Finding the Different Number Pair

This type of question asks us to identify a pattern that holds true for most of the given number-pairs and then find the one pair that does not follow that pattern. Let's carefully examine each pair to discover the underlying relationship between the first number and the second number.

Analyzing Each Number Pair

We are given four number-pairs:

• 12 : 288
• 14 : 392
• 19 : 622
• 11 : 242

Let's consider the first number in each pair as \(N\) and the second number as \(M\). We need to find a mathematical relationship between \(N\) and \(M\) that is consistent across three of the pairs.

Let's test some common relationships, such as multiplication, squares, cubes, or combinations of these operations.

Consider the square of the first number, \(N^2\).

• For 12 : 288, \(N = 12\). \(N^2 = 12^2 = 144\). How does 144 relate to 288? We notice that \(144 \times 2 = 288\). So, \(M = 2 \times N^2\).
• For 14 : 392, \(N = 14\). \(N^2 = 14^2 = 196\). How does 196 relate to 392? We notice that \(196 \times 2 = 392\). So, \(M = 2 \times N^2\).
• For 19 : 622, \(N = 19\). \(N^2 = 19^2 = 361\). How does 361 relate to 622? Let's check \(2 \times N^2 = 2 \times 361 = 722\). This is not equal to 622. So, this pair might not follow the pattern \(M = 2 \times N^2\).
• For 11 : 242, \(N = 11\). \(N^2 = 11^2 = 121\). How does 121 relate to 242? We notice that \(121 \times 2 = 242\). So, \(M = 2 \times N^2\).

Identifying the Pattern and the Different Pair

Based on our analysis, it appears that the pattern for three of the number-pairs is that the second number is equal to two times the square of the first number, i.e., \(M = 2 \times N^2\).

Let's summarize the findings in a table:

As clearly shown in the table, the number-pairs 12 : 288, 14 : 392, and 11 : 242 follow the pattern \(M = 2 \times N^2\). The number-pair 19 : 622 does not follow this pattern, as \(2 \times 19^2 = 722\), which is not equal to 622.

Therefore, the number-pair that is different is 19 : 622.

Conclusion

The number-pair that does not fit the pattern observed in the other three pairs is 19 : 622. This makes it the different pair among the given options.

Revision Table: Number Pair Analysis

Additional Information: Solving Reasoning Problems

Reasoning problems involving number patterns often require checking for various relationships between the numbers. Here are some common approaches:

• Arithmetic Operations: Check for addition, subtraction, multiplication, or division between the numbers or consecutive terms.
• Squares and Cubes: Look for relationships involving the squares or cubes of the numbers.
• Prime Numbers: See if the numbers are prime or related to prime numbers.
• Digits: Analyze the relationship between the digits of the numbers (sum of digits, product of digits, etc.).
• Series: If it's a series, look for differences, ratios, or other patterns between consecutive terms.

Practice with different types of number pattern problems helps in quickly identifying the pattern and finding the different element or the next term in a series.