Three of the following four numbers are alike in a certain way and one is different. Pick the number that is different from the rest.
43
Finding the Odd Number Out: Analysis of 39, 63, 57, 43
The question asks us to identify the number that is different from the rest among the given four numbers: 39, 63, 57, and 43. This type of problem requires finding a common property or pattern shared by three of the numbers, while the fourth number does not share that property.
Step-by-Step Analysis of the Numbers
Let's examine each number to identify potential patterns. We can look at properties like divisibility, prime vs. composite, sum of digits, etc.
- Number 39:
39 can be divided by numbers other than 1 and 39. For example, $39 \div 3 = 13$. So, 39 is a composite number.
- Number 63:
63 can be divided by numbers other than 1 and 63. For example, $63 \div 3 = 21$. Also, $63 \div 7 = 9$. So, 63 is a composite number.
- Number 57:
57 can be divided by numbers other than 1 and 57. For example, $57 \div 3 = 19$. So, 57 is a composite number.
- Number 43:
Let's check if 43 is divisible by any number other than 1 and 43. We can test prime numbers up to the square root of 43, which is about 6.5. The primes to check are 2, 3, 5.
- 43 is not divisible by 2 (it's an odd number).
- The sum of digits of 43 is $4 + 3 = 7$, which is not divisible by 3. So, 43 is not divisible by 3.
- 43 does not end in 0 or 5, so it's not divisible by 5.
Since 43 is not divisible by any prime number less than or equal to its square root, it is only divisible by 1 and 43. This means 43 is a prime number.
Identifying the Pattern and the Different Number
Based on our analysis, we can observe a clear pattern:
- 39 is a composite number (divisible by 3).
- 63 is a composite number (divisible by 3).
- 57 is a composite number (divisible by 3).
- 43 is a prime number.
Three of the numbers (39, 63, and 57) share the property of being divisible by 3 and therefore are composite numbers. The number 43 is different because it is a prime number and is not divisible by 3.
| Number | Divisible by 3? | Prime or Composite? |
|---|---|---|
| 39 | Yes ($39 = 3 \times 13$) | Composite |
| 63 | Yes ($63 = 3 \times 21$) | Composite |
| 57 | Yes ($57 = 3 \times 19$) | Composite |
| 43 | No | Prime |
Therefore, the number that is different from the rest is 43.
Conclusion
The number 43 is the odd one out because, unlike 39, 63, and 57, it is a prime number and is not divisible by 3. The other three numbers are composite numbers divisible by 3.
Revision Table: Number Properties
| Term | Definition | Example |
|---|---|---|
| Prime Number | A natural number greater than 1 that has no positive divisors other than 1 and itself. | 2, 3, 5, 7, 11, 43 |
| Composite Number | A natural number greater than 1 that is not a prime number (i.e., it has positive divisors other than 1 and itself). | 4, 6, 8, 9, 10, 39, 57, 63 |
| Divisibility Rule for 3 | A number is divisible by 3 if the sum of its digits is divisible by 3. | 12 (1+2=3, divisible by 3), 57 (5+7=12, divisible by 3) |
Additional Information: Finding Odd One Out Questions
Finding the 'odd one out' is a common type of question in reasoning and aptitude tests. These questions assess your ability to observe, compare, and identify patterns or rules that group a set of items together, with one item breaking that rule. The patterns can be based on various properties, such as:
- Number properties (prime/composite, even/odd, square/cube, divisibility)
- Arithmetic operations (addition, subtraction, multiplication, division patterns)
- Geometric properties
- Alphabetical patterns (for letter series)
- General knowledge categories
To solve these problems, systematically analyze each item and look for common characteristics or relationships. Often, testing for simple properties like divisibility or being prime is a good starting point for number-based questions.
Similar Questions
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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.
