Finding the Different Number Pair in Reasoning Problems

This question asks us to identify the number pair that is different from the other three, meaning three pairs follow a similar rule or pattern, and one does not. These types of problems test our ability to find mathematical or logical relationships between numbers.

We are given four number pairs:

• 25 ∶ 631
• 30 ∶ 908
• 22 ∶ 490
• 21 ∶ 447

Let's analyze the relationship between the first number and the second number in each pair. Often, in such reasoning questions, the relationship involves squaring, cubing, multiplication, addition, or subtraction of the first number.

Let's try to find a pattern based on squaring the first number.

Analyzing the Number Pairs

We will examine each pair and see if there's a consistent mathematical operation linking the two numbers.

Pair 1: 25 ∶ 631

Let's square the first number, 25:

\(25^2 = 25 \times 25 = 625\)

The second number is 631. The difference between 631 and 625 is:

\(631 - 625 = 6\)

So, the relationship could be \((\text{First number})^2 + 6\). Let's check if this pattern holds for other pairs.

Pair 2: 30 ∶ 908

Let's apply the possible pattern \((\text{First number})^2 + 6\) here. Square the first number, 30:

\(30^2 = 30 \times 30 = 900\)

Add 6 to this value:

\(900 + 6 = 906\)

The second number in this pair is 908. Since 906 is not equal to 908, this pair does not follow the pattern \((\text{First number})^2 + 6\).

This pair seems different. However, let's verify the pattern with the remaining pairs to be sure.

Pair 3: 22 ∶ 490

Apply the pattern \((\text{First number})^2 + 6\). Square the first number, 22:

\(22^2 = 22 \times 22 = 484\)

Add 6 to this value:

\(484 + 6 = 490\)

The second number in this pair is 490. This matches the calculated value, so this pair follows the pattern \((\text{First number})^2 + 6\).

Pair 4: 21 ∶ 447

Apply the pattern \((\text{First number})^2 + 6\). Square the first number, 21:

\(21^2 = 21 \times 21 = 441\)

Add 6 to this value:

\(441 + 6 = 447\)

The second number in this pair is 447. This matches the calculated value, so this pair also follows the pattern \((\text{First number})^2 + 6\).

Conclusion

Based on our analysis, three of the number pairs follow the pattern where the second number is obtained by squaring the first number and adding 6. The pattern is:

\(\text{Second Number} = (\text{First Number})^2 + 6\)

Let's summarize our findings in a table:

As the table clearly shows, the pair 30 ∶ 908 is the only one that does not follow the pattern \((\text{First number})^2 + 6\).

Therefore, the number-pair that is different is 30 ∶ 908.

Revision Table: Number Pair Reasoning

Additional Information: Solving Reasoning Patterns

When tackling reasoning questions involving number pairs or series, consider these common strategies:

• Arithmetic Operations: Look for simple addition, subtraction, multiplication, or division between the numbers.
• Powers and Roots: Check if the second number is related to the square, cube, square root, or cube root of the first number.
• Combinations: The pattern might involve a combination of operations, like \(x^2 + k\), \(x^3 - k\), \(ax + b\), etc.
• Digit Properties: Sometimes the pattern relates to the sum of digits, product of digits, or specific digits within the numbers.
• Prime/Composite Numbers: The relationship might be based on whether the numbers are prime or composite.
• Sequence Rules: If there's a series of pairs, the pattern might involve the position of the pair or a cumulative rule.

Systematically testing potential relationships is key to solving these reasoning pattern problems.