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 from the rest.
5121 : 12
Identifying the Different Number Pair
The question asks us to find the number-pair among the given options that follows a different rule or pattern compared to the others. We are given four pairs of numbers.
Analysing the Given Number Pairs
Let's examine each number pair to find a relationship between the first number (a four-digit number) and the second number (a two-digit number).
Pair 1: 4209 : 15
Let's try summing the digits of the first number, 4209.
Sum of digits = $4 + 2 + 0 + 9 = 15$.
The sum of the digits of 4209 is 15, which matches the second number in the pair.
Pair 2: 7456 : 22
Let's sum the digits of the first number, 7456.
Sum of digits = $7 + 4 + 5 + 6 = 22$.
The sum of the digits of 7456 is 22, which matches the second number in the pair.
Pair 3: 5121 : 12
Let's sum the digits of the first number, 5121.
Sum of digits = $5 + 1 + 2 + 1 = 9$.
The sum of the digits of 5121 is 9. The second number in the pair is 12. This pair does not follow the pattern observed in the first two pairs.
Pair 4: 8101 : 10
Let's sum the digits of the first number, 8101.
Sum of digits = $8 + 1 + 0 + 1 = 10$.
The sum of the digits of 8101 is 10, which matches the second number in the pair.
Identifying the Pattern and the Odd Pair
From the analysis above, we can see a clear pattern in three of the four pairs:
- Pair 1: $4+2+0+9 = 15$
- Pair 2: $7+4+5+6 = 22$
- Pair 4: $8+1+0+1 = 10$
In these three pairs, the second number is the sum of the digits of the first number.
However, in Pair 3:
- Pair 3: $5+1+2+1 = 9$. The second number is 12, not 9.
Therefore, the number-pair 5121 : 12 is different from the rest because it does not follow the rule where the second number is the sum of the digits of the first number.
Conclusion
Based on the pattern identified (the second number is the sum of the digits of the first number), the pair that is different is the one where this pattern is not followed. This is the pair 5121 : 12.
Let's summarize the findings in a table:
| Number Pair | First Number | Sum of Digits | Second Number | Follows Pattern? |
|---|---|---|---|---|
| 4209 : 15 | 4209 | $4+2+0+9=15$ | 15 | Yes |
| 7456 : 22 | 7456 | $7+4+5+6=22$ | 22 | Yes |
| 5121 : 12 | 5121 | $5+1+2+1=9$ | 12 | No |
| 8101 : 10 | 8101 | $8+1+0+1=10$ | 10 | Yes |
Revision Table: Number Analogy Patterns
| Concept | Description | Example |
|---|---|---|
| Sum of Digits | Adding up the individual digits of a number. Often used in number puzzles and reasoning questions. | Sum of digits of 1234 is $1+2+3+4=10$. |
| Number Analogy | Identifying a relationship between a pair of numbers and applying it to another pair or set to find a missing element or an odd one out. | If 12:3, then 16:? (Relationship could be sum of digits: $1+2=3$, so $1+6=7$). |
| Odd One Out | A type of question where you must identify the item (number, word, figure, etc.) that does not fit with the others in a given set based on a specific rule or characteristic. | Finding which number pair among the options is different from the rest. |
Additional Information: Solving Reasoning Questions
Reasoning questions involving numbers often require you to look for patterns or rules. Common patterns include:
- Arithmetic operations on the numbers themselves (addition, subtraction, multiplication, division).
- Operations on the digits of the numbers (sum of digits, product of digits, difference between digits, squares or cubes of digits, etc.).
- Relationships based on prime numbers, square numbers, cube numbers, etc.
- Sequences or series relationships.
To solve such questions effectively:
- Examine the first pair carefully to hypothesize a rule.
- Test the hypothesized rule on the other pairs.
- If the rule works for most but fails for one, that one is likely the odd one out.
- If the initial hypothesis doesn't work, try looking for other potential relationships.
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.
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(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.
