Select the pair that does NOT belong in the following group. (√64,9), (√81,10), (√36,8), (√121,12)
(√36,8)
Analyzing Number Pairs to Find the Outlier
The problem asks us to identify the pair that does not fit the pattern followed by the other pairs in the given group. The group consists of the following pairs: $(\sqrt{64},9)$, $(\sqrt{81},10)$, $(\sqrt{36},8)$, and $(\sqrt{121},12)$.
Let's analyze each pair individually to understand the relationship between the two numbers within each pair.
Analyzing Each Pair
- Pair 1: $(\sqrt{64},9)$
First number: $\sqrt{64} = 8$.
Second number: $9$.
Relationship: The second number is $9$. The first number is $8$. $8 + 1 = 9$. So, the second number is 1 more than the square root of the first number. - Pair 2: $(\sqrt{81},10)$
First number: $\sqrt{81} = 9$.
Second number: $10$.
Relationship: The second number is $10$. The first number is $9$. $9 + 1 = 10$. So, the second number is 1 more than the square root of the first number. - Pair 3: $(\sqrt{36},8)$
First number: $\sqrt{36} = 6$.
Second number: $8$.
Relationship: The second number is $8$. The first number is $6$. $6 + 2 = 8$. So, the second number is 2 more than the square root of the first number. - Pair 4: $(\sqrt{121},12)$
First number: $\sqrt{121} = 11$.
Second number: $12$.
Relationship: The second number is $12$. The first number is $11$. $11 + 1 = 12$. So, the second number is 1 more than the square root of the first number.
Identifying the Pattern
Based on the analysis above, we can observe a pattern in three out of the four pairs. The pattern is that the second number in the pair is obtained by taking the square root of the first number and adding 1.
Let the pair be $(a, b)$. The pattern is $b = \sqrt{a} + 1$.
Finding the Pair that Does Not Belong
Let's check which pair(s) follow this pattern:
- For $(\sqrt{64},9)$: $\sqrt{64} + 1 = 8 + 1 = 9$. This pair follows the pattern.
- For $(\sqrt{81},10)$: $\sqrt{81} + 1 = 9 + 1 = 10$. This pair follows the pattern.
- For $(\sqrt{36},8)$: $\sqrt{36} + 1 = 6 + 1 = 7$. The second number is $8$, which is not $7$. This pair does NOT follow the pattern.
- For $(\sqrt{121},12)$: $\sqrt{121} + 1 = 11 + 1 = 12$. This pair follows the pattern.
Three pairs follow the pattern $b = \sqrt{a} + 1$, while one pair, $(\sqrt{36},8)$, does not. In this pair, the relationship is $8 = 6 + 2$, or $b = \sqrt{a} + 2$.
Therefore, the pair that does NOT belong to the group is $(\sqrt{36},8)$.
| Pair | $\sqrt{\text{First Number}}$ | Second Number | Relationship | Follows $b = \sqrt{a} + 1$? |
|---|---|---|---|---|
| $(\sqrt{64},9)$ | $8$ | $9$ | $8+1=9$ | Yes |
| $(\sqrt{81},10)$ | $9$ | $10$ | $9+1=10$ | Yes |
| $(\sqrt{36},8)$ | $6$ | $8$ | $6+2=8$ | No |
| $(\sqrt{121},12)$ | $11$ | $12$ | $11+1=12$ | Yes |
Conclusion
Based on the analysis, the pair $(\sqrt{36},8)$ is the outlier as it does not follow the same pattern as the other pairs in the group.
Revision Table: Understanding Number Patterns
| Concept | Description | Example |
|---|---|---|
| Square Root | A number that, when multiplied by itself, equals the original number. Symbol: $\sqrt{}$. | $\sqrt{64} = 8$ because $8 \times 8 = 64$. |
| Number Pattern | A sequence of numbers that follows a predictable rule. | $2, 4, 6, 8, \dots$ (Add 2 to the previous number) |
| Outlier | An element in a set or group that is significantly different from the others. | In the set $\{5, 10, 15, 22, 25\}$, $22$ could be an outlier if the pattern is multiples of $5$. |
Additional Information: Logical Reasoning and Patterns
Questions like this test your ability in logical reasoning, specifically pattern recognition. Pattern recognition is a fundamental skill in mathematics and problem-solving. It involves observing a set of data or objects and identifying a recurring relationship or rule.
In this case, we looked for a relationship between the two numbers in each pair. We found that the relationship "$b = \sqrt{a} + 1$" holds true for most pairs, allowing us to identify the one that doesn't fit the established pattern.
To solve pattern-based problems, you can follow these steps:
- Examine the given elements (numbers, figures, etc.).
- Look for simple relationships (addition, subtraction, multiplication, division, squares, square roots, etc.) between consecutive elements or between corresponding parts of the elements.
- Hypothesize a rule based on the first few elements.
- Test the hypothesis on the remaining elements.
- If all elements fit the rule except one or a few, identify the outlier(s).
- If the initial hypothesis doesn't fit all elements, try a different relationship or a more complex rule.
Practicing with different types of patterns helps improve logical reasoning skills, which are useful in various academic subjects and real-life situations.
Similar Questions
Select the set that does NOT belong in the following group of sets.
(2, 14, 16), (6, 30, 36), (5, 35, 40), (3, 21, 24)- Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number results in the second number. Similarly, certain mathematical operation(s) on the second number results in the third number and so on. Which of the given options follows the same set of operations as in the given sets? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) 68 – 136 – 121 – 363; 29 – 58 – 43 – 129
- If 2 is added to each odd digit and 1 is subtracted from each even digit in the number 2741586, how many digits will appear more than once in the new number thus formed?
Select the number that does NOT belong in the following group.
71, 73, 77, 79
(2, 14, 16), (3, 21, 24), (8, 56, 64), (5, 35, 41)
The set that does NOT belong to the group is:Select the number pair that does NOT belong in the following group.
(1, 1), (4, 64), (8, 512), (9, 719)
Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 - Operations on 13 such as adding to/subtracting from/multiplying with 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
6 - 36 - 72 - 144 ; 7 - 49 - 98 - 196- Two sets of numbers are given below. In each set of numbers, a certain mathematical operation on the first number results in the second number. Similarly, certain mathematical operation on the second number results in the third number and so on. Which of the given options follows the same set of operations as in the given sets?
(NOTE - A two/three digit number cannot be broken into individual digits for operations e.g. if 37 is followed by 10, the operation cannot be 3+7 as a two digit number cannot be broken into individual digits)
42 - 45 - 270 - 265
25 - 28 - 168 - 163 Below are given two sets of numbers. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding to/subtracting from/multiplying with 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
10 - 100 - 50 - 25; 2 - 4 - 2 - 1
16 is related to 260 following a certain logic. Following the same logic, 25 is related to 630. To which of the following is 9 related, following the same logic?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding to/subtracting from/multiplying with 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
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.
