Finding the Number Relation Pattern

The question asks us to identify the relationship between the numbers in the set (4, 7, 359) and find which of the given options follows the same relationship or pattern. We need to analyze the numbers 4, 7, and 359 to discover how they are connected.

Analyzing the Given Set (4, 7, 359)

Let's denote the first number as $A$, the second number as $B$, and the third number as $C$. In the set (4, 7, 359), we have $A=4$, $B=7$, and $C=359$. We need to find a rule or formula that connects $A$, $B$, and $C$.

Let's try some common mathematical operations involving $A$ and $B$ to see if we can arrive at $C$.

• Addition: $A + B = 4 + 7 = 11$ (Not 359)
• Multiplication: $A \times B = 4 \times 7 = 28$ (Not 359)
• Powers: Let's consider squares and cubes of $A$ and $B$.
  • $A^2 = 4^2 = 16$
  • $B^2 = 7^2 = 49$
  • $A^3 = 4^3 = 64$
  • $B^3 = 7^3 = 343$

Now let's try combining these powers:

• $A^2 + B^2 = 16 + 49 = 65$ (Not 359)
• $A^3 + B^3 = 64 + 343 = 407$ (Not 359)
• $A^2 + B^3 = 16 + 343 = 359$ (This matches!)

It appears the pattern or relation in the given set (4, 7, 359) is: The third number is the sum of the square of the first number and the cube of the second number.

Pattern: $C = A^2 + B^3$

Testing the Pattern on the Options

Now we will apply this pattern ($A^2 + B^3 = C$) to each of the given options to see which one follows the same rule.

From the analysis above, only Option 1, (6, 8, 548), satisfies the identified pattern $A^2 + B^3 = C$, because $6^2 + 8^3 = 36 + 512 = 548$, which is equal to the third number in the set.

Conclusion

The numbers in the set (4, 7, 359) are related by the formula $A^2 + B^3 = C$. The option that shows the same relationship is (6, 8, 548).

Revision Table: Number Relation

Additional Information: Number Patterns in Reasoning

Number patterns and analogies are common in reasoning questions. These questions test your ability to observe, identify rules, and apply them. The rules can involve various mathematical operations:

• Basic operations (addition, subtraction, multiplication, division)
• Powers and roots (squares, cubes, square roots, cube roots)
• Combinations of operations
• Arithmetic or geometric progressions
• Digit manipulation (sum of digits, product of digits)

To solve such problems, it's helpful to systematically try different simple rules first before moving to more complex combinations of operations or powers. Calculating squares and cubes of small numbers can be very useful.