Finding the Odd Number Pair in Sequences

The problem asks us to identify the number pair that follows a different mathematical rule compared to the other pairs. In each pair (first number, second number), the second number is obtained by performing a specific operation or set of operations on the first number. This rule is consistent across all pairs except one.

Let's examine each number pair provided and try to find the relationship between the first and second numbers. A common approach for such problems is to look for basic arithmetic operations like addition, subtraction, multiplication, or division. Given that the second number is significantly larger than the first number in all pairs, multiplication or a combination involving multiplication seems likely.

Analyzing Each Number Pair

We will analyze each pair individually to determine the operation used to get the second number from the first number. We can test if the second number is a multiple of the first number by dividing the second number by the first number.

• Pair 1: (87, 522)
• Let's divide the second number by the first number: 522 ÷ 87
• Calculation: $\frac{522}{87}$
• To calculate this, we can estimate or perform long division. Let's try multiplying 87 by a small integer. $87 \times 5 = 435$. $87 \times 6 = 522$.
• So, $522 \div 87 = 6$. The operation is multiplying the first number by 6.

• Pair 2: (84, 672)
• Let's divide the second number by the first number: 672 ÷ 84
• Calculation: $\frac{672}{84}$
• Let's try multiplying 84 by a small integer. $84 \times 7 = 588$. $84 \times 8 = 672$.
• So, $672 \div 84 = 8$. The operation is multiplying the first number by 8.

• Pair 3: (92, 552)
• Let's divide the second number by the first number: 552 ÷ 92
• Calculation: $\frac{552}{92}$
• Let's try multiplying 92 by a small integer. $92 \times 5 = 460$. $92 \times 6 = 552$.
• So, $552 \div 92 = 6$. The operation is multiplying the first number by 6.

• Pair 4: (64, 384)
• Let's divide the second number by the first number: 384 ÷ 64
• Calculation: $\frac{384}{64}$
• Let's try multiplying 64 by a small integer. $64 \times 5 = 320$. $64 \times 6 = 384$.
• So, $384 \div 64 = 6$. The operation is multiplying the first number by 6.

Comparing the Operations

Let's summarize the operation found for each pair in a table:

From the table, we can clearly see the pattern. For pairs (87, 522), (92, 552), and (64, 384), the second number is obtained by multiplying the first number by 6. However, for the pair (84, 672), the second number is obtained by multiplying the first number by 8.

Therefore, the number pair (84, 672) is the one that does not follow the same mathematical operation as the others.

Conclusion

The common rule is that the second number is 6 times the first number. The pair (84, 672) deviates from this rule, as 672 is 8 times 84. Thus, (84, 672) is the odd number pair.

Revision Table: Number Pattern Analysis

Reviewing the concept of finding the odd one out based on mathematical operations.

• Identify the rule connecting the numbers in each pair.
• Test potential simple operations (addition, subtraction, multiplication, division).
• Apply the tested rule to all pairs.
• Find the pair that does not fit the rule.

Additional Information: Solving Number Series and Pairs

Problems involving number pairs or series often require identifying the underlying pattern. This pattern can be based on:

• Arithmetic Operations: Adding, subtracting, multiplying, or dividing by a constant or a sequence of numbers.
• Powers or Roots: Squaring, cubing, square roots, cube roots.
• Digit Operations: Sum of digits, product of digits.
• Positional Operations: Based on the position of the number in the sequence.
• Combinations: A mix of the above operations.

Practicing various types of number pattern questions helps improve logical reasoning and problem-solving skills for competitive exams.