36:216 :: 49:?

Appeared in: ESIC Nursing Officer 2016 (shift-1)

Explanation

The question establishes a relationship in the first pair of numbers (36:216) which needs to be applied to the second pair (49:?).
The number 36 is the square of 6 (6²), and 216 is the cube of 6 (6³). The pattern is x² : x³.
Applying this pattern, 49 is the square of 7 (7²).
Therefore, the missing number must be the cube of 7 (7³), which is 7 × 7 × 7 = 343.

Option A: 125 is the cube of 5 (5³). The pattern requires the cube of 7, as the given number is 49 (7²).
Option C: 625 is the fourth power of 5 (5⁴) or the square of 25 (25²). It does not fit the x²:x³ pattern established by the first pair.
Option D: 512 is the cube of 8 (8³). The pattern requires the cube of 7.

Visual 1: Infographic: A chart showing the squares and cubes of numbers from 1 to 10 to help visualize the pattern and quickly identify the relationship between the numbers in the analogy.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Number Analogy as background academic context rather than a clinical decision trigger.
This type of logical reasoning question, while not directly clinical, assesses critical thinking and pattern recognition skills.
These cognitive skills are fundamental for nurses in various tasks, such as interpreting vital sign trends, recognizing patterns in patient symptoms, and making quick, logical decisions in complex clinical situations.
What if the question was 36:216 :: 64:? Here, 64 is 8², so the answer would be 8³, which is 512. Recognizing the base number is the key.

How to Approach the Question

First, analyze the relationship between the first pair of numbers (36 and 216).
Identify the mathematical operation connecting them. Notice that 36 = 6² and 216 = 6³.
Formulate the rule from this relationship: The second number is the cube of the same base number whose square is the first number (x² : x³).
Apply this rule to the second pair. The first number is 49. Identify its square root, which is 7.
Calculate the cube of this new base number (7³) to find the missing term.
7 x 7 x 7 = 343. Select the option that matches this result.

Concept Tested & Keywords

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Practise the full ESIC Nursing Officer 2016 (shift-1)

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