Finding the Odd Number Pair by Mathematical Operation Analysis

The question asks us to identify a number pair that does not follow the same mathematical rule as the other pairs. We are given four pairs of numbers, where the second number is obtained from the first by some operation(s).

Let's analyze the given number pairs to find a consistent mathematical operation or pattern:

• Pair 1: 23 : 153
• Pair 2: 15 : 97
• Pair 3: 16 : 106
• Pair 4: 26 : 174

We need to find a relationship between the first number (let's call it $x$) and the second number (let's call it $y$) that holds true for most pairs.

Let's try some common operations like multiplication and then addition or subtraction.

Consider Pair 1: 23 and 153. If we multiply 23 by a number, say 6 or 7, we get close to 153. $23 \times 6 = 138$. $153 - 138 = 15$. So, $153 = (23 \times 6) + 15$. $23 \times 7 = 161$. $161 - 153 = 8$. So, $153 = (23 \times 7) - 8$.

Let's test the rule $y = 7x - 8$ on the other pairs:

Analysis of Number Pairs:

• Pair 1: 23 : 153

  Applying the rule $y = 7x - 8$ with $x = 23$:

  $y = (7 \times 23) - 8$

  $y = 161 - 8$

  $y = 153$

  This matches the given second number (153).

• Pair 2: 15 : 97

  Applying the rule $y = 7x - 8$ with $x = 15$:

  $y = (7 \times 15) - 8$

  $y = 105 - 8$

  $y = 97$

  This matches the given second number (97).

• Pair 3: 16 : 106

  Applying the rule $y = 7x - 8$ with $x = 16$:

  $y = (7 \times 16) - 8$

  $y = 112 - 8$

  $y = 104$

  This does not match the given second number (106). The rule gives 104, but the pair is 16 : 106.

• Pair 4: 26 : 174

  Applying the rule $y = 7x - 8$ with $x = 26$:

  $y = (7 \times 26) - 8$

  $y = 182 - 8$

  $y = 174$

  This matches the given second number (174).

From the analysis, we can see that the mathematical operation $y = 7x - 8$ is consistently applied in pairs 1, 2, and 4. Pair 3 (16 : 106) does not follow this rule, as the expected second number based on the rule is 104, not 106.

Therefore, the odd number pair is 16 : 106.

Revision Table: Mathematical Operation

This table summarizes the application of the rule to each number pair.

Additional Information: Pattern Identification in Number Series

Problems like this are common in logical reasoning and quantitative aptitude tests. They require identifying a mathematical pattern or rule governing a sequence or a set of pairs. Common patterns involve:

• Arithmetic operations (addition, subtraction, multiplication, division).
• Combinations of operations (e.g., multiply and then add/subtract).
• Squares, cubes, or other powers of the number.
• Operations based on digits of the number.

To solve such problems, it's helpful to:

• Look for a simple relationship first (e.g., is the second number a multiple of the first?).
• If multiplication is involved, estimate the multiplier by dividing the second number by the first.
• Test potential rules systematically on all given pairs.
• Pay attention to the difference or ratio between numbers.

Practicing different types of number series and pattern problems helps improve the ability to quickly spot the underlying rule.