Select the option in which the numbers shares the same relationship in set as that shared by the numbers in the given set. (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) (14, 55, 41) (36, 99, 63)
(128, 949, 821)
Understanding Number Relationships in Sets
This question asks us to identify the relationship between the numbers in the given sets and then find the option that follows the same rule. We are specifically told to perform operations on the whole numbers themselves, not on their individual digits.
Analyzing the Given Number Sets
Let's look at the first given set: (14, 55, 41).
- The numbers are 14, 55, and 41.
- Let's see if there's a simple relationship between these numbers.
- Consider adding the first and third numbers: $14 + 41$.
- Calculation: $14 + 41 = 55$.
- The result, 55, is exactly the second number in the set.
Let's check if this relationship holds for the second given set: (36, 99, 63).
- The numbers are 36, 99, and 63.
- Consider adding the first and third numbers: $36 + 63$.
- Calculation: $36 + 63 = 99$.
- The result, 99, is exactly the second number in this set as well.
It appears that the relationship shared by the numbers in the given sets is that the second number is the sum of the first and third numbers.
Relationship: $Number_2 = Number_1 + Number_3$
Testing the Relationship in the Options
Now we will test this relationship on each of the given options to find the set that shares the same pattern.
| Option | Set | First Number ($Number_1$) | Third Number ($Number_3$) | Sum ($Number_1 + Number_3$) | Second Number ($Number_2$) | Does it Match? ($Number_1 + Number_3 = Number_2$) |
|---|---|---|---|---|---|---|
| 1 | (76, 153, 67) | 76 | 67 | $76 + 67 = 143$ | 153 | $143 \neq 153$ (No) |
| 2 | (128, 949, 821) | 128 | 821 | $128 + 821 = 949$ | 949 | $949 = 949$ (Yes) |
| 3 | (28, 120, 82) | 28 | 82 | $28 + 82 = 110$ | 120 | $110 \neq 120$ (No) |
| 4 | (34, 107, 43) | 34 | 43 | $34 + 43 = 77$ | 107 | $77 \neq 107$ (No) |
Based on the analysis, only Option 2 follows the identified relationship where the second number is the sum of the first and third numbers.
Identifying the Correct Option
Option 2, (128, 949, 821), is the set that shares the same relationship as the given sets (14, 55, 41) and (36, 99, 63). The relationship is that the sum of the first and third numbers equals the second number.
Revision Table: Key Concepts in Number Relationships
| Concept | Description | How it Applies Here |
|---|---|---|
| Number Relationship | A rule or pattern connecting numbers in a sequence or set. | We found the additive relationship between the numbers in the set. |
| Set Analogy | Finding a set that follows the same underlying relationship as a given set. | We tested options to find the set analogous to the given ones based on the number relationship. |
| Whole Number Operations | Performing arithmetic directly on the numbers provided, not their digits. | We added 14 and 41 (not 1, 4, 5, 5, 4, 1). |
Additional Information: Strategies for Finding Number Patterns
When tackling number relationship problems, consider these common strategies:
- Basic Arithmetic: Look for relationships involving addition, subtraction, multiplication, or division between the numbers. Check sums, differences, products, or quotients of pairs of numbers in the set.
- Squares and Cubes: Numbers might be squares or cubes, or related to them (e.g., $n^2 + 1$, $n^3 - 1$).
- Differences/Ratios: Examine the differences or ratios between consecutive numbers or alternate numbers in the set.
- Combinations: Sometimes the relationship involves a combination of operations (e.g., multiply two numbers and then add a constant).
- Check the Constraints: Always note any specific rules given, such as performing operations only on whole numbers as specified in this question.
Important Questions from Letter and Number Based
Select the option in which the numbers are related in the same way as are the numbers of the following set.
(4, 8, 16)
Select the option that is related to the third number in the same way as the second number is related to the first number.
23 : 441 : : 28 : ?
Select the option that is related to the third number in the same way as the second number is related to the first number and the sixth number is related to the fifth number.
12 : 72 ∷ 18 : ? ∷22 : 242Select the option that is related to the third number in the same way as the second number is related to the first number.
7 : 56 :: 11 : ?
Select the option in which the numbers are related in the same way as are the numbers of the following set.
(12, 60, 84)
