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

Appeared in: BSF Staff Nurse - 2021

Explanation

The question presents a number analogy in the format a : b :: c : d.
The relationship in the first pair (13 : 169) is that the second number is the square of the first (13² = 169).
To find the missing number in the second pair (__ : 196), we must apply the same logic.
The missing number is the square root of 196, which is 14.
Therefore, the complete analogy is 13 : 169 :: 14 : 196.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Analogical Reasoning (Number Series) as background academic context rather than a clinical decision trigger.
While not a clinical question, logical reasoning is a critical skill for nurses.
It helps in quickly identifying patterns in patient symptoms, interpreting data from monitoring equipment, and making sound clinical decisions under pressure.
What if the series was 13 : 156? The pattern would be n : n × (n-1). Then for the second pair, the answer would be 13, since 13 x 12 = 156. This shows the importance of correctly identifying the underlying pattern.

How to Approach the Question

First, analyze the relationship between the numbers in the first given pair (13 and 169).
Recognize that 169 is the result of multiplying 13 by itself (13 x 13). This is a 'squaring' relationship.
Apply this same rule to the second pair, where the result is 196.
To find the missing first number, you need to perform the inverse operation of squaring, which is finding the square root.
Calculate the square root of 196 (√196).
Select the option that matches your calculated result (14).

Concept Tested & Keywords

QKdP3V2RRkgTV1Dvwralfe

Practise the full BSF Staff Nurse - 2021

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