Fill the blank in the following series:
13 : 169 :: __ : 196?

Appeared in: AIIMS CRE SNO - 2023

Explanation

The question follows a 'number : square of the number' pattern.
In the first pair, 13 is given, and its square, 13 × 13, is 169.
For the second pair, the square (196) is given. To find the original number, you must calculate the square root of 196.
The square root of 196 is 14, as 14 × 14 = 196.
Therefore, 14 is the correct number to complete the analogy 13 : 169 :: 14 : 196.

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 is not directly related to clinical nursing practice but assesses logical and mathematical reasoning skills.
Strong reasoning skills are essential for nurses for tasks like calculating drug dosages, interpreting lab results, and making quick, logical decisions in patient care.
What if the analogy was 13 : 156? The pattern would be n : n × (n-1). Then for the second part, you would look for a number 'x' such that x × (x-1) = 196. This requires solving a quadratic equation, showing how a small change in the pattern can increase complexity.

How to Approach the Question

First, analyze the relationship between the two numbers in the first pair (13 and 169).
Recognize that 169 is a perfect square. Test if it is the square of 13. Calculate 13 × 13, which equals 169.
You have now identified the pattern: 'x : x²'.
Apply this same pattern to the second pair. The second number is 196, which corresponds to x².
To find the missing number (x), calculate the square root of 196.
The square root of 196 is 14. Select this option as the answer.

Concept Tested & Keywords

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Practise the full AIIMS CRE SNO - 2023

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