Finding the Different Number: Odd One Out Analysis

In this question, we are given four numbers: 343, 731, 1331, and 2197. We need to identify the number that is different from the rest, implying that the other three numbers share a common property.

Let's examine each number to find a possible pattern or property they might share.

Analyzing Each Number

We will check if these numbers belong to any specific category, such as perfect squares, perfect cubes, prime numbers, etc.

• Number 1: 343

  Let's test if 343 is a perfect cube. We know that $6^3 = 216$ and $7^3 = 7 \times 7 \times 7 = 49 \times 7 = 343$.

  So, 343 is a perfect cube. Specifically, $343 = 7^3$.

• Number 2: 731

  Let's check if 731 is a perfect cube. We know $9^3 = 729$ and $10^3 = 1000$. 731 is between these two values, so it is not a perfect cube.

  Let's see if it has other properties. Is it a prime number? We can test for divisibility by small prime numbers. It's not divisible by 2, 3, 5. Let's try 7: $731 \div 7 \approx 104.4$. Let's try 11: $731 \div 11 \approx 66.4$. Let's try 13: $731 \div 13 \approx 56.2$. Let's try 17: $731 \div 17 = 43$.

  So, $731 = 17 \times 43$. It is a composite number, the product of two prime numbers.

• Number 3: 1331

  Let's check if 1331 is a perfect cube. We know $10^3 = 1000$. Let's try $11^3 = 11 \times 11 \times 11 = 121 \times 11 = 1331$.

  So, 1331 is a perfect cube. Specifically, $1331 = 11^3$.

• Number 4: 2197

  Let's check if 2197 is a perfect cube. We know $12^3 = 1728$ and $13^3 = 13 \times 13 \times 13 = 169 \times 13 = 2197$.

  So, 2197 is a perfect cube. Specifically, $2197 = 13^3$.

Identifying the Pattern and the Different Number

Based on our analysis:

• 343 is a perfect cube ($7^3$).
• 731 is not a perfect cube ($17 \times 43$).
• 1331 is a perfect cube ($11^3$).
• 2197 is a perfect cube ($13^3$).

Three of the numbers (343, 1331, 2197) share the property of being a perfect cube. The number 731 does not share this property; it is a composite number but not a perfect cube.

Therefore, 731 is the number that is different from the rest.

Revision Table: Key Concepts in Number Patterns

Additional Information: Understanding Odd One Out Questions

Odd One Out questions are common in reasoning and aptitude tests. They require you to find an item (number, word, figure, etc.) that does not belong to a group because it lacks a characteristic or property shared by the other items in the group.

Strategies to solve these questions often involve:

• Looking for common mathematical properties (like perfect squares/cubes, prime/composite, even/odd, divisibility rules).
• Checking for patterns in digits (sum of digits, product of digits, sequence).
• Identifying arithmetic or geometric progressions (though less common with just four numbers).
• Analyzing visual features (for figure-based questions).

Practicing with different types of Odd One Out problems helps in quickly identifying potential patterns.