Understanding Number Analogy Questions

Number analogy questions test your ability to find the relationship between a pair of numbers and apply that same relationship to another number to find the missing term. In the given question, we have the analogy 6 : 216 : : 5 : ?

Analysing the First Pair: 6 and 216

We need to determine the relationship between 6 and 216. Let's explore common mathematical operations:

• Addition: $216 - 6 = 210$. Adding 210 to 6 gives 216.
• Multiplication: $216 \div 6 = 36$. Multiplying 6 by 36 gives 216.
• Powers: Let's check powers of 6.
• $6^1 = 6$
• $6^2 = 6 \times 6 = 36$
• $6^3 = 6 \times 6 \times 6 = 36 \times 6 = 216$

The relationship between 6 and 216 is that 216 is the cube of 6 ($6^3$).

Applying the Relationship to the Second Pair: 5 and ?

Now, we apply the same rule (cubing the number) to the second number, which is 5. We need to find the cube of 5.

The cube of 5 is $5^3$.

Calculate $5^3$:

$5^3 = 5 \times 5 \times 5 = 25 \times 5 = 125$

Identifying the Correct Option

The missing number in the analogy 6 : 216 : : 5 : ? is 125.

Let's look at the given options:

• 1. 125
• 2. 50
• 3. 75
• 4. 150

The calculated number, 125, matches Option 1.

Step-by-Step Solution Summary

1. Identify the relationship between the first pair of numbers (6 and 216).
2. Determine that $216 = 6^3$. The relationship is cubing the first number.
3. Apply the same relationship to the first number of the second pair (5).
4. Calculate the cube of 5: $5^3 = 125$.
5. Select the option that matches the calculated number.

Revision Table: Cube Values

Additional Information: Types of Number Analogy Patterns

Number analogy questions can have various patterns. Recognizing these patterns quickly is key to solving them. Some common patterns include:

• Addition or Subtraction: Adding or subtracting a constant value or a value related to the number itself.
• Multiplication or Division: Multiplying or dividing by a constant value or a value related to the number.
• Squares or Cubes: The second number is the square or cube of the first number, or related to the square/cube.
• Square roots or Cube roots: The second number is the root of the first number.
• Combinations of Operations: A sequence of operations like multiply then add, square then subtract, etc.
• Digit Manipulation: Operations performed on the digits of the number.
• Prime Numbers, Composite Numbers, etc.: The numbers follow a sequence of prime or composite numbers.

Practicing different types of number analogy problems helps in identifying the pattern faster during exams.