Select the number that does NOT belong in the following group. 71, 73, 77, 79
77
Analyzing the Number Group
The question asks us to identify the number that does NOT belong to the group: 71, 73, 77, 79.
To find the number that is different, we need to look for a common property among most of the numbers and see which one doesn't share that property.
Let's examine each number in the group:
- 71
- 73
- 77
- 79
Identifying Number Properties: Prime vs. Composite
A common way to analyze numbers in a sequence like this is to look at their factors, specifically whether they are prime or composite numbers.
- A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
- A composite number is a natural number greater than 1 that is not prime. This means it has at least one divisor other than 1 and itself.
Let's find the factors for each number:
| Number | Factors | Type of Number |
|---|---|---|
| 71 | 1, 71 | Prime |
| 73 | 1, 73 | Prime |
| 77 | 1, 7, 11, 77 | Composite (\(7 \times 11 = 77\)) |
| 79 | 1, 79 | Prime |
Finding the Outlier Number
From the table above, we can see the following:
- 71 has only two factors (1 and 71), making it a prime number.
- 73 has only two factors (1 and 73), making it a prime number.
- 77 has more than two factors (1, 7, 11, and 77), making it a composite number.
- 79 has only two factors (1 and 79), making it a prime number.
The property shared by 71, 73, and 79 is that they are all prime numbers. The number 77 does not share this property because it is a composite number.
Therefore, 77 is the number that does NOT belong in the group.
Conclusion on the Grouped Numbers
Based on our analysis of the properties of the numbers 71, 73, 77, and 79, the number that differs from the others is 77.
Revision Table: Understanding Number Properties
| Term | Definition | Example |
|---|---|---|
| Prime Number | A natural number > 1 with exactly two factors: 1 and itself. | 2, 3, 5, 7, 11, ... 71, 73, 79 |
| Composite Number | A natural number > 1 that is not prime (has more than two factors). | 4 (factors: 1, 2, 4), 6 (factors: 1, 2, 3, 6), 77 (factors: 1, 7, 11, 77) |
Additional Information on Number Patterns
Problems like this test your understanding of number properties. While this example used prime and composite numbers, other patterns could involve:
- Even and odd numbers.
- Square numbers or cube numbers.
- Numbers in an arithmetic or geometric progression.
- Numbers divisible by a specific factor.
- Numbers with a specific sum of digits.
Always examine the basic properties of the numbers given in a group to find the underlying rule and the number that breaks it.
Similar Questions
Select the set that does NOT belong in the following group of sets.
(2, 14, 16), (6, 30, 36), (5, 35, 40), (3, 21, 24)- Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number results in the second number. Similarly, certain mathematical operation(s) on the second number results in the third number and so on. Which of the given options follows the same set of operations as in the given 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.) 68 – 136 – 121 – 363; 29 – 58 – 43 – 129
- If 2 is added to each odd digit and 1 is subtracted from each even digit in the number 2741586, how many digits will appear more than once in the new number thus formed?
(2, 14, 16), (3, 21, 24), (8, 56, 64), (5, 35, 41)
The set that does NOT belong to the group is:Select the pair that does NOT belong in the following group.
(√64,9), (√81,10), (√36,8), (√121,12)
Select the number pair that does NOT belong in the following group.
(1, 1), (4, 64), (8, 512), (9, 719)
Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given 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 to/subtracting from/multiplying with 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
6 - 36 - 72 - 144 ; 7 - 49 - 98 - 196- Two sets of numbers are given below. In each set of numbers, a certain mathematical operation on the first number results in the second number. Similarly, certain mathematical operation on the second number results in the third number and so on. Which of the given options follows the same set of operations as in the given sets?
(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)
42 - 45 - 270 - 265
25 - 28 - 168 - 163 Below are given two sets of numbers. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given 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 to/subtracting from/multiplying with 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
10 - 100 - 50 - 25; 2 - 4 - 2 - 1
16 is related to 260 following a certain logic. Following the same logic, 25 is related to 630. To which of the following is 9 related, following the same logic?
(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 to/subtracting from/multiplying with 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
Important Questions from Number Based
In the following question, four number pairs are given. The number on left side of (-) is related to the number of the right side of (-) with some Logic/Rule/Relation. Three are similar on basis of same Logic/Rule/Relation. Select the odd one out from the given alternatives.
Select the set in which the numbers are related in the same way as are the number of the following set.
(3, 7, 58)
Find the odd number/letters from the given alternatives.
Find the odd number/letters from the given alternatives.
Identify the number which is different from the other.
