Solving the Number Analogy Question

The question asks us to find the related number to 6 based on the relationship shown in the pair 8 : 512.

The analogy is presented as: 8 : 512 ∷ 6 : ?

We need to identify the pattern or relationship between the first pair of numbers (8 and 512) and then apply the same pattern to the second number (6) to find the missing number.

Identifying the Pattern in 8 : 512

Let's look for common mathematical relationships between 8 and 512:

• Addition/Subtraction: $512 - 8 = 504$. Adding 504 to 6 gives $6 + 504 = 510$. This is not among the options.
• Multiplication/Division: $512 \div 8 = 64$. Multiplying 6 by 64 gives $6 \times 64 = 384$. This is not among the options.
• Squaring: $8^2 = 8 \times 8 = 64$. This is not 512.
• Cubing: $8^3 = 8 \times 8 \times 8$. Let's calculate this:

First, $8 \times 8 = 64$.

Then, $64 \times 8$:

$\quad 64$

$\underline{\times \quad 8}$

$\quad 512$

So, $8^3 = 512$. The relationship between 8 and 512 is that 512 is the cube of 8.

The pattern is: Second Number = (First Number)$^3$.

Applying the Pattern to 6 : ?

Now we apply the same cubing relationship to the number 6. The missing number will be $6^3$.

Calculate $6^3$: $6^3 = 6 \times 6 \times 6$.

First, $6 \times 6 = 36$.

Then, $36 \times 6$:

$\quad 36$

$\underline{\times \quad 6}$

$\quad 216$

So, $6^3 = 216$.

Conclusion

Following the pattern identified in the first pair (8 : 512, where $8^3 = 512$), the related number for 6 is $6^3$, which is 216.

The correct answer is 216.

Revision Table: Number Analogy Patterns

Additional Information: Numerical Reasoning Skills

Number analogy questions are a key part of numerical reasoning tests. They assess your ability to identify patterns and logical relationships between numbers. To improve your skills, practice recognising different types of patterns:

• Arithmetic progressions (constant difference).
• Geometric progressions (constant ratio).
• Perfect squares and cubes.
• Prime numbers.
• Fibonacci sequence.
• Combinations of arithmetic operations and powers.

Being familiar with basic arithmetic operations, squares, cubes, and prime numbers is very helpful in solving these types of problems efficiently.