Finding the Odd Number Pair Based on Logic and Relation

The question asks us to identify the number pair that does not follow the same logic or relation as the other three pairs. We are given four pairs of numbers, where the number on the left is related to the number on the right by some rule. We need to find this rule and see which pair doesn't fit.

Analyzing the Given Number Pairs

Let's look at the provided number pairs:

1. 56885 - 11377
2. 38515 - 7701
3. 74235 - 14847
4. 82695 - 16539

The numbers on the left side are significantly larger than the numbers on the right side in each pair. This suggests that the operation relating the left number to the right number might be division, or the right number is a fraction or multiple of the left number.

Discovering the Logic/Relation

Let's test if the left number is a multiple of the right number by dividing the left number by the right number for each pair.

Pair 1: 56885 - 11377

Let's divide 56885 by 11377:

\( \frac{56885}{11377} \)

Performing the division:

\( 11377 \times 5 = 56885 \)

So, for this pair, \( 56885 = 5 \times 11377 \). The relation is that the left number is 5 times the right number.

Pair 2: 38515 - 7701

Let's divide 38515 by 7701:

\( \frac{38515}{7701} \)

Let's try multiplying 7701 by 5:

\( 7701 \times 5 = 38505 \)

Comparing 38505 with 38515, we see that \( 38515 = 5 \times 7701 + 10 \). The left number is NOT exactly 5 times the right number.

Pair 3: 74235 - 14847

Let's divide 74235 by 14847:

\( \frac{74235}{14847} \)

Let's try multiplying 14847 by 5:

\( 14847 \times 5 = 74235 \)

So, for this pair, \( 74235 = 5 \times 14847 \). The relation is that the left number is 5 times the right number.

Pair 4: 82695 - 16539

Let's divide 82695 by 16539:

\( \frac{82695}{16539} \)

Let's try multiplying 16539 by 5:

\( 16539 \times 5 = 82695 \)

So, for this pair, \( 82695 = 5 \times 16539 \). The relation is that the left number is 5 times the right number.

Identifying the Odd One Out

We found the following relations for each pair:

• Pair 1: \( \text{Left Number} = 5 \times \text{Right Number} \)
• Pair 2: \( \text{Left Number} \neq 5 \times \text{Right Number} \) (specifically, \( 38515 = 5 \times 7701 + 10 \))
• Pair 3: \( \text{Left Number} = 5 \times \text{Right Number} \)
• Pair 4: \( \text{Left Number} = 5 \times \text{Right Number} \)

Pairs 1, 3, and 4 follow the same logic where the left number is exactly 5 times the right number. Pair 2 does not follow this logic as the left number is not exactly 5 times the right number; there is a remainder of 10 when 38515 is divided by 7701.

Therefore, the odd one out is the pair 38515 - 7701.

Based on the analysis, the pair 38515 - 7701 is the odd one out because it does not fit the rule \( \text{Left Number} = 5 \times \text{Right Number} \) that the other three pairs follow.

Revision Table: Number Series and Odd One Out

Additional Information: Strategies for Finding Logic in Number Pairs

When faced with questions asking to find the logic in number pairs or series, consider these strategies:

• Look for Basic Operations: Check for simple addition, subtraction, multiplication, or division between the numbers in the pair or consecutive terms in a series.
• Consider Powers and Roots: See if one number is the square, cube, square root, or cube root of the other, or related to them.
• Check for Differences/Ratios: Calculate the difference or ratio between the numbers. Sometimes the pattern is in the differences or ratios themselves.
• Examine Digit Properties (if allowed): Although not allowed in this specific question's note, sometimes the logic involves the sum of digits, product of digits, or other properties of the digits themselves.
• Combine Operations: The rule might involve multiple steps, like multiplying by a number and then adding/subtracting a constant.
• Be Mindful of Constraints: Pay close attention to any notes, like the one in this question, that restrict the types of operations (e.g., no breaking down digits).

Applying these strategies systematically helps uncover the hidden relation and find the odd one out effectively.