Number Doesn't Belong: Prime Number Analysis
The question asks us to identify the number from the given list that does not share a common property with the others. The list of numbers is 103, 109, 107, and 111.
Analyzing Number Properties
To find the number that doesn't belong, let's examine the properties of each number, particularly focusing on whether they are prime or composite.
- Prime Numbers: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
- Composite Numbers: A composite number is a natural number that has more than two positive divisors.
Checking Each Number
- 103: Let's check for divisors. It's not divisible by 2, 3 (sum of digits = 4), 5, 7 (103 / 7 ≈ 14.7), 11 (alternating sum = 1-0+3 = 4). The square root of 103 is approximately 10.1. We only need to check primes up to 10 (2, 3, 5, 7). Since it's not divisible by any of these, 103 is a prime number.
- 109: Checking for divisors: not divisible by 2, 3 (sum = 10), 5, 7 (109 / 7 ≈ 15.5), 11 (alternating sum = 1-0+9 = 10). The square root of 109 is approximately 10.4. We check primes up to 10 (2, 3, 5, 7). Since it's not divisible by these, 109 is a prime number.
- 107: Checking for divisors: not divisible by 2, 3 (sum = 8), 5, 7 (107 / 7 ≈ 15.3), 11 (alternating sum = 1-0+7 = 8). The square root of 107 is approximately 10.3. We check primes up to 10 (2, 3, 5, 7). Since it's not divisible by these, 107 is a prime number.
- 111: Checking for divisors:
- Is it divisible by 2? No, it's an odd number.
- Is it divisible by 3? Let's sum the digits: \(1 + 1 + 1 = 3\). Since 3 is divisible by 3, 111 is divisible by 3.
- Calculation: \(111 \div 3 = 37\).
Conclusion
Comparing the numbers:
- 103 is prime.
- 109 is prime.
- 107 is prime.
- 111 is composite.
The numbers 103, 109, and 107 are all prime numbers. The number 111 is a composite number because it is divisible by 3 and 37.
Therefore, the number that doesn't belong in the list is 111.
Similar Questions
- Four of the following five are alike in a certain way and hence form a group. Which is the one that does not belong to that group?
A. BRIGHT: DSJHF
B. CUSTOM: FVUUP
C. FLIGHT: HNIJI
D. CHANCE: EKBMF
E. STRONG: VUQPR - Find the number that doesn't belong:
11, 13, 17, 19 - A coding rule is followed by Roll numbers ending with an even digit belong to Batch 1 and Roll numbers ending with an odd digit
belong to Batch 2.
Identify the roll number for Batch 1 and Batch 2. - Choose the number that is different from the others.
Which figure breaks the pattern?
- Guitar, Piano, Violin, Microphone - which is the odd one?
Which one of the following figures breaks the pattern followed by the others?
Choose the figure that is different from the rest in terms of the observed sequence or rule.
- Identify the odd pair:
- Apple, Banana, Carrot, Mango - which is the odd one?
Important Questions from Classification
Three of the following four are alike in a certain way and thus form a group. Which is the one that does NOT belong to that group?
(Note: The odd one out is not based on the number of consonants/vowels or their position in the letter cluster.)Three of the following numbers are alike in a certain way and one is different. Pick the odd one out.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/deleting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
The following contains two pairs of words which are related to each other in a certain way. Three of the following four word-pairs are alike as these have the same relationship and thus form a group. Which word-pair does NOT belong to that group?
(The words must be considered as meaningful English words and must not be grouped based on the number of letters/number of consonants/vowels in the word)Three of the following four options are alike in a certain way and thus form a group. Which is the one that does NOT belong to that group?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g., 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
The following contains two pairs of words which are related to each other in a certain way. Three of the following four word-pairs are alike as these have the same relationship and thus form a group. Which word-pair does NOT belong to that group?
(The words must be considered as meaningful English words and must not be grouped based on the number of letters/number of consonants/vowels in the word)
