Understanding the Odd Number Pair Question

This question asks us to identify the number pair that does not follow the same rule or pattern as the other three pairs. We are given four pairs of numbers, and the constraint is that we cannot perform any operations on the individual digits of the numbers. This means we must look for a relationship between the first number and the second number in each pair as whole values.

Analyzing Each Number Pair for a Pattern

Let's examine each number pair and try to find a consistent mathematical relationship between the first number and the second number. We can test common relationships like addition, subtraction, multiplication, or a combination of these with constants.

• Pair 1: 308 ∶ 101

  Let's explore a relationship involving multiplication. If we multiply the second number (101) by a small integer and add or subtract a constant to get the first number (308).

  Trying multiplication by 3: \(101 \times 3 = 303\). The difference between 308 and 303 is \(308 - 303 = 5\). So, the relationship could be \(101 \times 3 + 5 = 308\). This fits the first pair.

• Pair 2: 239 ∶ 78

  Let's test the same potential pattern found in the first pair: multiply the second number (78) by 3 and add 5.

  \(78 \times 3 = 234\). Now add 5: \(234 + 5 = 239\). This matches the first number in the pair. So, the pattern \(78 \times 3 + 5 = 239\) holds for the second pair as well.

• Pair 3: 326 ∶ 107

  Let's apply the pattern again: multiply the second number (107) by 3 and add 5.

  \(107 \times 3 = 321\). Now add 5: \(321 + 5 = 326\). This also matches the first number in the pair. The pattern \(107 \times 3 + 5 = 326\) is consistent with the first two pairs.

• Pair 4: 197 ∶ 66

  Let's test the pattern \(B \times 3 + 5\) with this pair, where B is 66.

  \(66 \times 3 = 198\). Now add 5: \(198 + 5 = 203\). The first number in the pair is 197, and 203 ≠ 197. This pair does not follow the pattern \(B \times 3 + 5\).

  Let's see if there's a slightly different pattern. What if we multiplied by 3 and subtracted a number? \(66 \times 3 = 198\). The difference between 198 and 197 is \(198 - 197 = 1\). So, the relationship for this pair is \(66 \times 3 - 1 = 197\).

Identifying the Different Number Pair

Based on our analysis, the first three number pairs (308 ∶ 101, 239 ∶ 78, 326 ∶ 107) all follow the same pattern where the first number is obtained by multiplying the second number by 3 and adding 5. The fourth number pair (197 ∶ 66) follows a different pattern where the first number is obtained by multiplying the second number by 3 and subtracting 1.

Therefore, the number pair that is different from the others is 197 ∶ 66.

Summarizing Number Pair Patterns

The table clearly shows that the first three pairs fit the \(B \times 3 + 5\) pattern, while the fourth pair fits a different pattern, \(B \times 3 - 1\). Thus, the fourth pair is the odd one out.

Revision Table: Key Concepts

Additional Information: Number Series and Pattern Recognition

Questions involving finding the "odd one out" or the next term in a sequence are common in logical reasoning and quantitative aptitude tests. These questions often test your ability for pattern recognition and logical deduction.

When faced with such problems, especially with number pairs or series, consider these common types of patterns:

• Arithmetic Progressions: A constant difference between consecutive terms.
• Geometric Progressions: A constant ratio between consecutive terms (multiplication or division).
• Combinations: Patterns involving both arithmetic and geometric operations, often with a constant addition or subtraction after multiplication/division, as seen in this problem (\(B \times K \pm C\)).
• Squares and Cubes: Patterns based on perfect squares (\(n^2\)) or cubes (\(n^3\)).
• Prime Numbers: Sequences or pairs involving prime numbers.
• Digit-based Operations: While excluded in this specific question, some problems involve operations on the digits of a number (e.g., sum of digits, product of digits).

To solve pattern recognition problems effectively, it's helpful to:

• Practice with various types of patterns.
• Systematically test different potential relationships (addition, subtraction, multiplication, division, squares, cubes, etc.).
• Look for the simplest possible rule that fits most of the given examples.
• Verify the found pattern with all the elements provided.

Understanding these strategies will improve your ability to quickly identify the underlying rule in number-based reasoning questions.