Which one set of the following sets of numbers (3, 5,19, 13), (11, 19, 2, 3), (3, 29, 2, 13), (2, 31, 11, 4) is different (if any) from the other sets, in accordance with some rule?
Number Sets Analysis
The question asks us to identify which one set of numbers is different from the others based on a specific rule. We are given four sets of numbers:
- Set 1: (3, 5, 19, 13)
- Set 2: (11, 19, 2, 3)
- Set 3: (3, 29, 2, 13)
- Set 4: (2, 31, 11, 4)
Understanding Prime and Composite Numbers
To find the rule, let's recall the definitions of prime and composite numbers:
- Prime Numbers: A natural number greater than 1 that has no positive divisors other than 1 and itself. Examples include 2, 3, 5, 7, 11, 13, 17, 19, etc.
- Composite Numbers: A natural number greater than 1 that is not prime. This means it has at least one divisor other than 1 and itself. Examples include 4, 6, 8, 9, 10, 12, etc.
Analyzing Each Number Set
Let's examine each number in all the given sets to determine if it is a prime or a composite number.
First Number Set: (3, 5, 19, 13)
- 3: Is a prime number (divisors are 1, 3).
- 5: Is a prime number (divisors are 1, 5).
- 19: Is a prime number (divisors are 1, 19).
- 13: Is a prime number (divisors are 1, 13).
Observation: All numbers in the set (3, 5, 19, 13) are prime numbers.
Second Number Set: (11, 19, 2, 3)
- 11: Is a prime number (divisors are 1, 11).
- 19: Is a prime number (divisors are 1, 19).
- 2: Is a prime number (divisors are 1, 2). It is the smallest prime number and the only even prime number.
- 3: Is a prime number (divisors are 1, 3).
Observation: All numbers in the set (11, 19, 2, 3) are prime numbers.
Third Number Set: (3, 29, 2, 13)
- 3: Is a prime number (divisors are 1, 3).
- 29: Is a prime number (divisors are 1, 29).
- 2: Is a prime number (divisors are 1, 2).
- 13: Is a prime number (divisors are 1, 13).
Observation: All numbers in the set (3, 29, 2, 13) are prime numbers.
Fourth Number Set: (2, 31, 11, 4)
- 2: Is a prime number (divisors are 1, 2).
- 31: Is a prime number (divisors are 1, 31).
- 11: Is a prime number (divisors are 1, 11).
- 4: Is a composite number (divisors are 1, 2, 4). Since it has divisors other than 1 and itself (namely 2), it is not prime.
Observation: The number 4 in the set (2, 31, 11, 4) is a composite number, while the other numbers in this set (2, 31, 11) are prime.
Conclusion
Based on our analysis:
- The first three sets (3, 5, 19, 13), (11, 19, 2, 3), and (3, 29, 2, 13) consist exclusively of prime numbers.
- The fourth set (2, 31, 11, 4) contains one composite number, which is 4, along with prime numbers.
Therefore, the set (2, 31, 11, 4) is different from the other sets because it is the only one that includes a composite number.
Important Questions from Number Based
- Below are given two sets of numbers. In each set of numbers, a certain mathematical operation on the first number results in the second number. Similarly, certain mathematical operations on the second number result in the third number and so on. Which of the given options follows the same set of operations as in question?
(NOTE – A two/three-digit number cannot be broken into individual digits for operations, e.g., if 37 is followed by 10, the operation cannot be 3+7 as a two-digit number cannot be broken into individual digits.)
12 – 26 – 46 – 70; 20 – 34 – 54 – 78 - Below are given two sets of numbers. In each set of numbers, a certain mathematical operation on the first number results in the second number. Similarly, certain mathematical operations on the second number result in the third number and so on. Which of the given options follows the same set of operations as in the question?
(NOTE – A two/three-digit number cannot be broken into individual digits for operations. E.g. if 37 is followed by 10, the operation cannot be 3+7 as a two-digit number cannot be broken into individual digits.)
5 – 20 – 60 – 120
8 – 32 – 96 – 192 Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(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 to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.
(15, 7, 100)
(25, 8, 195)- Select the set in which the numbers are related in the same way as are the numbers of the following sets.
5-7-9
11-13-15
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its 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) - Replace the question mark with an option that follows the same logic applied in the first pair.
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