Four number-pairs have given, out of which three are alike in some manner and one is different. Select the number-pair that is different.
25/41 : 8
Understanding the Number Pair Pattern
The question asks us to identify the number-pair that is different from the other three. This is a common type of logical reasoning problem where you need to find a pattern or rule that applies to most of the given items and then spot the one that doesn't follow the rule. We have four number-pairs presented as a fraction followed by a number, like Numerator/Denominator : Result.
Analyzing Each Number Pair
Let's examine each number pair and try to find a consistent pattern connecting the fraction to the number on the right. A good approach is often to look at the digits within the numbers.
Let's consider the sum of the digits in the numerator and the sum of the digits in the denominator for each pair. We will then see how these sums might relate to the number given after the colon.
| Number-Pair | Numerator (N) | Sum of Digits in N ($\Sigma$ digits of N) | Denominator (D) | Sum of Digits in D ($\Sigma$ digits of D) | $\Sigma$ digits of N + $\Sigma$ digits of D | Given Number |
|---|---|---|---|---|---|---|
| 16/20 : 6 | 16 | $1+6 = 7$ | 20 | $2+0 = 2$ | $7 + 2 = 9$ | 6 |
| 30/51 : 9 | 30 | $3+0 = 3$ | 51 | $5+1 = 6$ | $3 + 6 = 9$ | 9 |
| 4/5 : 3 | 4 | $4$ | 5 | $5$ | $4 + 5 = 9$ | 3 |
| 25/41 : 8 | 25 | $2+5 = 7$ | 41 | $4+1 = 5$ | $7 + 5 = 12$ | 8 |
Identifying the Pattern
Looking at the table, let's focus on the column "$\Sigma$ digits of N + $\Sigma$ digits of D":
- For 16/20 : 6, the sum is 9.
- For 30/51 : 9, the sum is 9.
- For 4/5 : 3, the sum is 9.
- For 25/41 : 8, the sum is 12.
We can see a clear pattern here: for the first three number-pairs, the sum of the sums of digits of the numerator and the denominator is 9. For the fourth number-pair, this sum is 12.
Conclusion
Based on this pattern, the number-pair 25/41 : 8 is different from the other three because the sum of the sums of the digits of its numerator and denominator is 12, whereas for the other three pairs, this sum is 9.
Therefore, the number-pair that is different is 25/41 : 8.
Revision Table: Key Concepts
| Concept | Description | Relevance to Problem |
|---|---|---|
| Odd One Out | A type of logical reasoning question where one item in a group is different from the others based on a rule or pattern. | The main task is to find the number-pair that doesn't fit the pattern of the others. |
| Sum of Digits | Adding up the individual digits of a number (e.g., sum of digits of 41 is 4 + 1 = 5). | This is the specific mathematical operation used to find the pattern in this problem. |
| Pattern Recognition | The ability to identify underlying rules or regularities in a set of data or items. | Crucial for solving this type of reasoning question by comparing the number-pairs. |
Additional Information: Logical Reasoning Patterns
Logical reasoning questions often involve identifying patterns based on various mathematical operations or properties. Some common types of patterns seen in similar questions include:
- Arithmetic operations (addition, subtraction, multiplication, division) between numbers or their digits.
- Properties of numbers (prime, composite, square, cube, even, odd).
- Relationships between digits (sum of digits, product of digits, difference of digits, position of digits).
- Sequential patterns (arithmetic progression, geometric progression, Fibonacci sequence).
- Visual patterns (in figures or diagrams).
To solve these questions effectively, it's helpful to systematically test different potential patterns until the one that fits most items is found.
Similar Questions
Four number-pairs have been given, out of which three are alike in some manner and one is different. Select the number-pair that is different. (Any operation on digits is not allowed)
Select the odd group of numbers. (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)
The second number in the given number pairs is obtained by performing certain mathematical operation(s) on the first number. The same operation(s) are followed in all the number pairs except one. Find that odd number pair.
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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.
