Three of the following four number-pairs are alike in a certain way and one is different. Pick the number-pair that is different from the rest.
10 : 98
Finding the Different Number Pair
The question asks us to identify the number-pair that is different from the rest among the given four options. We need to look for a pattern or relationship between the two numbers in each pair.
Let's examine each pair and try to find a rule connecting the first number (let's call it \(n\)) to the second number.
Analyzing Each Number Pair
We will test a common pattern often found in such problems: relating the second number to the square of the first number.
- Pair 1: 7 : 51
The first number is 7. Let's square it: \(7^2 = 49\). The second number is 51. We can see that \(49 + 2 = 51\). So, the pattern seems to be \(n : n^2 + 2\).
- Pair 2: 10 : 98
The first number is 10. Let's square it: \(10^2 = 100\). The second number is 98. We can see that \(100 - 2 = 98\). So, the pattern here seems to be \(n : n^2 - 2\).
- Pair 3: 8 : 66
The first number is 8. Let's square it: \(8^2 = 64\). The second number is 66. We can see that \(64 + 2 = 66\). This pair follows the pattern \(n : n^2 + 2\).
- Pair 4: 13 : 171
The first number is 13. Let's square it: \(13^2 = 169\). The second number is 171. We can see that \(169 + 2 = 171\). This pair also follows the pattern \(n : n^2 + 2\).
Identifying the Different Pair
Let's summarize the patterns observed for each number-pair:
| Number-Pair | First Number (\(n\)) | Second Number | Relationship to \(n^2\) | Pattern |
|---|---|---|---|---|
| 7 : 51 | 7 | 51 | \(7^2 + 2 = 49 + 2 = 51\) | \(n : n^2 + 2\) |
| 10 : 98 | 10 | 98 | \(10^2 - 2 = 100 - 2 = 98\) | \(n : n^2 - 2\) |
| 8 : 66 | 8 | 66 | \(8^2 + 2 = 64 + 2 = 66\) | \(n : n^2 + 2\) |
| 13 : 171 | 13 | 171 | \(13^2 + 2 = 169 + 2 = 171\) | \(n : n^2 + 2\) |
From the analysis, we can see that three number-pairs (7 : 51, 8 : 66, and 13 : 171) follow the pattern \(n : n^2 + 2\), where \(n\) is the first number and the second number is \(n^2 + 2\). The number-pair 10 : 98 follows a different pattern, which is \(n : n^2 - 2\).
Therefore, the number-pair that is different from the rest is 10 : 98.
Revision Table: Number Pair Patterns
| Number Pair | Pattern Found | Result |
|---|---|---|
| 7 : 51 | \(n^2 + 2\) | \(7^2 + 2 = 51\) (Matches) |
| 10 : 98 | \(n^2 - 2\) | \(10^2 - 2 = 98\) (Matches) |
| 8 : 66 | \(n^2 + 2\) | \(8^2 + 2 = 66\) (Matches) |
| 13 : 171 | \(n^2 + 2\) | \(13^2 + 2 = 171\) (Matches) |
The pair 10 : 98 is the odd one out because it follows a different rule compared to the other three pairs.
Additional Information: Number Series and Analogy Questions
Number series and number analogy questions, like this one involving number-pairs, are common in logical reasoning tests. They assess your ability to identify patterns and relationships between numbers.
Common patterns include:
- Arithmetic progression (adding/subtracting a constant)
- Geometric progression (multiplying/dividing by a constant)
- Squares or cubes of numbers
- Combinations of arithmetic/geometric operations with squares/cubes
- Prime numbers
- Fibonacci sequence
- Operations on digits of the number
To solve these questions, it's helpful to try different types of patterns systemically. Squaring or cubing the numbers is often a good starting point when the numbers grow rapidly, as seen in this number-pair problem.
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.
