Finding the Odd Number Out in the Series

The question asks us to identify the number that is different from the other three in a given set of four numbers. The numbers are 325, 195, 544, and 416. To find the odd number out, we need to look for a pattern or a common property that three of the numbers share, but the fourth one does not.

Let's examine the numbers and look for potential patterns:

• Number 1: 325
• Number 2: 195
• Number 3: 544
• Number 4: 416

Analyzing the Numbers for a Pattern

We can check for various properties like divisibility, sum/product of digits, or other mathematical relationships.

Checking Divisibility by Common Factors

Let's test divisibility by some common prime numbers or other numbers.

We can test divisibility by 5:

• 325 ends in 5, so it is divisible by 5. \(325 \div 5 = 65\).
• 195 ends in 5, so it is divisible by 5. \(195 \div 5 = 39\).
• 544 ends in 4, so it is not divisible by 5.
• 416 ends in 6, so it is not divisible by 5.

This doesn't help us find the odd one out, as two numbers are divisible by 5 and two are not.

Let's test divisibility by other numbers. How about 13?

• Is 325 divisible by 13? \(325 \div 13\). \(13 \times 20 = 260\), \(325 - 260 = 65\). \(13 \times 5 = 65\). So, \(325 = 13 \times 25\). Yes, 325 is divisible by 13.
• Is 195 divisible by 13? \(195 \div 13\). \(13 \times 10 = 130\), \(195 - 130 = 65\). \(13 \times 5 = 65\). So, \(195 = 13 \times 15\). Yes, 195 is divisible by 13.
• Is 544 divisible by 13? \(544 \div 13\). \(13 \times 40 = 520\), \(544 - 520 = 24\). 24 is not divisible by 13. So, 544 is not divisible by 13.
• Is 416 divisible by 13? \(416 \div 13\). \(13 \times 30 = 390\), \(416 - 390 = 26\). \(13 \times 2 = 26\). So, \(416 = 13 \times 32\). Yes, 416 is divisible by 13.

Let's summarize the divisibility by 13:

Conclusion

From the analysis, we can see that three numbers (325, 195, and 416) are divisible by 13, while one number (544) is not divisible by 13. This property makes 544 the odd number out in the given series.

Therefore, the odd number out is 544.

Revision Table: Checking Odd Number Out

Additional Information: Logical Reasoning and Number Patterns

Logical reasoning questions often involve finding patterns in numbers, series, or figures. For number series, common patterns include:

• Arithmetic progression (adding or subtracting a constant).
• Geometric progression (multiplying or dividing by a constant).
• Differences between consecutive terms.
• Squares, cubes, or other powers.
• Divisibility rules.
• Sum or product of digits.
• Alternating patterns.

To solve "odd number out" questions, you need to test different potential rules or properties that might apply to the numbers. Once a rule is found that applies to all but one number, that number is the odd one out. It's important to systematically test different possibilities until the underlying pattern is discovered.