Select the set in which the numbers are related in the same way as are the numbers of the given sets. (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.) (15, 28, 41) (19, 32, 45)
(22, 35, 48)
The question asks us to find a set of numbers from the given options that shares the same relationship as the numbers in the two provided sets: (15, 28, 41) and (19, 32, 45).
To solve this type of problem, we first need to carefully analyze the relationship between the numbers in the given sets. We should look for patterns based on operations like addition, subtraction, multiplication, division, or a sequence of these operations performed on the whole numbers.
Analyzing the Given Number Sets Pattern
Let's examine the first set: (15, 28, 41)
- Consider the difference between the second and first number: $28 - 15 = 13$.
- Consider the difference between the third and second number: $41 - 28 = 13$.
It appears that the difference between consecutive numbers in this set is 13.
Now let's examine the second set: (19, 32, 45)
- Consider the difference between the second and first number: $32 - 19 = 13$.
- Consider the difference between the third and second number: $45 - 32 = 13$.
The second set also shows the same pattern: the difference between consecutive numbers is 13.
Based on the analysis of both given sets, the relationship between the numbers in a set is that each subsequent number is 13 greater than the previous number. This means the numbers form an arithmetic progression with a common difference of 13.
Checking the Options for the Pattern
Now we will check each option to see which one follows this identified pattern.
Option 1: (16, 28, 43)
- Difference between 28 and 16: $28 - 16 = 12$.
- Difference between 43 and 28: $43 - 28 = 15$.
The differences (12 and 15) are not consistently 13. So, this option does not match the pattern.
Option 2: (12, 25, 36)
- Difference between 25 and 12: $25 - 12 = 13$.
- Difference between 36 and 25: $36 - 25 = 11$.
The differences (13 and 11) are not consistently 13. So, this option does not match the pattern.
Option 3: (24, 38, 55)
- Difference between 38 and 24: $38 - 24 = 14$.
- Difference between 55 and 38: $55 - 38 = 17$.
The differences (14 and 17) are not consistently 13. So, this option does not match the pattern.
Option 4: (22, 35, 48)
- Difference between 35 and 22: $35 - 22 = 13$.
- Difference between 48 and 35: $48 - 35 = 13$.
The differences (13 and 13) are consistent and match the pattern found in the given sets.
Conclusion on Number Set Relationship
The set (22, 35, 48) is the only option where the numbers follow the same relationship as the numbers in the given sets (15, 28, 41) and (19, 32, 45). The relationship is that the difference between consecutive numbers is 13.
| Set | Difference 1 (2nd - 1st) | Difference 2 (3rd - 2nd) | Matches Pattern? |
|---|---|---|---|
| (15, 28, 41) | $28 - 15 = 13$ | $41 - 28 = 13$ | Yes (Given) |
| (19, 32, 45) | $32 - 19 = 13$ | $45 - 32 = 13$ | Yes (Given) |
| (16, 28, 43) | $28 - 16 = 12$ | $43 - 28 = 15$ | No |
| (12, 25, 36) | $25 - 12 = 13$ | $36 - 25 = 11$ | No |
| (24, 38, 55) | $38 - 24 = 14$ | $55 - 38 = 17$ | No |
| (22, 35, 48) | $35 - 22 = 13$ | $48 - 35 = 13$ | Yes |
Revision Table: Number Set Analysis
This table summarizes the analysis for quick review:
| Set | Relationship Observed | Pattern Match (Common Difference = 13) |
|---|---|---|
| (15, 28, 41) | Consecutive difference is 13 | Yes |
| (19, 32, 45) | Consecutive difference is 13 | Yes |
| (16, 28, 43) | Consecutive differences are 12, 15 | No |
| (12, 25, 36) | Consecutive differences are 13, 11 | No |
| (24, 38, 55) | Consecutive differences are 14, 17 | No |
| (22, 35, 48) | Consecutive difference is 13 | Yes |
Additional Information on Number Patterns
Understanding number patterns is a key part of logical and numerical reasoning. Here are some related concepts:
- Arithmetic Progression (AP): A sequence of numbers such that the difference between consecutive terms is constant. This constant difference is called the common difference (d). In this question, the sets are short arithmetic progressions with a common difference of 13.
- Geometric Progression (GP): A sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
- Fibonacci Sequence: A sequence where each number is the sum of the two preceding ones, usually starting with 0 and 1 (e.g., 0, 1, 1, 2, 3, 5, 8...).
- Difference Series: Sometimes the pattern isn't in the numbers themselves but in the differences between consecutive numbers (as seen in this problem). Higher-order differences might also reveal patterns.
- Number Analogies: Questions like this require identifying a specific relationship or rule within a given set of numbers and applying it to find a similar relationship in another set.
Practicing various types of number series and set analogy problems helps in quickly identifying the underlying patterns.
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