Finding the Different Number Pair

In this question, we are given four number pairs, and we need to identify the one pair that does not follow the same rule or pattern as the other three pairs. This is a common type of question in logical reasoning tests.

Analyzing the Given Number Pairs

The four number pairs provided are:

• 6 ∶ 26
• 5 ∶ 24
• 8 ∶ 34
• 7 ∶ 30

We need to look for a mathematical relationship between the first number and the second number in each pair. Let's assume the first number is \(x\) and the second number is \(y\). We are looking for a pattern that applies to three of these pairs.

Identifying the Pattern

Let's test a few possible patterns, such as multiplication and addition/subtraction, or squaring and addition/subtraction.

• Could it be $y = x \times a + b$?
• Could it be $y = x \times a - b$?
• Could it be $y = x^2 + b$?
• Could it be $y = x^2 - b$?

Let's examine the first pair: 6 ∶ 26.

• $6 \times 4 = 24$. $24 + 2 = 26$. So, $6 \times 4 + 2 = 26$.

Let's check if this pattern, $y = x \times 4 + 2$, applies to the other pairs.

Applying the Pattern to Each Pair

Let's apply the rule $y = x \times 4 + 2$ to the first number (\(x\)) in each pair and see if it results in the second number (\(y\)).

• Pair 1: 6 ∶ 26
  $x = 6$. Calculate $6 \times 4 + 2 = 24 + 2 = 26$. This matches the given second number (26).
• Pair 2: 5 ∶ 24
  $x = 5$. Calculate $5 \times 4 + 2 = 20 + 2 = 22$. This does not match the given second number (24). The result is 22, not 24.
• Pair 3: 8 ∶ 34
  $x = 8$. Calculate $8 \times 4 + 2 = 32 + 2 = 34$. This matches the given second number (34).
• Pair 4: 7 ∶ 30
  $x = 7$. Calculate $7 \times 4 + 2 = 28 + 2 = 30$. This matches the given second number (30).

We can see that three of the number pairs (6 ∶ 26, 8 ∶ 34, and 7 ∶ 30) follow the pattern $y = x \times 4 + 2$. The pair 5 ∶ 24 does not follow this pattern.

Conclusion

Based on the analysis, the number-pair 5 ∶ 24 is the one that is different from the other three pairs because it does not fit the common rule $y = x \times 4 + 2$.

Revision Table: Number Pair Analysis

This table summarizes how each number pair fits or doesn't fit the identified pattern.

Additional Information: Number Analogy Questions

Questions like this are often called Number Analogy or Odd One Out questions. They test your ability to find relationships and patterns between numbers. Common patterns include:

• Arithmetic operations (addition, subtraction, multiplication, division)
• Combinations of operations (like $x \times a + b$)
• Squares or cubes of numbers
• Prime numbers, composite numbers
• Even or odd numbers
• Digit sums or products

Solving these requires careful observation and systematic testing of potential rules.