Finding the Odd One Out Number

The question asks us to identify the number that is different from the others in a given set of four numbers. We are given the numbers 135, 108, 172, and 153. Three of these numbers share a common characteristic, while the fourth one does not. We need to find this distinguishing characteristic.

Analyzing the Numbers for Patterns

Let's examine each number to find a potential pattern or property that connects three of them. Common patterns in such questions involve properties like divisibility, sum of digits, prime/composite nature, or other arithmetic relationships.

• Number 135:
  • Sum of digits: \(1 + 3 + 5 = 9\).
  • Since the sum of digits (9) is divisible by 3, 135 is divisible by 3.
  • Since the sum of digits (9) is divisible by 9, 135 is divisible by 9.
• Number 108:
  • Sum of digits: \(1 + 0 + 8 = 9\).
  • Since the sum of digits (9) is divisible by 3, 108 is divisible by 3.
  • Since the sum of digits (9) is divisible by 9, 108 is divisible by 9.
• Number 172:
  • Sum of digits: \(1 + 7 + 2 = 10\).
  • Since the sum of digits (10) is not divisible by 3, 172 is not divisible by 3.
  • Since the sum of digits (10) is not divisible by 9, 172 is not divisible by 9.
• Number 153:
  • Sum of digits: \(1 + 5 + 3 = 9\).
  • Since the sum of digits (9) is divisible by 3, 153 is divisible by 3.
  • Since the sum of digits (9) is divisible by 9, 153 is divisible by 9.

Identifying the Different Number

Based on the analysis of the sum of digits and divisibility, we can observe a clear pattern among the numbers.

From the table and the analysis, it is evident that numbers 135, 108, and 153 all have a sum of digits equal to 9, which makes them divisible by both 3 and 9. Number 172, however, has a sum of digits equal to 10, which means it is not divisible by either 3 or 9.

Therefore, the number 172 is different from the other three numbers based on the property of divisibility by 3 and 9.

Conclusion: Odd One Out Number

The pattern is that three of the numbers (135, 108, 153) are divisible by 3 and 9, while one number (172) is not. Hence, 172 is the odd one out.

Revision Table: Number Pattern Analysis

Additional Information: Divisibility Rules

Understanding divisibility rules can be very helpful in solving number pattern questions. Here are the rules used in this problem:

• Divisibility Rule for 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
• Divisibility Rule for 9: A number is divisible by 9 if the sum of its digits is divisible by 9.

These rules provide a quick way to check for divisibility without performing long division. They are based on the properties of place value and modular arithmetic.