DIRECTIONS: Select the related numbers from the given alternatives?

125:5:: 64::?

Appeared in: DHS Staff Nurse - 2018 (Shift-2nd)

Explanation

The question presents a number analogy where the relationship between the first pair of numbers must be applied to the second pair.
In the first pair (125:5), 125 is the cube of 5 (5³ = 125).
To find the missing number in the second pair (64:?), we must find the cube root of 64.
The cube root of 64 is 4, as 4 × 4 × 4 = 64.

Option A: The number 8 is the square root of 64 (8² = 64), not the cube root. The established pattern is based on cubes, not squares.
Option C: The number 2 is the cube root of 8 (2³ = 8), not 64.
Option D: The number 32 is half of 64. This introduces a division relationship, which does not match the cube relationship (125 / 25 = 5) from the first pair.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Number Analogy (Cubes and Cube Roots) as background academic context rather than a clinical decision trigger.
While not a clinical question, logical reasoning and pattern recognition are essential skills for nurses.
These skills are crucial for interpreting patient data, recognizing trends in vital signs, and making sound clinical judgments.
For example, a nurse needs to quickly calculate drug dosages, which involves similar mathematical aptitude.

How to Approach the Question

First, analyze the relationship between the first pair of numbers (125 and 5).
Consider common mathematical operations: addition, subtraction, multiplication, division, squares, cubes, square roots, and cube roots.
Identify the pattern: 125 is the cube of 5 (5 x 5 x 5 = 125). So, the relationship is x³ : x.
Apply the same pattern to the second pair of numbers (64 and ?).
Find the number 'x' such that x³ = 64. This means you need to find the cube root of 64.
Calculate or recall that the cube root of 64 is 4. Select the option that matches this result.

Concept Tested & Keywords

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Practise the full DHS Staff Nurse - 2018 (Shift-2nd)

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