Find the Odd Number Pair Logic

This question asks us to identify the odd number pair out of the given four options. The pairs are related by a specific rule or logic, and we need to find the pair that does not follow this common rule. The rule is applied to the whole number on the left side of the hyphen to get the number on the right side.

Analyzing the Number Pairs to Find the Logic

Let's examine each number pair and try to find a relationship between the left number (let's call it 'n') and the right number.

• Pair 1: 19 - 364
• Let $n = 19$. We need to relate 19 to 364. Let's try squaring the number: $19^2 = 361$. The number on the right is 364. The difference is $364 - 361 = 3$. So, the rule might be $n^2 + 3$. Let's check if this rule applies to other pairs.

• Pair 2: 21 - 444
• Let $n = 21$. Let's apply the possible rule $n^2 + 3$: $21^2 = 441$. $441 + 3 = 444$. This matches the number on the right. So, this pair follows the rule $n^2 + 3$.

• Pair 3: 17 - 292
• Let $n = 17$. Let's apply the possible rule $n^2 + 3$: $17^2 = 289$. $289 + 3 = 292$. This also matches the number on the right. So, this pair follows the rule $n^2 + 3$.

• Pair 4: 13 - 174
• Let $n = 13$. Let's apply the possible rule $n^2 + 3$: $13^2 = 169$. $169 + 3 = 172$. The number on the right is 174, which is not 172. So, this pair does not follow the rule $n^2 + 3$.
• Let's see what rule it might follow. The difference between 174 and $13^2$ (169) is $174 - 169 = 5$. So, this pair seems to follow the rule $n^2 + 5$.

Identifying the Odd Pair

We have found that:

• Pair 1 (19 - 364) follows the rule $n^2 + 3$.
• Pair 2 (21 - 444) follows the rule $n^2 + 3$.
• Pair 3 (17 - 292) follows the rule $n^2 + 3$.
• Pair 4 (13 - 174) follows the rule $n^2 + 5$.

Three out of the four pairs follow the same logic ($n^2 + 3$), while one pair follows a different logic ($n^2 + 5$). Therefore, the odd one out is the pair 13 - 174.

Summary of the Logic

Based on the analysis, the pair 13 - 174 is the odd one out because it follows a different logical rule compared to the other three pairs.

Revision Table: Number Pattern Analysis

Reviewing the process of finding the odd number pair:

• Check if the number on the right is a simple multiple of the number on the left. (Not the case here).
• Consider squares or cubes of the left number and see how they relate to the right number.
• Look for constant additions or subtractions after squaring or cubing.
• Test the potential logic on all pairs.
• Identify the pair that deviates from the common logic found in the majority of pairs.

Additional Information: Reasoning Skills

Questions involving number pairs and finding the odd one out are common in reasoning sections of competitive exams. They test your ability to identify patterns, apply mathematical operations, and use logical deduction. Common patterns include:

• Arithmetic operations (addition, subtraction, multiplication, division).
• Squaring or cubing numbers.
• Operations based on digits (though explicitly disallowed in this specific question).
• Prime or composite numbers.
• Even or odd numbers.
• Sequences and series logic.

Practicing these types of number pattern problems helps improve analytical thinking and problem-solving skills.