is 40, which is not 6 × 7 (which would be 42).
This deviation makes it the correct answer.

Option A: This pair is incorrect because it follows the established pattern. 12 = 3 × 4 and 20 = 4 × 5, which fits the form n × (n+1) : (n+1) × (n+2) for n=3.
Option C: This pair is incorrect because it follows the established pattern. 42 = 6 × 7 and 56 = 7 × 8, which fits the form n × (n+1) : (n+1) × (n+2) for n=6.
Option D: This pair is incorrect because it follows the established pattern. 20 = 4 × 5 and 30 = 5 × 6, which fits the form n × (n+1) : (n+1) × (n+2) for n=4.

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.
While not a clinical question, the underlying skill of pattern recognition is crucial in nursing.
Nurses must identify trends and anomalies in patient data, such as vital signs, lab results, or ECG strips, to detect deterioration or improvement.
For example, recognizing a subtle but consistent rise in a patient's heart rate over several hours is a pattern that could indicate developing sepsis or hypovolemia.

How to Approach the Question

First, analyze the relationship between the two numbers within each pair.
Look for a common mathematical rule or pattern that connects the first number to the second. Consider operations like addition, subtraction, multiplication, division, squares, or products of consecutive numbers.
Test this rule against all four options.
The option that does not conform to the rule followed by the other three is the 'odd one out'.
In this case, the pattern is n×(n+1) : (n+1)×(n+2). Check which pair violates this relationship.

Concept Tested & Keywords

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Practise the full UPUMS Nsg.Officer-2024

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