Understanding the Odd One Out Question

In this type of logical reasoning question, we are given a set of items (in this case, numbers) and need to find the one that does not fit the pattern or rule that applies to the others. We need to carefully examine the given numbers: 67, 47, 17, and 57, and look for a common property shared by three of them, while the remaining one lacks that property.

Analyzing the Given Numbers: 67, 47, 17, 57

Let's look closely at each number:

• 17: Is this a prime number? A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. We can check for factors of 17. The only numbers that divide 17 evenly are 1 and 17. So, 17 is a prime number.
• 47: Is this a prime number? Let's check for small prime factors (2, 3, 5, 7, etc.). 47 is not divisible by 2 (it's odd). The sum of its digits is $4 + 7 = 11$, which is not divisible by 3, so 47 is not divisible by 3. It doesn't end in 0 or 5, so it's not divisible by 5. $47 \div 7 = 6$ with a remainder of 5. Since the next prime is 11 and $11^2 = 121 > 47$, we only need to check primes up to 7. Since 47 is not divisible by any primes up to its square root, 47 is a prime number.
• 67: Is this a prime number? Let's check for prime factors (2, 3, 5, 7). 67 is odd, so not divisible by 2. $6 + 7 = 13$, not divisible by 3. Doesn't end in 0 or 5. $67 \div 7 = 9$ with a remainder of 4. $67 \div 11 = 6$ with a remainder of 1. $67 \div 13 = 5$ with a remainder of 2. Since the next prime is 17 and $17^2 = 289 > 67$, we only need to check primes up to 13. Since 67 is not divisible by any primes up to its square root, 67 is a prime number.
• 57: Is this a prime number? Let's check for prime factors. 57 is odd. $5 + 7 = 12$. Since 12 is divisible by 3 ($12 \div 3 = 4$), 57 is divisible by 3. $57 \div 3 = 19$. Since 57 can be divided evenly by a number other than 1 and itself (specifically, 3 and 19), 57 is not a prime number. It is a composite number.

Identifying the Pattern: Prime vs. Composite Numbers

Based on our analysis, we found that:

• 17 is a prime number.
• 47 is a prime number.
• 67 is a prime number.
• 57 is a composite number.

Three of the numbers (17, 47, 67) share the property of being prime numbers, while the fourth number (57) is a composite number. This is the pattern that makes one number different from the others in this set.

Conclusion: The Odd One Out

The number that does not fit the pattern of being a prime number is 57. Therefore, 57 is the odd one out among the given numbers.

Revision Table: Key Concepts

Additional Information: Testing for Primes

A common way to test if a number 'n' is prime is to check for divisibility by all prime numbers up to the square root of 'n'. If 'n' is not divisible by any of these primes, then 'n' is a prime number. For example, to test 67, we look at primes up to $\sqrt{67}$. Since $8^2 = 64$ and $9^2 = 81$, $\sqrt{67}$ is between 8 and 9. We check primes 2, 3, 5, 7. None of these divide 67, confirming it's prime.