Analyzing the Given Numbers to Find the Odd One Out

We are presented with four numbers: 5720, 6710, 2640, and 4270. The goal is to find which one of these numbers is different from the rest based on a certain property or rule.

Exploring Number Properties and Patterns

To identify the odd number, we need to look for a common characteristic or pattern that applies to three of the numbers but not to the fourth. Let's examine potential mathematical properties, such as divisibility rules or relationships between the digits.

Applying the Divisibility Rule for 11

A common test in such problems involves divisibility rules. Let's check the divisibility of each number by 11 using the alternating sum of digits rule. This rule states that a number is divisible by 11 if the sum of its digits in the odd-numbered places (from right) minus the sum of its digits in the even-numbered places (from right) is 0 or a multiple of 11.

Checking 5720 for Divisibility by 11

For the number 5720:

Digits in odd places (1st and 3rd from right): 0, 7

Digits in even places (2nd and 4th from right): 2, 5

Alternating sum = (Sum of digits in odd places) - (Sum of digits in even places)

\(= (0 + 7) - (2 + 5)\)

\(= 7 - 7\)

\(= 0\)

Since the alternating sum is 0, the number 5720 is divisible by 11.

Checking 6710 for Divisibility by 11

For the number 6710:

Digits in odd places: 0, 7

Digits in even places: 1, 6

Alternating sum = \((0 + 7) - (1 + 6)\)

\(= 7 - 7\)

\(= 0\)

Since the alternating sum is 0, the number 6710 is divisible by 11.

Checking 2640 for Divisibility by 11

For the number 2640:

Digits in odd places: 0, 6

Digits in even places: 4, 2

Alternating sum = \((0 + 6) - (4 + 2)\)

\(= 6 - 6\)

\(= 0\)

Since the alternating sum is 0, the number 2640 is divisible by 11.

Checking 4270 for Divisibility by 11

For the number 4270:

Digits in odd places: 0, 2

Digits in even places: 7, 4

Alternating sum = \((0 + 2) - (7 + 4)\)

\(= 2 - 11\)

\(= -9\)

Since the alternating sum is -9, which is not a multiple of 11, the number 4270 is not divisible by 11.

Identifying the Odd Number Out

Our analysis shows that:

• 5720 is divisible by 11.
• 6710 is divisible by 11.
• 2640 is divisible by 11.
• 4270 is not divisible by 11.

Thus, the number 4270 is the odd one out because it does not share the property of being divisible by 11 with the other three numbers.

Revision Table: Divisibility Analysis

Additional Information: Understanding Number Series and Patterns

Questions asking to find the odd one out or identify the next term in a series often rely on recognizing mathematical patterns or properties. These can include:

• Arithmetic or geometric progressions
• Prime or composite numbers
• Square or cube numbers
• Divisibility rules for various numbers (like 2, 3, 4, 5, 6, 8, 9, 10, 11)
• Sum, product, or difference of digits
• Patterns based on the position of digits

Systematically testing these common patterns is key to solving logical reasoning problems involving numbers.