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.
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