Find the Odd One Out Number

In this type of question, we are given a set of numbers, and we need to find the number that does not fit the pattern or rule followed by the other numbers. We need to examine the given numbers and look for a common property or relationship among three of them, while one number lacks that property or relationship.

The given numbers are:

• 250
• 95
• 159
• 150

Let's analyze the numbers to find a pattern:

We can look at various properties like divisibility, prime or composite nature, sum of digits, ending digits, etc.

Analyzing Divisibility Pattern

Let's check for divisibility by common small numbers:

• Divisibility by 2: 250 and 150 are divisible by 2 (they are even). 95 and 159 are not divisible by 2 (they are odd). This pattern doesn't isolate one number.
• Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5.
  • 250 ends in 0, so it is divisible by 5. \( \frac{250}{5} = 50 \)
  • 95 ends in 5, so it is divisible by 5. \( \frac{95}{5} = 19 \)
  • 159 ends in 9, so it is not divisible by 5.
  • 150 ends in 0, so it is divisible by 5. \( \frac{150}{5} = 30 \)

Based on divisibility by 5, three numbers (250, 95, and 150) are divisible by 5, while one number (159) is not.

This establishes a clear pattern where 159 is the odd one out because it does not share the property of being divisible by 5 with the other three numbers.

Checking Other Potential Patterns

• Sum of Digits:
  • 2 + 5 + 0 = 7
  • 9 + 5 = 14
  • 1 + 5 + 9 = 15
  • 1 + 5 + 0 = 6
  There isn't an obvious pattern connecting three of these sums (7, 14, 15, 6).
• Prime or Composite:
  • 250 is composite (e.g., \( 5 \times 50 \)).
  • 95 is composite (e.g., \( 5 \times 19 \)).
  • 159 is composite ( \( 3 \times 53 \) ).
  • 150 is composite (e.g., \( 5 \times 30 \)).
  All numbers are composite, so this doesn't distinguish one number.

The pattern of divisibility by 5 is the most consistent and logical rule that makes one number different from the rest.

Therefore, 159 is the odd one out.

Revision Table: Identifying Odd Numbers

Based on the analysis, 159 is the number that is different from the others.

Additional Information: Strategies for Odd One Out Questions

When tackling odd one out number questions, consider the following strategies:

• Divisibility Rules: Check for divisibility by small prime numbers (2, 3, 5, 7, 11, etc.). Rules for divisibility by 2 (even/odd), 3 (sum of digits), 5 (ends in 0 or 5), 10 (ends in 0) are common.
• Prime vs. Composite: See if three numbers are prime and one is composite, or vice versa.
• Squares and Cubes: Check if numbers are perfect squares, cubes, or related to them.
• Sum, Difference, Product of Digits: Sometimes a pattern is based on operations performed on the digits of the number.
• Sequential Patterns: In some series, there might be a pattern based on arithmetic or geometric progression, though less common in simple odd-one-out sets.
• Ending or Beginning Digits: Look for patterns in the first or last digits.
• Position in Number Line: While less mathematical, sometimes numbers are grouped by size ranges, though this is usually less definitive.

Always test a potential rule against all given options to confirm that it applies to exactly three numbers and excludes only one.