Sequence Analysis: Find the Odd Number Out

This question asks us to identify the number that does not follow the pattern established by the other numbers in the given sequence: 13, 23, 33, 43, 53.

Number Properties Analysis

To find the odd one out, let's examine the properties of each number in the list:

• 13: This is a prime number. It is only divisible by 1 and itself. The sum of its digits is $1 + 3 = 4$.
• 23: This is a prime number. It is only divisible by 1 and itself. The sum of its digits is $2 + 3 = 5$.
• 33: This is a composite number. It is divisible by 1, 3, 11, and 33. The sum of its digits is $3 + 3 = 6$.
• 43: This is a prime number. It is only divisible by 1 and itself. The sum of its digits is $4 + 3 = 7$.
• 53: This is a prime number. It is only divisible by 1 and itself. The sum of its digits is $5 + 3 = 8$.

Odd Number Conclusion

Observing the properties:

• Most numbers in the sequence (13, 23, 43, 53) are prime numbers.
• The number 33 is the only composite number in the sequence.
• Alternatively, we can consider divisibility by 3. A number is divisible by 3 if the sum of its digits is divisible by 3.
  • For 13, the sum is 4 (not divisible by 3).
  • For 23, the sum is 5 (not divisible by 3).
  • For 33, the sum is 6 (divisible by 3).
  • For 43, the sum is 7 (not divisible by 3).
  • For 53, the sum is 8 (not divisible by 3).

Based on these observations, the number 33 stands out because it is the only composite number and the only one divisible by 3 in the given list. Therefore, 33 is the odd one out.